RU2753557C1 - Lyamin's woven spatial structure (variants) - Google Patents

Abstract

FIELD: building.SUBSTANCE: invention relates to the field of building, namely to structural elements. The structure is comprised of linear elements of finite length, bent in space, called curved bars. The curved bars are bent, intertwined and tied together forming a woven polygon in form of a face, with the ends of the curved rods extending therefrom. The faces are interconnected by the tied ends of the curved bars forming a structural block in form of a polyhedron. The curved bars are interconnected forming the sides of the structural frame block. The structural blocks and the structural frame blocks are interconnected by the ends of curved bars forming a woven spatial structure.EFFECT: increased stability of the structure.12 cl, 24 dwg, 2 tbl

Description

Technology area

The invention relates to the field of structural elements, prefabricated structures consisting of these elements. More specifically, to structures made up of two or more elongated elements attached along the edges and intended to be attached to like elements in different mutual positions. The invention can be used in mechanical engineering, aircraft construction, construction and other industries.

Prior art

Known spatial system of the structure of the structure, described in US patent No. 4,156,997, "Light weight tension-compression equilibrium structures)); IPC: F16S 3/00 (20060101); E04C 003/10; authors: Decker, deceased; Bert J. (LATE OF Buffalo, NY), Decker, executrix; Jean S. (Buffalo, NY); priority: 07/14/1975, published 06/05/1979.

A lightweight, substantially flat, structural block that contains at least three compression members in contact with each other in the interior of the block and a plurality of tension members in contact with such compression members and balancing forces acting on the compression members in the plane of the structural block and holding compression elements in position in relation to each other to strengthen them. The specified participants in tension produce compressive forces in the elements of compression, which are directed in the plane of the structural unit to the point of contact of compression of the elements in the inner part of the plane of the structural unit. The specified forces, also compressive forces applied to the participants in compression, exceed the amount of force usually required to hold the specified compression members together. The tension members are distributed along the length of the compression members such that the distances between the tension members along the compression members are less than the length in which the compression members alone would buckle under full compressive forces.

Features that coincide with the essential features of the invention, the structural block contains at least three elements in contact with each other, balancing the forces acting on the elements.

The disadvantage of this tensely compressed structural unit can be considered the dependence of the integrity of the structure on the integrity of each single element. Failure of any of the tension or compression members will result in the destruction of the structural block. The fabrication of the structural block requires pre-fabrication of tension and compression elements. This complicates and increases the cost of delivering elements to the assembly site of a structure from structural blocks.

As a prototype for the claimed wicker spatial structure, a lightweight tensely compressed structural unit described in US patent No. 5,505,035, priority June 24, 1992, was chosen; publ. 04/09/1996; IPC: E04B 1/18; author: Heresh Lalvani.

The spatial system of the structure of the structure consists in the fact that it contains many elements connected by many spacers, that the node is inscribed in an irregular polyhedron, a polyhedron includes an interior and a surface, the specified surface includes vertices, edges and faces, where at least one of the said faces is incorrect polygon, a polygon that has at least two different angles between the indicated edges, and where it is said that an irregular polyhedron is asymmetric to a regular parallelepiped and a regular prism, regular parallelepipeds, and regular prisms consist only of regular polygons, where the nodes are obtained from the indicated lines, the lines are connected in to the point lying inside the polyhedron, the lines connect the point inside the polyhedron and the points on the faces of the polyhedron, these lines are spacers, the indicated cells are connected to the spacers with the ability to make a variety of spatial configurations.

Features that coincide with the essential features of the invention, the spatial system of the structure contains many connected elements, a polyhedron includes a surface, a surface includes vertices, edges and edges, regular prisms consist only of regular polygons.

The disadvantage of this spatial system of the structure of the structure is the fact that the individual elements are made only in a rectilinear form. The assembly of a volumetric body from single elements requires additional fasteners, material and equipment. The integrity of a structure depends on the integrity of each single element. Destruction of any of the elements will lead to the destruction of the structural block.

Disclosure of invention

The problem to be solved by the claimed invention is to increase the stability of the spatial structure, and when several blocks are destroyed in its composition.

The technical result achieved when solving this problem is to balance the forces of interaction of elements in each structural block of the spatial structure.

A wicker spatial structure containing nodes and linear elements, according to the invention, each linear element is made of finite length, and is bent in space to obtain a shape corresponding to a pre-calculated mathematical model using spline theories. In this case, the curved element is a curved bar. Curved rods are intertwined with each other and connected to each other to form a braided polygon, with the ends of the curved rods protruding from it. Braided polygons are connected by connected ends of curved rods to form a polyhedron-shaped structural block. Structural blocks are interconnected by the ends of curved rods to form a braided spatial structure.

In the second version, a woven spatial structure containing nodes and linear elements, according to the invention, each linear element is made of finite length and curved in space to obtain a shape corresponding to a pre-calculated mathematical model using spline theories. In this case, the curved element is a curved bar. Curved rods are connected to each other to form the outline of polygons, which are connected to each other to form a wireframe structural unit. Frame structural blocks are interconnected by the ends of curved rods to form a braided spatial structure.

The set of essential features provides a technical result, balancing the forces of interaction of elements in each structural block and frame block, which allows solving the problem of increasing the resistance of a wicker spatial structure to destruction when several blocks in its composition are destroyed.

Skeleton structural and structural blocks can be interconnected by the ends of curved rods, which are calculated by mathematical models on the principles of tangential motion, "free geometry" using spline theories.

Each curved bar can be calculated by methods based on the principles of tangential motion, "free geometry" using spline theories.

Braided polygons can be connected to each other by the ends of curved rods extending from the vertices of the braided polygons, or extending from the sides of the braided polygons.

Structural blocks and frame blocks can be interconnected by the ends of curved rods emerging from adjacent vertices of structural blocks, or emerging from adjacent edges of these blocks, or emerging from the edges of one block and the vertices of another block adjacent to it.

Structural blocks can be interconnected by the ends of curved rods emerging from adjacent braided polygons forming the edges of the structural blocks; or emerging from a braided polygon forming a face of one structural block, and from an edge of an adjacent block; or emerging from the braided polygon forming the face of one structural block and from the vertex of the adjacent block.

This makes it possible to exclude fasteners between the connected linear elements, to balance the forces arising in the structural block and in the joints of the structural blocks.

Thus, this technical solution ensures the absence of fasteners and other constructive methods of connections within the structural blocks and in the connections between the structural blocks of the structure in the structures. In this case, the forces of interaction of elements in each structural block of the structure are balanced. This makes it possible to increase the resistance of the structure to destruction when several blocks in its composition are destroyed.

In the cited analogs characterizing the prior art, there is no means in which all the features of the invention, expressed by the proposed formula, are inherent in such a way that all the features of the previously known means are contained in one source of information. This confirms the compliance of the claimed invention with the "novelty" condition.

The information contained in the prior art, by combining, changing or sharing, cannot create the proposed invention. From the prior art, no solutions have been identified that have features that coincide with the distinctive features of the invention under consideration. It was concluded that the invention does not