WO2008137178A1 - Containers having internal reinforcing structures - Google Patents

Containers having internal reinforcing structures Download PDF

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Publication number
WO2008137178A1
WO2008137178A1 PCT/US2008/005871 US2008005871W WO2008137178A1 WO 2008137178 A1 WO2008137178 A1 WO 2008137178A1 US 2008005871 W US2008005871 W US 2008005871W WO 2008137178 A1 WO2008137178 A1 WO 2008137178A1
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Prior art keywords
plurality
struts
reinforcing structure
apparatus
container
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PCT/US2008/005871
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French (fr)
Inventor
Mulalo Doyoyo
Dirk Mohr
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Georgia Tech Research Corporation
Centre National De La Recherche Scientifique
Ecole Polytechnique
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    • HELECTRICITY
    • H01BASIC ELECTRIC ELEMENTS
    • H01MPROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL INTO ELECTRICAL ENERGY
    • H01M8/00Fuel cells; Manufacture thereof
    • H01M8/04Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04082Arrangements for control of reactant parameters, e.g. pressure or concentration
    • H01M8/04201Reactant storage and supply, e.g. means for feeding, pipes
    • HELECTRICITY
    • H01BASIC ELECTRIC ELEMENTS
    • H01MPROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL INTO ELECTRICAL ENERGY
    • H01M2250/00Fuel cells for particular applications; Specific features of fuel cell system
    • H01M2250/20Fuel cells in motive systems, e.g. vehicle, ship, plane
    • HELECTRICITY
    • H01BASIC ELECTRIC ELEMENTS
    • H01MPROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL INTO ELECTRICAL ENERGY
    • H01M8/00Fuel cells; Manufacture thereof
    • H01M8/04Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04082Arrangements for control of reactant parameters, e.g. pressure or concentration
    • H01M8/04201Reactant storage and supply, e.g. means for feeding, pipes
    • H01M8/04216Reactant storage and supply, e.g. means for feeding, pipes characterised by the choice for a specific material, e.g. carbon, hydride, absorbent
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02T90/30Application of fuel cell technology to transportation
    • Y02T90/32Fuel cells specially adapted to transport applications, e.g. automobile, bus, ship

Abstract

The present invention is directed towards systems, apparatus, and methods for reinforcing containers. More particularly, the present invention is directed towards containers having an internal reinforcing structure resembling a skeleton-like structure. An embodiment of the present invention comprises a container comprising a medium containing volume and a reinforcing structure within the containing volume, wherein the reinforcing structure enables the non-directional flow of a medium within the containing volume. Various embodiments of the present invention comprise a container having a reinforcing structure that can have many shapes, for example but not limited to a rectangular shape, a cylindrical shape, a spherical shape, a hemispherical shape, a cube shape, a cuboid shape, a tetrahedron shape, a cone shape, a prism shape, a rectangular prism shape, a pyramid shape, a dodecahedron shape, an oval shape, a 'U' shape, a lobed shape, a multi-lobed shape, an arbitrary three dimensional shape, or combinations thereof, among others.

Description

CONTAINERS HAVING INTERNAL REINFORCING STRUCTURES

RELATED APPLICATIONS

This application claims, under 35 U.S. C. § 119(e), the benefit of U.S. Provisional Application Serial No. 60/916,364, filed 7 May 2007, the entire contents and substance of which are hereby incorporated by reference as if fully set forth below.

TECHNICAL FIELD

The present invention is directed towards systems, apparatus, and methods for reinforcing containers. More particularly, the present invention is directed towards containers having an internal reinforcing structure resembling a skeleton-like structure.

BACKGROUND

A fuel cell is an electrochemical energy conversion device. A fuel cell produces electricity from various external quantities of fuel (on the anode side) and an oxidant (on the cathode side), which react in the presence of an electrolyte. Generally, the reactants flow into the cell, and reaction products flow out of the cell, while the electrolyte remains in the cell. Fuel cells can operate virtually continuously as long as the necessary flows are maintained. Fuel cells are different from batteries in that they consume reactant, which must be replenished, whereas batteries chemically store electrical energy in a closed system. Additionally, while the electrodes within a battery react and change as a battery is charged or discharged, a fuel cell's electrodes are catalytic and relatively stable. Many combinations of fuel and oxidant are possible. For example, a hydrogen fuel cell uses hydrogen as fuel and oxygen as oxidant. Considering that hydrogen burns 1.33 times more efficiently than gasoline with zero greenhouse gas emissions, there is an interest in the utilization of hydrogen as an energy source for vehicles. Four conventional approaches to hydrogen storage are currently in use: (a) liquid hydrogen, (b) compressed gas, (c) cryo-adsorption, and (d) metal hydride storage systems. The liquid hydrogen storage approach offers good solutions in terms of technology maturity and economy, for both mobile storage and large-volume storage systems with volumes ranging from 100 liters to 5000 m3. However, the containers for storing the liquefied hydrogen are open systems to prevent overpressure and require near-perfect thermal insulation, necessitating the use of very expensive super-insulating materials. The compressed gas storage approach is usually applied in underground supply systems, similar to a network of natural gas pipelines. This is an economical and simple approach; however, compressed hydrogen gas in a large steel tank could be an explosion hazard, reducing its safety and portability. The cryo-adsorbing storage approach involves moderate weight and volume. In this approach, hydrogen molecules are bound to a sorbent by physical adsorption forces, and remain in the gaseous state. The adsorbing temperature is in the range of 60° to 100° K. Activated carbon is commonly used as the sorbent due to its large number of small pores serving as hydrogen storage sites. The efficiency of hydrogen uptake is no more than 7 wt %, which is equivalent to about 20 kg hydrogen per cubic meter of activated carbon. The disadvantages of this approach are related to the low capacity and the cryogenic temperature required, which makes it necessary to use expensive super-insulated containers. A metal hydride storage system can store large quantities of hydrogen via a chemical reaction of H + M "^==1 M-H, wherein M is a selected metal element. Two metal systems (i.e., Fe-Ti and Mg-Ni) have been applied as hydrogen storage media and have been put into use in automobiles driven by an H2/O2 fuel cell. The operating temperature is 40-70 0C for the Ti-Fe system and 250-350 0C for the Mg-Ni system. The hydrogen storage capacity is less than 5 wt % for Ni-Mg and 2 wt % for Fe-Ti, which corresponds to less than 70 kg H2/m3 of metals. Furthermore, metal hydride systems normally require 20-40 bar pressure to keep the hydrogen in equilibrium. This renders the container for the metal hydride heavy and expensive, and limits the practical exploitation of these systems for portable electronic and mobility applications. A major drawback in the utilization of hydrogen-based fuel cells for powering vehicles is the lack of an acceptable lightweight and safe hydrogen storage medium. Although hydrogen bums 1.33 times more efficiently than gasoline with zero greenhouse gas emissions, hydrogen is less dense than gasoline, and thus occupies significantly more volume for an equivalent energy content. For example, 5 kg of compressed hydrogen can be stored at 248 bars of pressure at room temperature in a 320 liter tank as compared to only 7.12 liters of the same mass of gasoline (gasoline density = 0.702 kg/1) while providing 320 km range in a 17 km/1 car. The same mass can be stored in a 71 liter liquid hydrogen tank. Hydrogen, however, violently explodes when contacted with air, necessitating storage in tanks that are thicker and heavier than those used for gasoline to ensure safety. Using traditional steel tanks, storing 25 kg of gasoline requires a tank with a mass of 17 kg, whereas the storage of 9.5 kg of hydrogen requires a 55 kg tank. As a result, compressed hydrogen fuel cells struggle to achieve the same driving range and performance as gasoline engines since there is simply not enough room to store hydrogen in a reasonably-sized vehicle without sacrificing safety and cabin space. Tank weights and volumes for different types of hydrogen storage are compared in Table 1.

TABLE 1

Figure imgf000004_0001

Tank weight and volume for different hydrogen forms as compared to gasoline combustion engines are demonstrated in Table 2. TABLE 2

Figure imgf000005_0001

Typically, pressure vessels capable of containing media, such as liquids or gases, at significant pressures have involved fixed shape cylinders or spheres formed of high-strength metals such as steel or aluminum. Such pressure vessels, while successful for their designed applications, involve a number of problems. First, such metallic cylinders are relatively heavy compared to the gases or liquids that they contain. Second, metallic cylinders have a definite shape and cannot be adapted to fit readily in many space-constrained applications. Thus, a need exists for lighter weight pressure vessels capable of operating at high pressures and possessing round, non- round, and arbitrary shapes

BRIEF SUMMARY Various embodiments of the present invention are directed towards systems, apparatus, and methods for storing media under pressure. Broadly described, an aspect of the present invention comprises a container comprising: a medium containing volume; and a reinforcing structure within the containing volume, wherein the reinforcing structure enables the non-directional flow of a medium within the containing volume.

A medium containing volume can have a first surface and a second surface. The reinforcing structure can comprise a plurality of elements that traverse the containing volume and are associated with the first surface and second surface of the containing volume; a plurality of struts that interconnect the plurality of elements at a first node; a plurality of struts that interconnect a plurality of struts at a second node; and a plurality of struts that connect the plurality of elements to the second surface at a third node. In an embodiment of the present invention, the plurality of elements can be a plurality of trusses. In another embodiment of the present invention, the plurality of elements can be a plurality of plates. In an embodiment of the present invention, a truss can be a parallel cord truss. The plurality of trusses can comprise a plurality of chords. The plurality of struts can comprise a lattice. A container of the present invention can be made of many materials. In an embodiment of the present invention, the container can be made of a metal alloy (e.g., steel or stainless steel). In an embodiment of the present invention, the reinforcing structure can made of a metal alloy. Particularly, the reinforcing structure can made of steel. More particularly, the reinforcing structure can be made of stainless steel. In an embodiment of the present invention, the plurality of elements and the plurality of struts of the reinforcing structure can be solid. In an embodiment of the present invention, the plurality of elements and the plurality of struts of the reinforcing structure can be hollow. The plurality of elements and the plurality of struts of the reinforcing structure can be porous. In an embodiment of the present invention, the reinforcing structure occupies about 5% to about 50% of the containing volume. In another embodiment of the present invention, the reinforcing structure occupies about 10% to about 20% of the containing volume.

An aspect of the present invention comprises the arrangement of the nodes of the reinforcing structure in a cubic close packed arrangement. Another aspect of the present invention comprises the arrangement of the nodes of the reinforcing structure in a hexagonally close packed arrangement.

An apparatus for containing a medium can comprise: a container having a medium containing volume, wherein the medium containing volume has a first surface and a second surface; a medium contained within the medium containing volume; and a reinforcing structure comprising a plurality of elements that traverse the containing volume and are associated with the first surface and second surface of the containing volume; a plurality of struts that interconnect the plurality of elements at a first node; a plurality of struts that interconnect a plurality of struts at a second node; and a plurality of struts that connect the plurality of elements to the second surface at a third node.

The medium can comprise a solid, a fluid, a liquid, a solution, a suspension, a gas, a gel, a dispersion, or combination thereof. In an embodiment of the present invention, the medium can be hydrogen.

In an embodiment of the present invention, the plurality of elements of a reinforcing structure can be a plurality of trusses. In an embodiment of the present invention, the truss is a parallel cord truss. The plurality of trusses of the reinforcing structure can comprise a plurality of chords. In an embodiment of the present invention, the plurality of struts can comprise a lattice.

An apparatus for containing a medium can be made of many materials. In an embodiment of the present invention, an apparatus for containing a medium can be made of a metal alloy (e.g., steel or stainless steel). In an embodiment of the present invention, the reinforcing structure can made of a metal alloy. Particularly, the reinforcing structure can made of steel. More particularly, the reinforcing structure can be made of stainless steel. In an embodiment of the present invention, the plurality of elements and the plurality of struts of the reinforcing structure can be solid. In an embodiment of the present invention, the plurality of elements and the plurality of struts of the reinforcing structure can be hollow. The plurality of elements and the plurality of struts of the reinforcing structure can be porous. In an embodiment of the present invention, the reinforcing structure occupies about 5% to about 50% of the containing volume. In another embodiment of the present invention, the reinforcing structure occupies about 10% to about 20% of the containing volume.

An aspect of the present invention comprises the arrangement of the nodes of the reinforcing structure in a cubic close packed arrangement. Another aspect of the present invention comprises the arrangement of the nodes of the reinforcing structure in a hexagonally close packed arrangement.

An apparatus for containing hydrogen can comprise: a tank having a containing volume, wherein the containing volume has a first surface and a second surface; hydrogen contained within the containing volume; and a reinforcing structure comprising a plurality of elements that traverse the containing volume and are associated with the first surface and second surface of the containing volume; a plurality of struts that interconnect the plurality of elements at a first node; a plurality of struts that interconnect a plurality of struts at a second node; and a plurality of struts that connect the plurality of elements to the second surface at a third node.

An aspect of an apparatus for containing hydrogen can further comprise a plurality of microspheres. In an embodiment of the present invention, the plurality of trusses and the plurality of struts of the reinforcing structure can be solid or hollow. In an embodiment of the present invention, the plurality of trusses and the plurality of struts of the reinforcing structure are made of a porous material. An aspect of an apparatus for containing hydrogen can further comprise a plurality of microspheres, wherein the plurality of microspheres are located within a lumen of the hollow trusses and struts. An aspect of an apparatus for containing hydrogen can further comprise palladium. In an embodiment of the present invention, the palladium can be in a particulate form or a powder form.

An aspect of an apparatus for containing hydrogen can further comprise palladium. In an embodiment of the present invention, the palladium can be in a particulate form or a powder form.

Other aspects and features of embodiments of the present invention will become apparent to those of ordinary skill in the art, upon reviewing the following detailed description in conjunction with the accompanying figures.

BRIEF DESCRIPTION OF DRAWINGS

The various embodiments of the invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the various embodiments of the present invention. In the drawings, like reference numerals designate corresponding parts throughout the several views.

Figure 1 illustrates a perspective view of longitudinal section and cross- section of a container having a reinforcing structure. Figure 2 illustrates a top view of a longitudinal section and cross-section of a container having a reinforcing structure.

Figure 3 illustrates a side view of a longitudinal section and cross-section of a container having a reinforcing structure.

Figure 4 illustrates a cross sectional view of a cylindrical container having a reinforcing structure.

Figure 5 illustrates a cross sectional view of rectangular container having a reinforcing structure.

Figure 6 schematically demonstrates the replacement of conventional fluid containers with thin-walled arbitrarily shaped tanks that are internally-reinforced by space-filling skeletons.

Figures 7 A-Y illustrates the shapes of the chords and struts of the reinforcing structure.

Figures 8 A-B schematically demonstrate skeleton phenomenology of (a) equivalent pressure due to the skeleton, and (b) "strut-pressure" effects in a pressurized skeleton.

Figures 9 A-C provides notations of skeleton -reinforced vessels: (a) a reinforced cylindrical vessel, (b) a reinforced rectangular vessel, and (c) a 3D sketch of a finite sized rectangular vessel.

Figures 10 A-B illustrate the effect of skeleton modulus (a) and tank thickness (b) on the pressure gain coefficient in an infinite cylindrical vessel. Figures 11 A-B illustrate the influence of the reinforcing skeleton on maximum pressure (a) and weight reduction (b) on an infinite cylindrical vessel

following ASME code.

Figures 12 A-B illustrate the effects of the skeleton on the deflection (a) and

moments (b) for infinitely long rectangular pressure vessels.

Figures 13 A-B illustrate the effects of the skeleton on bending moment (a) and deflection (b) in a finite-sized rectangular vessel based on the "skeleton foundation" analysis.

Figures 14 A-B illustrate the effects of the skeleton on the plastic yield intensity in a finite-sized rectangular vessel based on the "skeleton foundation"

analysis.

Figures 15 A-B illustrate the effects of the skeleton in a finite-sized rectangular vessel as analyzed using FEA on (a) deflections (i) in a non-reinforced

vessel and (ii) in a reinforced vessel , and (b) stresses on (i) skeleton at 10 bars and (ii) skeleton at 70 bars.

Figures 16 A-B illustrate the effects of the skeleton on FEA-analyzed finite- sized rectangular pressure vessel on (a) deflection and (b) plastic yield intensity.

DETAILED DESCRIPTION The various embodiments of the present invention are directed to systems, apparatus, and methods for reinforcing a container. Other embodiments of the present invention are directed to medium storage containers having internal reinforcing structures resembling a skeleton-like structure.

An embodiment of the present invention comprises a structure for reinforcing a container. An embodiment of the present invention comprises a container comprising a medium containing volume, and a reinforcing structure within the containing volume, wherein the reinforcing structure enables the non-directional flow of a medium within the containing volume.

The term "medium" is used herein for convenience and refers generically to many solids, liquids, gases, solutions, suspensions, powders, gels, dispersions, or combination thereof comprising at least one of the foregoing.

The term "non-directional" as used herein refers to lack of directionality in the flow or movement of a medium within a containing volume. Although a medium could not move through the reinforcing structure, a medium could move around the reinforcing structure, permitting multi-directional flow of a medium within the containing volume. Thus, the flow of a medium is not constrained to a single direction within the containing volume.

The medium containing volume of the container comprises a first surface and a second surface. The reinforcing structure comprises a plurality of elements that traverse the containing volume and are associated with the first surface and second surface of the containing volume; a plurality of struts that interconnect the plurality of elements at a first node; a plurality of struts that interconnect a plurality of struts at a second node; and a plurality of struts that connect the plurality of elements to the second surface at a third node. The term "plurality" is used herein for convenience and refers to more than one. The plurality of trusses comprises a plurality of chords and a plurality of struts.

Figure 1 provides a perspective view of a portion of a container having a reinforcing structure 100. More particularly, Figure 1 illustrates a perspective view of longitudinal section and cross-section of a container having a reinforcing structure 100. An exemplary embodiment of a container having a reinforcing structure can comprise a medium containing volume 110, and a reinforcing structure 120 within the containing volume 110. The medium containing volume 110 can comprise a first surface 130 and a second surface 140. The use of the phrases "first surface" and "second surface" are for convenience in the description of a two-dimensional drawing. In the context of a three dimensional drawing, such a container may have many surfaces that can be described as a first surface or a second surface. In an embodiment of the present invention, a plurality of elements can comprise a plurality of trusses or a plurality of plates. The reinforcing structure 120 of the illustrated embodiment comprises a plurality of trusses 150. In an exemplary embodiment, the reinforcing structure 120 can comprise a skeleton-like structure. The plurality of trusses 150 can comprises a plurality of chords 160. hi an embodiment of the present invention, the plurality of chords 160 can comprises chords associated with a first surface 130 and a second surface 140 of the containing volume 110, which traverse the containing volume 110. In an embodiment of the present invention, the chords 160 can be substantially parallel to one another. The plurality of struts 170 can comprise, for example but not limited to, a lattice or web of struts, or the like. In an embodiment of the present invention, a strut 170 may be associated with at least one chord 160. In an embodiment of the present invention, a strut 170 may be associated with an first surface 130 or a second surface 140 of the containing volume 110. In an embodiment of the present invention, a plurality of struts 170 can converge on an first surface 130 or a second surface 140 of the containing volume 110 to form a node 180. In an embodiment of the present invention, a plurality of struts can converge on a chord 160 to form a node 180. In an embodiment of the present invention, a plurality of struts 170 can intersect at a point to form a node 180.

Figure 2 provides a top view of a portion of a container having a reinforcing structure 200. More particularly, Figure 2 illustrates a top view of a longitudinal section and cross-section of a container having a reinforcing structure 200. An exemplary embodiment of a container having a reinforcing structure can comprise a medium containing volume 110, and a reinforcing structure 120 within the containing volume 110. The medium containing volume 110 can comprise a first surface 130 and a second surface 140. In an embodiment of the present invention, a plurality of elements can comprise a plurality of trusses or a plurality of plates. The reinforcing structure 120 of the illustrated embodiment comprises a plurality of trusses 150. In an exemplary embodiment, the reinforcing structure 120 can comprise a skeleton-like structure. The plurality of trusses 150 can comprises a plurality of chords 160. hi an embodiment of the present invention, the plurality of chords 160 can comprises chords associated with a first surface 130 and a second surface 140 of the containing volume 110, which traverse the containing volume 110. In an embodiment of the present invention, the chords 160 can be substantially parallel to one another. The plurality of struts 170 can comprise, for example but not limited to, a lattice or web of struts, or the like. In an embodiment of the present invention, a strut 170 may be associated with at least one chord 160. In an embodiment of the present invention, a strut 170 may be associated with an first surface 130 or a second surface 140 of the containing volume 110. In an embodiment of the present invention, a plurality of struts 170 can converge on an first surface 130 or a second surface 140 of the containing volume 110 to form a node 180. In an embodiment of the present invention, a plurality of struts can converge on a chord 160 to form a node 180. In an embodiment of the present invention, a plurality of struts 170 can intersect at a point to form a node 180.

Figure 3 illustrates a side view of a portion of a container having a reinforcing structure 300. More particularly, Figure 3 illustrates a side view of a longitudinal section and cross-section of a container having a reinforcing structure 300. An exemplary embodiment of a container having a reinforcing structure can comprise a medium containing volume 110, and a reinforcing structure 120 within the containing volume 110. The medium containing volume 110 can comprise a first surface 130 and a second surface 140. hi an embodiment of the present invention, a plurality of elements can comprise a plurality of trusses or a plurality of plates. The reinforcing structure 120 of the illustrated embodiment comprises a plurality of trusses 150. hi an exemplary embodiment, the reinforcing structure 120 can comprise a skeleton-like structure. The plurality of trusses 150 can comprises a plurality of chords 160. hi an embodiment of the present invention, the plurality of chords 160 can comprises chords associated with a first surface 130 and a second surface 140 of the containing volume 110, which traverse the containing volume 110. In an embodiment of the present invention, the chords 160 can be substantially parallel to one another. The plurality of struts 170 can comprise, for example but not limited to, a lattice or web of struts, or the like. In an embodiment of the present invention, a strut 170 may be associated with at least one chord 160. In an embodiment of the present invention, a strut 170 may be associated with an first surface 130 or a second surface 140 of the containing volume 110. In an embodiment of the present invention, a plurality of struts 170 can converge on an first surface 130 or a second surface 140 of the containing volume 110 to form a node 180. In an embodiment of the present invention, a plurality of struts can converge on a chord 160 to form a node 180. In an embodiment of the present invention, a plurality of struts 170 can intersect at a point to form a node 180.

Figure 4 illustrates a cross sectional view of a cylindrical container having a reinforcing structure 400. An exemplary embodiment of a container having a reinforcing structure can comprise a medium containing volume 110, and a reinforcing structure 120 within the containing volume 110. The medium containing volume 110 can comprise a first surface 130 and a second surface 140. In an embodiment of the present invention, a plurality of elements can comprise a plurality of trusses or a plurality of plates. The plurality of elements may form multiple layers within the containing volume. The reinforcing structure 120 of the illustrated embodiment comprises a plurality of trusses 150. In an exemplary embodiment, the reinforcing structure 120 can comprise a skeleton-like structure. The plurality of trusses 150 can comprises a plurality of chords 160. In an embodiment of the present invention, the plurality of chords 160 can comprises chords associated with a first surface 130 and a second surface 140 of the containing volume 110, which traverse the containing volume 110. In an embodiment of the present invention, the chords 160 can be substantially parallel to one another. The plurality of struts 170 can comprise, for example but not limited to, a lattice or web of struts, or the like. In an embodiment of the present invention, a strut 170 may be associated with at least one chord 160. In an embodiment of the present invention, a strut 170 may be associated with an first surface 130 or a second surface 140 of the containing volume 110. In an embodiment of the present invention, a plurality of struts 170 can converge on an first surface 130 or a second surface 140 of the containing volume 110 to form a node 180. In an embodiment of the present invention, a plurality of struts can converge on a chord 160 to form a node 180. In an embodiment of the present invention, a plurality of struts 170 can intersect at a point to form a node 180. Figure 5 illustrates a cross sectional view of a rectangular container having a reinforcing structure 500. An exemplary embodiment of a container having a reinforcing structure can comprise a medium containing volume 110, and a reinforcing structure 120 within the containing volume 110. The medium containing volume 110 can comprise a first surface 130 and a second surface 140. In an embodiment of the present invention, a plurality of elements can comprise a plurality of trusses or a plurality of plates. The plurality of elements may form multiple layers within the containing volume 110. The reinforcing structure 120 of the illustrated embodiment comprises a plurality of trusses 150. In an exemplary embodiment, the reinforcing structure 120 can comprise a skeleton-like structure. The plurality of trusses 150 can comprises a plurality of chords 160. In an embodiment of the present invention, the plurality of chords 160 can comprises chords associated with a first surface 130 and a second surface 140 of the containing volume 110, which traverse the containing volume 110. hi an embodiment of the present invention, the chords 160 can be substantially parallel to one another. The plurality of struts 170 can comprise, for example but not limited to, a lattice or web of struts, or the like, hi an embodiment of the present invention, a strut 170 may be associated with at least one chord 160. In an embodiment of the present invention, a strut 170 may be associated with an first surface 130 or a second surface 140 of the containing volume 110. In an embodiment of the present invention, a plurality of struts 170 can converge on an first surface 130 or a second surface 140 of the containing volume 110 to form a node 180. In an embodiment of the present invention, a plurality of struts can converge on a chord 160 to form a node 180. In an embodiment of the present invention, a plurality of struts 170 can intersect at a point to form a node 180. One of skilled in the art would realize that the a container having a reinforcing structure can have many shapes, for example but not limited to a rectangular shape, a cylindrical shape, a spherical shape, a hemispherical shape, a cube shape, a cuboid shape, a tetrahedron shape, a cone shape, a prism shape, a rectangular prism shape, a pyramid shape, a dodecahedron shape, an oval shape, a "U" shape, a lobed shape, a multi-lobed shape, an arbitrary three dimensional shape, or combinations thereof, among others. One of skilled in the art would realize that the design of a strong, light- weight container utilizing embodiments of the present invention could be customized based upon the desired location and function of the container. For example, Figure 6 schematically demonstrates the replacement of conventional medium containers with thin-walled arbitrarily shaped containers that are internally-reinforced by space-filling skeletons. The schematic on the right illustrates the concept of an arbitrarily shaped strut lattice tank (top) as an alternative to conventional cylindrical pressure vessels (bottom).

In an embodiment of the present invention, container having a reinforcing structure can contain many media, including solids, liquids, and gases In an embodiment of the present invention, a container having a reinforcing structure can contain many media, including but not limited to fluids, liquids, solutions, suspensions, gases, gel, dispersions, or combination thereof. In an embodiment of the present invention, an apparatus for containing a medium can contain a medium under high pressure. In an embodiment of the present invention, an apparatus for containing a medium can contain a fluid under high pressure. In an embodiment of the present invention, an apparatus for containing a medium can contain hydrogen, oxygen, nitrogen, carbon dioxide, flammable gases, fluids performing functions that combine thermal and strength effects (e.g., liquid shield insulation, heat shield insulation), among others, hi an exemplary embodiment of the present invention, a container having a reinforcing structure may contain liquid hydrogen, compressed hydrogen gas, cryogenic compressed hydrogen gas, hydrogen in a metal hydride, or combinations thereof, among others.

In an embodiment of the present invention, container can have many forms and functions, for example, but not limited to, an apparatus for containing a medium, a storage device, a reservoir, a fuel tank, a tank for a tank truck, a microsphere, a septic tank, a wall structure, a blast wall structure, armor, vehicle structures, airplane structures, space station structures, space vehicle structures, stents, prosthetics, medical or surgical devices, other biomedical structures, and various devious where an increase in strength and a decrease in weight would be a desirable trait, among others. For example, an embodiment of the present invention permits the design of hydrogen fuel storage containers that can be fitted into empty regions of the vehicle to significantly increase storage volume. According to the various embodiments of the invention, a container having a reinforcing structure permits the design of lighter and stronger tanks having thinner walls with shapes that can fit into the under-utilized regions of the vehicle, increasing storage volume and safety. Increasing the hydrogen fuel storage capacity of a vehicle generates secondary benefits, including but not limited to, the reduction of gas transportation costs using lighter space-filling tanks, design of adaptable supply networks for compressed gases, and development of safe and efficient receiver-systems in hydrogen (or other similar gases) production plants/units.

One of skilled in the art would realize that a container having a reinforcing structure can be made of many materials. In an embodiment of the present invention, a container having a reinforcing structure can be made of many materials. In an embodiment of the present invention, a container having a reinforcing structure can be made of, for example but not limited to, a metal, a metal alloy, a polymer, polymers, glass, ceramic, carbon, a composite material, a nanocomposite materials, composite materials, nanocomposite materials, multi-layer composite materials, or combinations thereof, among others. In an embodiment of the present invention, a container having a reinforcing structure can be made of a lightweight material or an ultralightweight material, hi an embodiment of the present invention, a container having a reinforcing structure can be made of a porous material. In an exemplary embodiment of the present invention, a container having a reinforcing structure can be made of steel. In another exemplary embodiment of the present invention, a container having a reinforcing structure can be made of stainless steel. In an embodiment of the present invention, the container and a reinforcing structure can be made of the same materials. In an embodiment of the present material, the container and a reinforcing structure can be made of the different materials.

One of skill in the art would realize that the material(s) used for construction of the apparatus for containing a medium can be considered in light of the medium to be contained. The material(s) selected for construction of the apparatus for containing a medium may be selected on the basis of, for example but not limited to, being non- reactive with the medium to be contained.

In an embodiment of the present invention, the chords 160 and struts 170 of the reinforcing structure 120 can comprise many shapes. In an embodiment of the present invention, the chords and struts of the reinforcing structure 120 can comprise a hexagonal shape, a rectangular shape, a cylindrical shape, a spherical shape, a cube shape, a cuboid shape, a triangular shape, an oval shape, an octagonal shape, a star- shape, a pentagonal shape, or combinations thereof, among others. (Figures 7 A-Y). In an embodiment of the present invention, the chords 160 or struts 170 of the reinforcing structure 120 can be solid (Figures 7 Q-Y). In an alternative embodiment of the present invention, the reinforcing structure 120 can comprise hollow chords 160 and struts 170. (Figures 7 A-P) In an embodiment of the present invention, a hollow cord and strut may have a circular lumen (Figures 7 A-H) or a lumen that mimics the exterior shape of the chord or strut (Figures 7 I-P). In an embodiment of the present invention, the reinforcing structure 120 can comprise combinations of hollow chords 160 and struts 170 and solid chords 160 and struts 170. In an embodiment of the present invention, holes can be bored into the chords 160 and/or struts 170 of the reinforcing structure 120. In an embodiment of the present system, the plurality of trusses 150 can be replaced by a plurality of plates. In an embodiment of the present invention, the struts 170 of the reinforcing structure 120 can converge and can be associated with a first surface 130 or a second surface 140 of the containing volume 110 to form a node 180. In an embodiment of the present invention, the struts 170 of the reinforcing structure 120 may be directly connected to a first surface 130 or a second surface 140 of the containing volume 110. The struts 170 of the reinforcing structure 120 may be directly connected to a first surface 130 or a second surface 140 of the containing volume 110 by many means of attachment know in the art, including but not limited to arc welding, gas welding, resistance welding, energy beam welding, solid-state welding (e.g., sonic welding), radio frequency welding, adhesives, mechanical fastening, brazing, laser fusion, and bracing, among others. In an embodiment of the present invention, the plurality of struts 170 of the reinforcing structure 120 can converge and can be connected to a chord 160 to form a node 180. In an embodiment of the present invention, the struts 170 of the reinforcing structure 120 may be directly connected a chord 160. The struts 170 of the reinforcing structure 120 may be directly connected to a chord 160 by many means of attachment know in the art, including but not limited to arc welding, gas welding, resistance welding, energy beam welding, solid-state welding (e.g., sonic welding), radio frequency welding, adhesives, mechanical fastening, brazing, laser fusion, and bracing, among others. In an embodiment of the present invention, a plurality of struts 170 can intersect at a point to form a node 180. In an embodiment of the present invention, the struts 170 of the reinforcing structure 120 may be directly connected to another strut 170. The struts 170 of the reinforcing structure 120 may be directly connected to a strut 170 by many means of attachment know in the art, including but not limited to arc welding, gas welding, resistance welding, energy beam welding, solid-state welding (e.g., sonic welding), radio frequency welding, adhesives, mechanical fastening, brazing, laser fusion, and bracing, among others.

In an embodiment of the present invention, a container having a reinforcing structure 120 can be made by casting (e.g., investment casting). In an embodiment of the present invention, the reinforcing structure 120 can be made by casting (e.g., investment casting).

In an embodiment of the present invention, a reinforcing structure 120 of the present invention occupies about 5% to about 50% of the containing volume 110. In an embodiment of the present invention, a reinforcing structure 120 of the present invention occupies about 10% to about 20% of the containing volume 110. In an embodiment of the present invention, an apparatus for containing a medium can contain a medium while bearing mechanical loads. In an embodiment of the present invention where a reinforcing structure 120 of the present invention occupies about 10% to about 20% of the volume of the interior of the container, the remaining about 80% to about 90% of the volume of the interior of the container can be used to contain media. An embodiment of the present invention comprises an apparatus for containing a medium at high pressures.

In an embodiment of the present invention, a plurality of struts 170 can comprise, for example but not limited to, a lattice or web of struts, or the like. In an embodiment of the present invention, the plurality of struts 170 may converge on a chord 130, a first surface 130, a second surface 140, and/or point to form a node 180. In an embodiment of the present invention, the nodes 180 of the present invention may be arranged in a close-packed manner. In an embodiment of the present invention, the nodes 180 may be cubic close packed (e.g., face-centered cubic, body- centered cubic, or simple cubic) or hexagonally close packed. In an embodiment of the present invention, the plurality of struts 170 may be arranged to adopt an octetruss formation.

Various embodiments of the present invention comprising a reinforcing structure 120 can be configured and constructed to perform many desired functions. One of skill in the art would realize that design aspects of these structures comprise, for example but not limited to, topologies (e.g., periodic, stochastic), length scales (from micro- to space station sizes), and materials (for example, in the use of base metallic alloys, constructions comprising classical alloys versus novel alloys, such as shape memory alloys, among others). One having skill in the art would also realize that given the design flexibility of a reinforcing structure 120 of the present invention, a researcher could think of a function and then design and optimize a particular lattice/web/skeleton topology to perform that function.

In an embodiment of the present invention, a container having a reinforcing structure can contain a medium while bearing mechanical loads. Conceptually, the reinforcing structure can mimic the architecture of bones, which have of arbitrary shape and comprise a porous core material covered by a membrane. By way of example, the reinforcing structure of the present invention corresponds to the porous core material of the bone and the partially hollow container corresponds to the membrane. In designing a reinforcing structure, the smaller the lattice spacing (e.g., positioning of the nodes) the better the support of the surrounding container. The lattice thus provides a quasi-continuous support of the container. Due to this support, the container can be significantly thinner and thus, the container no longer relies on the membrane action of its surface. Instead, the mechanical loads are carried through the interior lattice material structure. Therefore, containers (e.g., hydrogen storage containers) no longer need to be of a cylindrical shape. Embodiments of the present invention can provide the design of ultralight high pressure containers (e.g., hydrogen tanks) of arbitrary shape. Embodiments of the present invention can reduce the incidence and magnitude of cracks to storage containers, thus minimizing the likelihood of a catastrophic event of as a result of skin damage to a container, thereby increasing the safety. Teitel (see U.S. Patent Serial Nos. 4,211,537 and 4,302,217) proposed a system for supplying hydrogen to an apparatus (e.g., a combustion engine). This system contains a metal hydride-based hydrogen supply component and a micro cavity-based hydrogen storage-supply component which in tandem supply hydrogen for the apparatus. The metal hydride-based component includes a first storage tank filled with a metal hydride material which, when heated, decomposes to become a metal and hydrogen gas. When cooled, the metal will absorb hydrogen to refuel the component (via the re-formation of metal hydride). This first storage tank is equipped with a heat exchanger for both adding heat to and extracting heat from the material to regulate the absorption/desorption of hydrogen from the material. The micro cavity- based component includes a second tank containing individual micro cavities that contain or "encapsulate" hydrogen molecules held therein under high pressure. The hydrogen is released from the micro cavities by heating the cavities. This heating is accomplished by including a heating element within the micro cavity-containing tank. The metal hydride-based component supplies hydrogen for short term hydrogen utilization needs such as peak loading or acceleration. The micro cavity component supplies an overall constant demand for hydrogen and is also used to regenerate or refuel the metal hydride component.

The micro cavity storage component consists of a large plurality of micro cavities filled with hydrogen gas at pressures up to 10,000 psi (689.5 MPa or 680.3 atm). The micro cavities generally are microspheres with a diameter from about 5 to about 500 microns. The walls of the micro cavities are generally from about 0.01 to about 0.1 that of the diameter of the micro cavities. The filled micro-spheres may be moved from operation to operation like a fine sand or suspended in a gas or liquid for transportation. Hollow micro-spheres can be made of plastic, carbon, metal, glasses or ceramics depending upon the performance characteristics desired. Teitel suggested the preferred microspheres to be made of silicate glasses. Under refueling conditions (e.g., under high hydrogen pressures and elevated temperatures) hydrogen will diffuse into the micro cavities. When stored at normal temperatures and under atmospheric pressure the hydrogen remains inside the micro cavity under high pressure. Upon reheating the micro cavity, the hydrogen is caused to diffuse outside the cavity and is available for utilization by the apparatus.

In an embodiment of the present invention, an apparatus for containing hydrogen comprises a tank having a containing volume, wherein the containing volume 110 has a first surface 130 and a second surface 140; hydrogen contained within the containing volume 110; a reinforcing structure 120 comprising a plurality of elements 150 that traverse the containing volume 110 and are associated with the first surface 130 and second surface 140 of the containing volume 110, a plurality of struts 170 that interconnect the plurality of elements at a first node 180, a plurality of struts 170 that interconnect a plurality of struts 170 at a second node 180, and a plurality of struts 170 that connect the plurality of elements 150 to the second surface 140 at a third node 180; and a plurality of microspheres. In an embodiment of the present invention, the microspheres can be contained within containing volume 110. In an embodiment of the present invention, the microspheres can be contained within the porous, hollow chords 160 and struts 170 of the reinforcing structure 120. Di an embodiment of the present invention, where the microspheres are contained within the porous, hollow chords 160 and struts 170 of the reinforcing structure 120, the pores of the hollow chords 160 and struts 170 of the reinforcing structure 120 may be smaller than the size of the microspheres to prevent migration of the microspheres from the hollow chords 160 and struts 170. hi an embodiment of the present invention, the microspheres can be made of materials disclosed in U.S. Patent No. 7,186,474, which is hereby incorporated by reference in its entirety. In an embodiment of the present invention, a container having a reinforcing structure can comprise palladium. Palladium hydride is metallic palladium that contains a substantial quantity of hydrogen within its crystal lattice. At room temperature and atmospheric pressure, palladium can absorb up to 935 times its own volume of hydrogen in a reversible process. Various embodiments the present invention can comprise the use of palladium. In an embodiment of the presetnt invention, an apparatus for containing a medium can be made of palladium. In an embodiment of the present invention, a reinforcing structure can be made of palladium, hi an embodiment of the present invention, palladium utilized within the container may be in a particles or powder form.

It must be understood that, as used in this specification and the appended claims, the singular forms "a" or "an" and "the" include plural referents unless the context clearly indicates otherwise.

All patents, patent applications, and references included herein are specifically incorporated by reference in their entireties.

It should be understood, of course, that the foregoing relates only to preferred embodiments of the present invention and that numerous modifications or alterations may be made therein without departing from the spirit and the scope of the invention as set forth in the Examples and appended claims. The present invention is further illustrated by the following examples, which are not to be construed in any way as imposing limitations upon the scope thereof. On the contrary, it is to be clearly understood that resort may be had to various other embodiments, modifications, and equivalents thereof, which, after reading the description herein, may suggest themselves to those skilled in the art without departing from the spirit of the present invention and/or the scope of the appended claims. EXAMPLES

EXAMPLE l : EXPERIMENTAL RATIONALE.

The present study focuses on a reinforcement system (e.g., an internal skeleton) for cylindrical and rectangular tanks because they are associated with two different types of deformations. Cylinders, similar to other round-vessels, undergo smaller uniform radial deformations due to membrane effects, whereas rectangular vessels, similar to other flat-sections, act as plates undergoing larger non-uniform bending and stretching deformations due to corner constraints. In the present study, several general restrictions on the skeleton-reinforced vessel were imposed. First, the percentage volume density of the skeleton is p% = 10 - 20%: the amount of fluid stored. Thus, the amount of fluid stored in the reinforced vessel is 80 — 90% if that stored in the same empty vessel. Second, the skeleton is composed of thin elements of uniform sections whose characteristic lengths are small compared to tank thickness. This study neglects additional forces that may be exerted on the struts depending on whether the joints are symmetric (e.g. cubic truss) or asymmetrical. Third, while pressure vessels are of finite sizes, they are quite long so that the effects of closure heads are typically neglected. Supporting this argument is that the stresses they cause due to differential growth/dilatation are not uniform across the vessel, relatively local in extent, and limited in magnitude. Although derivations will not focus on closure heads, finite element simulations will and will probe skeleton coupling effects with the axial direction and finite-size strengthening due to in-plane loads. Fourth, the present study only considers uniform fields of pressure and temperature change acting on the solid components. The present study does not address other effects of solid-fluid interactions such as those that would occur when the fluid is suddenly perturbed (causing non-steady/ turbulent flow) due to shock loading during drastic driving events or behaviors. Fifth, the vessel and the skeleton are made up of isotropic linear thermoelastic solids. The vessel has Young's modulus (E), elastic Poisson's ratio (v), coefficient of thermal expansion (α), and specific heat per unit volume (c). The same quantities for the skeleton are E', v', α', and c'. Note that uniform properties are only considered here for clarity, but the developed theory is applicable for non-uniform properties. For example, advantageous effective skeleton properties can be designed if struts within the skeleton are composed of different materials . Sixth, from a homogenization perspective, the present study denotes S as the area of a representative surface element containing one joint and S' as the equivalent joint area. In the present study, a single underline in an equation denotes vectors while double underline denotes tensors.

EXAMPLE 2: SKELETON PHENOMENOLOGY.

When subjected to high enough internal pressure, the vessel will tend to expand generally along the direction of the current external normal n to its surface due to either membrane stretching or bending depending on section shape. This in turn will make the wall attempt to pull the skeleton along with it. The extent at which the skeleton resists being pulled by the wall will reduce the amount of wall deformation. The process can not be "perfectly" quantified as it depends exactly on how the skeleton is connected to the wall, or more precisely on how the joints are manufactured. The joints should distribute the transfer of effort between the skeleton and the wall in such a way as to reduce stress concentration that would most adversely affect the thin skeleton elements at the interface. Next, this phenomenology was quantified for cylindrical and rectangular shapes. For cylinders, let p denote the pressure of gas stored in the vessel and q(x) = -pn , the exact surface load intensity seen at point x by the wall (Fig. 8a). An assumption is made that the skeleton makes the membrane feel as though it is subjected to a reduced "local" equivalent pressure/?' given by

P'(x) = p[l -η(x)] (1)

When averaging over a representative element of surface dS at the skeleton-wall interface, one should have

Figure imgf000025_0001
. The coefficient η(jc) describes the gain in the pressure that the vessel can support due to the skeleton's presence. We validate Equation (1) can be validated through finite element modeling of a plate of size 0.6 m x 0.6 m x 2.5 cm under uniform pressures p = 8.5 and 10 bars, and uniformly distributed (one per cm2) concentrated load F = 15 N. Deflections and moments were underestimated by less than 7%, thus Equation (1) is rather accurate. For rectangular sections, a vessel wall is viewed as a plate on skeleton foundation of effective stiffness k = K/d, where d and K are the skeleton depth and equivalent elastic modulus obtained from the thermoelastic homogenization of strut blocks. Stating that k - KJd implies that various directions are not coupled, which is incorrect and is used here for simplicity. Regardless, if the skeleton reaction is directly proportional to wall deflection (w), then/?' is

Figure imgf000026_0001

or , p'(x) = />[l -

Figure imgf000026_0002
, where x is the position vector, and η(x) = kw{x)l p = Kw{x)l pd . In this study, η will be conveniently referred to as the pressure gain coefficient.

CONSTITUTIVE RELATION OF A PRESSURIZED SKELETON. Pressure-induced strains on the struts within a pressurized skeleton can cause the skeleton to contract/expand just as temperature changes do. For the loading state in Figure 8B, a uniform state of stress and strain on the strut under pressure/? and axial force F can be deduced

F l \ σ^ = — e, ® e, - p\e^® e2 + e3 ® e3 j (3)

where S' is the cross-sectional area of the strut.

Figure imgf000026_0003
It follows from above that the longitudinal stress-strain relation for a pressurized strut is

Figure imgf000027_0001

As intuitively expected, the last expression reveals similarity between "strut-pressure" and temperature effects if one replaces 2vp' /E' with a'T . For a generalized pressurized skeleton, the solution of a well-posed equilibrium problem can be obtained using the thermal analogy and with the addition of equivalent nodal pressure forces (for symmetric joints considered here, such forces are zero). Thus, the pressurized skeleton with macroscopic stress and strain denoted by Σ^ and EJ respectively, will be described by

r = K : V - CT - &p (6)

Here, W_ , C^ , and K are the effective pressure, thermal, and elasticity tensors, respectively. Note that in the following section and due to the simplifying assumptions, a scalar parameter B[ is used for pressurized cylindrical vessel.

EXAMPLE 3: SKELETON-REINFORCED CYLINDRICAL VESSELS

Consider an infinite cylinder of internal radius R1 and external radius Re under uniform pressure p and temperature change T (Figure 9A). T is the actual temperature V relative to a reference T°. The inner displacement of a non-reinforced cylinder u(R,) is obtained by solving heat and equilibrium equations for an isotropic linear thermoelastic solid:

AT = O, T(R1 ) = T, T(Re) = 0 (7)

divσ = 0, σ(R,X-Je = -p_eJ.,

Figure imgf000027_0002
0 (8)
Figure imgf000028_0001

obtaining

Figure imgf000028_0002

Consider a case where the reinforcing skeleton possesses radial symmetry. Following Equation (6), then the skeleton-reinforced cylindrical vessel is effectively described by

Figure imgf000028_0003

The pressure seen by the wall of a skeleton-reinforced cylinder is deduced from Equation (1)

Figure imgf000028_0004

Despite the skeleton, radial symmetry is preserved (for the case where the cylindrical vessel is reinforced by a skeleton whose geometry preserves radial symmetry). Thus, the inner displacement U(R1 ) of the reinforced cylinder is similar to Equation (10) with p replaced by/?', and Equation (11) becomes:

Figure imgf000028_0005
where φ = gf— Y 2R' Y R% R' , Combining Equations (12) and (13),
Figure imgf000029_0001
then η is

Figure imgf000029_0002

where γ =t/R, is the thickness-to-inner radius ratio. From Equation (14), when thermal effects are negligible, then η is independent of p. For this case, the main parameter is KJE which increases with 77 : 77 — > 1 as K/ E → ∞ . The "strut-pressure" factor B' is also significant. Since the struts will only experience positive pressure, then in general B' >0 and will always oppose the role of KIE . If the struts are severely "soft", then B' dominates and may lead to negative η, making the skeleton useless. Note that in general C" >0 because materials of most strut skeletons would typically possess positive effective thermal expansion coefficients (although this is not generally the case). Now, consider the last term on the RHS of Equation (14): if C < K§JR, and T < 0 (which is typically the case for hydrogen and other gases whose densities decrease as temperature rise), then η will desirably increase. Physically, the pressurized cylinder will tend to contract a little, while the skeleton will shrink even more. As a result, the efforts applied by the skeleton on the membrane are higher, leading to pressure gain. The exact opposite happens when temperature increases or when T > 0. However, if such a decrease occurs when C" < K^/ R1, then it could also lead to pressure gain. Unfortunately, the decrease in temperature undesirably also leads to the loss of ductility of the base metals.

INFLUENCE OF THE SKELETON ON PRESSURE GAIN AND WEIGHT REDUCTION. For realistic estimations of pressure gain and weight reduction of skeleton-reinforced cylinders, we first evaluate the order of magnitudes of K, B', and C. Consider a hypothetical skeleton consisting of radial reinforcement of N equally-spaced struts of section S' connecting the center of the cylinder to the wall. In this study, an assumption is made that the struts are made up of stainless steel with E' =210 GPa, v' = 0.3, and α' = 1/73 x \0'5/K. This skeleton is not "perfect" because the struts contact each other close to the center. For p°/o=l 0%, we must have NS'R,=π Rf I = OA, where / is the internal circumferential distance between the two rows of struts. Let / = 2πRi/N, S = I2, then S" = 0.055 and Equation ( 10) becomes

— « 0.05 — u(R,)- OΛvp - 0.05EaT (15)

S R,

For stainless steel, it follows that B'~ 0.03 and C'~ 0.21 MPa.K"1. For internal radius R, =25 cm, then K -10.5 GPa and K / E- 0.05. ASIDE: The equivalent longitudinal modulus of an octetruss skeleton (e.g., made up of stainless steel with p%=16% is equal to 5.9 GPa. Thus, despite the above abstract scenario, one can expect the quantities of any actual skeleton of similar density to be close to this hypothetical value. Figure 10 illustrates how η is affected by (a) normalized skeleton modulus (for fixed thickness) K / E and (b) normalized tank thickness γ (for fixed K). (Note that Figure 10 is obtained from Equation (14) at room temperature for the quantities presented in this paragraph). As expected, η increases with K /E. When K/ E - 0.05, then the wall "feels" as though it is subjected to only about 70% of the pressure that it would feel if it was not reinforced. It helps if the skeleton is increasingly "harder" and the wall "softer". Note that η decreases as γ increases (Figure 10B). That is, the thicker the tank, the less effective the skeleton.

In what follows, we use examples of real-life design limits to evaluate how the skeleton affects pressure gain and weight reduction using the ASME Pressure Vessel Code (ASME, 1986). According to the code, the thickness of a medium-walled (t < 0:5i?,) pressurized tank shall not be less than (1) PR1 / (σae'+ 0.6P) for circumferential stress or (2) PR1 / (2σae' + OAP) for longitudinal stress. Here, σa is the maximum allowable stress of the material, e and e' the respective joint efficiencies (equal to 1 or lie between 0.6 and 1 for welded sections), and P the maximum allowable working pressure. No axial coupling due to closure heads is considered so that we only use design limit (1). We will adopt the value 1 for calculations but retain the symbol e in the derivations. Figure 1 IA shows that the coefficient h decreases rapidly for small to medium pressure (that is, 0 to about 250 bars). In fact, it is less than 20% for high pressures for K=E =0.05. The code weight, W0, of a non-reinforced cylinder of length L designed for maximum pressure P is deduced as

Figure imgf000031_0001

Here, p^ represents the "mass density" of the tank wall material. If the base "mass density" of the skeleton is denoted by pi , then the weight W of the reinforced vessel is given as

P1R.

W' = psπ R. + - - R: L + pφπRfL (17) σ^e - O.βP'

where P' = P(I -η) is the reduced maximum allowable pressure due to the presence of the skeleton. In the present study, p^ = pi so that the weight reduction ratio $ =W°=W becomes

Figure imgf000031_0002

The ratio β is computed for R1 =0.25 m and K/ E=O.03, 0.05 by iteratively calculating η for each thickness that obeys the stainless steel code. Figure 1 IB shows that weight reduction is largest when the skeleton is stiff and less dense. But these two parameters tend to be not really complimentary as a stiffer skeleton may be associated with higher density. Reducing weight with less dense and "soft" skeleton is not advisable in the present study due to issues such as low "strut-joint" efficiencies and diminished allowable stresses. Regardless, it is worthwhile to design for weight reduction using denser and stiffer skeletons. Clearly, the range β < 1 is the most significant and it would be interesting to clearly present the expected pressure range for such vessels. However, due to the various issues presented above on the many different parameters needed for a more in-depth design, the above question will be addressed in future studies.

INFLUENCE OF CLOSURE HEADS ON SKELETON-REINFORCED VESSEL DESIGN. AS already stated, for an elongated cylindrical pressure vessel far from the closure heads the deformation of the vessel can be represented by that of an infinitely long cylindrical shell, that is also subjected to uniform longitudinal stress due to the pressure exerted on the heads. Nevertheless, closure heads do not typically undergo radial deformations. Instead, they deform in such as way as to induce differential growth on the vessel walls, developing additional stresses they may lead to localized stress concentration at the vessel-head joint. The influence of the lattice skeleton on the closure heads depends on the structure of the lattice. Without the lattice, closure heads tend to create bending in the vessel as well as subjecting the vessel to additional longitudinal efforts that may tend to reduce the overall vessel deflection. With the lattice, the coupling effects may reinforce this phenomenon, but may also decrease the longitudinal stresses. The comparison of the two phenomena is important and may be taken as criteria for design. For instance, if we consider a cylindrical shell closed by two hemispheres of the same thickness, it is well known that the theoretical dilatation of the cylinder is twice that of the sphere. If such a difference of dilatation occurs, the cylinder is forced to bend and radial displacement is no longer uniform. A wise design needs to be carried out to ensure that only a reasonable stress field is created. For instance, choosing a thicker cylinder for the same closure heads is advisable in practical design.

For pressure vessels of finite length, once again the introduction of a lattice should be rather positive: not only does it decrease the effective pressure seen by the wall far from the heads, but it also decreases - if well designed, the effective pressure seen by the heads themselves according to the previous reasoning. The lattice skeleton reduces the longitudinal stresses in the cylinder and thus increases its global resistance. If the skeleton is well chosen, it should also ensure a quasi-continuous support of the shell reducing its tendency to bend and to develop stress concentrations. However, one drawback of inserting a filling lattice is the fact that the three directions will be coupled in the lattice whose resistance has to be tested. It must be reminded that the lattice may be more complex near the closure heads to facilitate a strong connection and thus could introduce some undesired manufacturing issues. One way to avoid such problems might be to connect the lattice only to the cylindrical wall and not to reinforce the heads that are supposed to be theoretically stronger. Then, the lattice should lessen an existing differential growth and thus the additional stress. No derivation or computation has been done because the aim of this paper is to test the global efficiency of an internal skeleton. A more realistic study (taking into account finite length) would require the choice of a specific lattice topology similar to what was done in the next sections for rectangular vessels through a finite-element modeling.

EXAMPLE 4 SKELETON-REINFORCED RECTANGULAR VESSELS

In the present study, we first analyze an infinite skeleton-reinforced rectangular vessel was analyzed followed by analysis of finite-sized skeleton- reinforced rectangular vessel. We will not repeat the treatment of thermal and "strut- pressure" effects as their roles will be the same regardless of vessel shape. Note that the ASME code for rectangular pressure vessels only contains design limits for vessels of infinite length. It estimates the allowable stresses based on stress distributions in a rigid frame. It does not account for the strengthening effect associated with finite length. A rectangular vessel is a structure consisting of six orthogonally joined walls under pressure and in-plane loads and it is complex to analyze. When it is skeleton-reinforced, we earlier proposed to view its walls as plates on skeleton foundations. The two walls in Figure 9B have two different stiffnesses: ka = K I b for edge(l) and fa = K I a for edge(2). A wall of a skeleton-reinforced rectangular vessel does not "perfectly" behave as a plate on an elastic foundation. It is also neither simply supported nor fixed so that its actual behavior lies somewhere in between. Thus, a coherent study should consist of: (1) computing wall deflection, first for a simply supported wall and then subjected to moments on its edges; (2) using superposition to determine the angle of rotation of each wall on its edges; and (3) allowing walls joined at the same corner to have the same rotation. This last condition should enable determination of all the unknown coefficients of wall deflection.

The above steps were adopted for non-reinforced rectangular vessels without accounting for in-plane loads. The above steps can not be easily applied when a skeleton is introduced as it means more unknowns and complexities. Nevertheless, it will turn out that a simply-supported wall is reasonable for preliminary assessment.

INFINITELY-LONG RECTANGULAR VESSEL. The deflection w(X) of an infinite skeleton-reinforced wall is obtained from

EI - + kw = p (19)

which gives deflections w and w for edge(l) and (2) respectively as

w(x) (20)

Figure imgf000034_0001

w(y) = — + A cos(λyjch(λy)+ Bsin(λy)sh(Xy) (21)

where λ =

Figure imgf000034_0002
The boundary conditions at corner A (see Figure 9B) and global equilibriums for each edge are respectively given by

£»(_β/2) = -£(»/2) , fl ,φa /2) (22) ax ay dx ay

Figure imgf000035_0001

A Matlab program is created to solve the above four independent equations. The wall displacement of a non-reinforced infinite vessel can simply be obtained. For example, the deflection of edge(l) is wo(x)= ξ0x4 ÷ ξ^2 + ξ2 , where ζo = p/24EI, ζi =

/?(a2+2ab-2b2) /4SEI, and ζ> = j?αό/4E/-pα4/384ΕI-ζ1a2/4. Note that the axial load and bending moment acting on edge(l) for the non-reinforced vessel are respectively

JV0 = pb/2 and M0 = EIBw0 Idx2 , while N = 2Etw(a/2)/b and M = Eldwldx2 for the same edge in the presence of the skeleton. Similar expressions are found for edge(2). Figure 12 compares deflections and moments in an increasingly skeleton- reinforced stainless steel vessel of size α =0.6 m, b =0.4 m, and t =2.5 cm under 10 bars. The thickness was chosen by referring to the ASME code. The skeleton significantly alters the deformation mode of the vessel (Figure 12: note the insert images of deformed skeleton-reinforced(i) and nonreinforced(ii) tanks). For the non- reinforced vessel, the deflection of the longer edge(l) is positive while that of the shorter edge(2) is negative. As the skeleton is introduced, the deflection of edge(2) becomes gradually positive with increasing skeleton modulus, while the deformed shape is "symmetrized" by the skeleton (image(i): Figure 12). The Von Mises yield criterion of the wall is

Figure imgf000035_0002

for some constant K, where H represents both an inertial coefficient and another related to the percentage of the thickness allowed to yield. For K equal to 4 GPa, the maximum moments under 10 bars are reduced by a factor larger than 2, while under 40 bars they are distributed differently, but do not even exceed those of the non- reinforced vessel under 10 bars. The criterion does not exceed that of the non- reinforced vessel under 10 bars. Thus, the maximum pressure can be increased by a factor of 4 due to the skeleton.

FINITE-LENGTH RECTANGULAR VESSEL. The action of pressure on the finite vessel will induce in-plane loads on the walls. As an approximation, we will assess the effect of a skeleton on a pressurized simply-supported wall. In the present study, the assumption was made that the walls are thin enough to apply the simplified plate theory. The walls are additionally supposed to be uniformly loaded in their mid-planes by N° , Ny°, and Nx^1. The intensity of the skeleton's reaction is again supposed to be proportional to wall deflection. Note that pressure makes the edges stretch with wθ of deflection in addition to bending deflection w. Neglecting edge-stretching, the governing relation is

U

Figure imgf000036_0001

where D = Et3/ 12(l-v2) is the bending rigidity. Complying with the boundary conditions and seeking solutions in series forms, we obtain wall deflection as

\ βp an mπK . nπy w(x,y) = -ssiin sin (26) π2D » n=l,3,5 mn a b

Tim )

— (27) n )

Figure imgf000036_0002

Clearly, both the skeleton and in-plane loads tend to reduce wall deflection. Neglecting in-plane loads, the deflection becomes

Figure imgf000037_0001

It directly follows from above that the moments are given as

Figure imgf000037_0002
Figure imgf000037_0003
Figure imgf000037_0004

To quantify the skeleton's role, let's consider a reinforced-square stainless steel vessel of size a =0.6 m and t =0.025 m under 10 bars. Figure 13A shows the bending moment Mx when the walls are skeleton-reinforced (computed by adding up the first 400 terms of the series which converge rapidly). A similar distribution is observed for My. Due to the skeleton, the maximum moment does not occur at the center of the wall. Instead, it occurs close to the edge. Its maximum value Mn, is 1500 N.m which is much less than 8700 N.m of the non-reinforced wall. Figure 13B shows wall deflection for a cut along x=a /2. Indeed, the stiff er the foundation the more effective it is in reducing the deflection. The Von Mises criterion VM for plastic yield with no in-plane loads is: VM(x,y) = ξφ'2{Mx 2 + My 2 -MxMy + SMl) (32)

for some constant ζ. Irrespective of the reinforcement, the maximum value of this function is reached at the edges (see Figure 14A). Figure 14B describes FM along the diagonal of the wall under 10 bars for different thicknesses (between 1 cm and 2.5 cm). Comparisons are made with a non-reinforced square vessel of thickness 2.5 cm. Our observations are as follows. First, for the same wall thickness, the skeleton reduces the maximum value of VM or VMn, by roughly a factor of 5. Note that both VM (Equation (31)) and moments ((Equations 29-31) are directly proportional to pressure. Thus, due to the skeleton, the vessel can support a pressure 5 times higher for the same VMn, as the non-reinforced vessel. Second, when wall thickness is reduced, the distributions of moments and VM change, even though the maximum values are still attained at the edges. Expectedly, the maximum values increase for thinner vessels, while they remain lower than the value for thicker non-reinforced vessel. The variation of VMn, with thickness is rather complex:

Figure imgf000038_0001

for some constant ξ,. This equation shows that wall thickness could have been reduced by 3/5 times due to the skeleton without risking plastic failure. Essentially, the skeleton reinforces the ability of a simply supported vessel to resist pressure. It can be expected that its influence on a fixed vessel, though quantitatively different, would be similar. In that case, VMn, should occur at the middle of the longer edge(2) for a non-reinforced wall, but the strengthening effect should be the same. Actually, the maximum wall deflection occurs at the center where, as a result, the skeleton tends to be more effective in reducing the equivalent pressure while globally, the deflection is reduced. With the skeleton's action being smooth over the wall (there is no discontinuity), then moments are gradually decreased even though their distributions change. Following these discussions, the pressure gain in a given skeleton-reinforced rectangular steel vessel with a skeleton modulus of about 10 GPa can be expected to lie between 1 and 10 times, and more precisely around 5 times.

FINITE ELEMENT MODELING OF A FINITE-SIZED RECTANGULAR VESSEL. Finite element simulations (Abaqus software, HKS 2003) are used to investigate coupling effects between various skeleton directions and to account for fixed edges. In this finite element model, the skeleton is represented as a homogeneous structure, with equivalent elastic properties, attached directly to the vessel. The rectangular vessel in Fig. 9C is made up of stainless-steel with 0.6 m x 0.6 m x 0.4 m and thickness 2.5 cm under a pressure of 10 bars. The six walls are joined at sharp right angles, although round corners are preferred to reduce stress concentrations. The skeleton is made up of a 16% dense octetruss chosen for its high stiffness-to-weight ratio and known equivalent thermoelastic properties. The cross-sectional area of its uniform struts is 1% the square of their length. Thus, 99% of the wall is under pressure while the rest is connected to the skeleton. The skeleton and the vessel are rigidly connected. Due to symmetry, only one-eighth of the vessel or ABCDEFGH is modeled.

Figure 15 A presents contour plots of wall deflections for non-reinforced(i) and skeleton-reinforced(ii) vessels at a pressure of 10 bars, while Figure 15B shows contour plots for Σ~ stress on skeleton-reinforced vessels at 10 bars(i) and 70 bars(ii). The numbers on the color code are not significant, but "red" in Fig. 10 denotes regions where a quantity has the highest value, and "blue" the lowest value. Around the center of the larger wall (point D), the component Σ~ is about 95% of the pressure. The maximum deflection at the center of the wall is reduced by nearly one-tenth when the skeleton is introduced. Figure 16A shows the deflection along the x-axis for the larger wall (the wall on which deflection is higher in the absence of the skeleton). The ASME code requires a thickness of 2.5 cm for 10 bars and more than 7 cm for 70 bars. When not reinforced, the weight of the latter vessel would beW° ~ 1000 kg. The same vessel would weigh only W ~ 534 kg when reinforced.

It appears that the skeleton is not effective near the edges. One idea is to make it less dense there. Thus, the skeleton density is reduced (or the skeleton is "extruded") near the edges over a section of size 14.375 cm x 14.375 cm x 9.375 cm while keeping the same material elsewhere. This is a "cross-shaped" reduction resulting in one-eighth of the skeleton being removed. The vessel is then loaded at 70 bars and the results are presented in Figure 16. Deflection and Von Mises criterion along y =0 are hardly modified by the extrusion. The value of the Von Mises criterion is rather high at the beginning of the extrusion. Thus, it would probably have been better to simply uniformly decrease the skeleton density. Nevertheless, finite element modeling confirms that skeleton reinforcement is a good idea. The results show that when a skeleton is introduced, the pressure vessel can support 7 to 8 times higher pressure than it would if it is not reinforced. This is consistent with the previous results but even better. This gain might be related to the coupling effects associated with the effective Poisson's ratio of the homogenized skeleton. When the skeleton is pulled in one direction, in one direction, then it acts on the wall in the other direction. Note that for this vessel of finite length, even without the skeleton, deflections and moments are very different from the ones computed for the infinitely long vessel. This shows the strengthening effect of the closure heads. For the present pressure amounts, the use of the skeleton allows for the reduction of the total weight of the vessel since both the deflection and moments are greatly reduced. For a pressure of about 0.3 bars, the required thickness (cf. ASME code) of rectangular pressure vessels is usually reasonable: 3 mm for a steel tank of 37 cm x 33 cm x 17 cm. The cost of introducing the skeleton for very low pressures would most probably not be worth the gain in weight-reduction, if any.

EXAMPLE 5 PRACTICALITY OF THE SKELETON CONCEPT

The present validation of the 'skeleton reinforcement of pressure vessels' concept relies on a few assumptions.

1. Equivalent pressure. It was assumed that the wall of the tank reacts to the introduction of the skeleton as if the latter only modifies the effective pressure it supports locally. This is relevant only as long as the characteristic length of the skeleton is much smaller than the wall thickness. Otherwise, if the wall is connected to long struts, it will behave as a plate supporting concentrated loads or a row of columns and the results will be different from the ones obtained here. Moreover, the fact that the wall whose majority of its surface points are under pressure is locally stretched by the struts, may modify the stress pattern within the wall. This assumption was proven to be reasonable in Example 2 for skeleton elements whose characteristic sections are small compared to the wall. 2. Skeleton as an elastic foundation. For derivations in the present study, the skeleton was treated as an elastic foundation without accounting for any coupling effects. In a real system, the behavior would be much complex under this assumption. Lateral coupling will not only influence the deflection of the plate but will also induce in-plane loads that will tend to expand/contract the wall locally. This phenomenon would be accompanied by huge stresses near the joints. So as to be more representative, the finite element model replaces the skeleton by its homogenized equivalence. However, homogenization, based in part on an assumption of periodicity, is known to be efficient only far from a boundary layer where the behavior of the skeleton is not well-known. These finite boundary effects have not been addressed here.

3. Manufacturing. Several manufacturing issues related to the joints between struts and between struts and the wall may reduce the efficiency of the skeleton reinforcement. The effect of pressure on the struts was accounted for through a simplified model in Example 2. Further, stress concentrations could occur at the strut- wall joints that could significantly alter stress patterns in the wall, and this was not dealt with. The tanks under consideration were also idealized: the holes and modifications in the perfect wall to accommodate fueling and control devices have not been taken into account. Because of all these manufacturing problems, it should be expected that the real gain could be inferior to the "ideal" one obtained here. 4. Safety. The introduction of a skeleton clearly increases safety margins for high pressure vessels. However, it relies on sustainable skeleton-wall interactions. The fracture of a joint or yield of a strut will induce undesirable extra stresses. Thus, in-depth design of joint-shapes within the skeleton and at the skeleton- wall interface is indispensable. Despite these assumptions, this study examines the parameters that intervene in the potential reinforcement of the wall of a pressure vessel by an internal ultralight skeleton. The latter actually needs to deform to resist deformation of the wall, and thus it is all the more efficient when the deflection of the un-reinforced vessel is high. For this reason, the concept is apparently more efficient for rectangular pressure vessels. In general, the data indicate the concept is apparently more efficient if the skeleton materials are stiffer and stronger than the wall materials. The design of a reinforcing skeleton could also benefit from thermal effects on a material adapted to the change of temperature that can be expected with a desired use

Claims

CLAIMSWhat is claimed is:
1. A container comprising: a medium containing volume; and a reinforcing structure within the containing volume, wherein the reinforcing structure enables the non-directional flow of a medium within the containing volume.
2. The container of Claim 1 , a medium containing volume has a first surface and a second surface.
3. The container of Claim 1, wherein the reinforcing structure comprises a plurality of elements that traverse the containing volume and are associated with the first surface and second surface of the containing volume; a plurality of struts that interconnect the plurality of elements at a first node; a plurality of struts that interconnect a plurality of struts at a second node; and a plurality of struts that connect the plurality of elements to the first surface or second surface at a third node.
4. The container of Claim 3, wherein the plurality of elements is a plurality of trusses.
5. The container of Claim 3, wherein the plurality of elements is a plurality of plates.
6. The container of Claim 4, where in the truss is a parallel cord truss.
7. The container of Claim 4, wherein the plurality of trusses comprise a plurality of chords.
8. The container of Claim 3, wherein the plurality of struts comprise a lattice.
9. The container of Claim 1 , wherein the reinforcing structure is made of a metal alloy.
10. The container of Claim 9, wherein the metal alloy is steel.
11. The container of Claim 9, wherein the metal alloy is stainless steel
12. The container of Claim 3, wherein the plurality of elements and the plurality of struts of the reinforcing structure are hollow.
13. The container of Claim 3, wherein the plurality of elements and the plurality of struts of the reinforcing structure are solid.
14. The container of Claim 12, wherein the plurality of elements and the plurality of struts of the reinforcing structure are porous.
15. The container of Claim 13, wherein the plurality of elements and the plurality of struts of the reinforcing structure are porous.
16. The container of Claim 1, wherein, the reinforcing structure occupies about 5% to about 50% of the containing volume.
17. The container of Claim 1, wherein, the reinforcing structure occupies about 10% to about 20% of the containing volume.
18. The container of Claim 3, wherein the nodes are cubic close packed.
19. The container of Claim 3, wherein the nodes are hexagonally close packed.
20. An apparatus for containing a medium comprising: a container having a medium containing volume, wherein the medium containing volume has a first surface and a second surface; a medium contained within the medium containing volume; and a reinforcing structure comprising a plurality of elements that traverse the containing volume and are associated with the first surface and second surface of the containing volume; a plurality of struts that interconnect the plurality of elements at a first node; a plurality of struts that interconnect a plurality of struts at a second node; and a plurality of struts that connect the plurality of elements to the first surface or second surface at a third node.
21. An apparatus of Claim 20, wherein the medium comprises a solid, a fluid, a liquid, a solution, a suspension, a gas, a gel, a dispersion, or combination thereof.
22. An apparatus of Claim 21 , wherein the medium is hydrogen.
23. An apparatus of Claim 20, wherein the plurality of elements is a plurality of trusses.
24. An apparatus of Claim 23, where in the truss is a parallel cord truss.
25. An apparatus of Claim 23, wherein the plurality of trusses comprise a plurality of chords.
26. An apparatus of Claim 20, wherein the plurality of struts comprise a lattice.
27. An apparatus of Claim 20, wherein the apparatus for containing a medium is made from a metal alloy.
28. An apparatus of Claim 27, wherein the metal alloy is steel.
29. An apparatus of Claim 27, wherein the metal alloy is stainless steel.
30. An apparatus of Claim 20, wherein the reinforcing structure is made from a metal alloy.
31. An apparatus of Claim 30, wherein the metal alloy is steel.
32. An apparatus of Claim 30, wherein the metal alloy is stainless steel.
33. An apparatus of Claim 20, wherein the plurality of elements and the plurality of struts of the reinforcing structure is solid.
34. An apparatus of Claim 20, wherein the plurality of elements and the plurality of struts of the reinforcing structure is hollow.
35. An apparatus of Claim 20, wherein the plurality of elements and plurality of struts of the reinforcing structure are porous.
36. An apparatus of Claim 20, wherein, the reinforcing structure occupies about 5% to about 50% of the containing volume.
37. An apparatus of Claim 20, wherein, the reinforcing structure occupies about 10% to about 20% of the containing volume.
38. An apparatus if Claim 20, wherein the nodes are cubic close packed.
39. An apparatus if Claim 20, wherein the nodes are hexagonally close packed.
40. An apparatus for containing hydrogen comprising: a tank having a containing volume, wherein the containing volume has a first surface and a second surface. hydrogen contained within the containing volume; and a reinforcing structure comprising a plurality of elements that traverse the containing volume and are associated with the first surface and second surface of the containing volume; a plurality of struts that interconnect the plurality of elements at a first node; a plurality of struts that interconnect a plurality of struts at a second node; and a plurality of struts that connect the plurality of elements to the first surface or second surface at a third node.
41. An apparatus of Claim 40 further comprising a plurality of microspheres.
42. An apparatus of Claim 40, wherein the plurality of trusses and the plurality of struts of the reinforcing structure is solid.
43. An apparatus of Claim 40, wherein the plurality of trusses and the plurality of struts of the reinforcing structure is hollow.
44. An apparatus of Claim 43, wherein the plurality of trusses and the plurality of struts of the reinforcing structure are made of a porous material.
45. An apparatus of Claim 44 further comprising a plurality of microspheres, wherein the plurality of microspheres are located within a lumen of the hollow trusses and struts.
46. An apparatus of Claim 40 further comprising palladium.
47. An apparatus of Claim 46, wherein the palladium is in a particulate form.
48. An apparatus of Claim 46, wherein the palladium is in a powder form
49. An apparatus of Claim 45 further comprising palladium.
50. An apparatus of Claim 48, wherein the palladium is in a particulate form.
51. An apparatus of Claim 49, wherein the palladium is in a particulate form.
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CN105020566A (en) * 2015-05-07 2015-11-04 重庆大学 Section-variable metal lattice structure and machining method thereof

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US5700443A (en) * 1989-08-04 1997-12-23 Canon Kabushiki Kaisha Hydrogen storing member and process for storing hydrogen into the hydrogen storing member
US5816009A (en) * 1994-11-14 1998-10-06 Hexas Llc Stress steering structure
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US5700443A (en) * 1989-08-04 1997-12-23 Canon Kabushiki Kaisha Hydrogen storing member and process for storing hydrogen into the hydrogen storing member
US5351847A (en) * 1992-11-04 1994-10-04 George Greenbaum Solamar potable water system
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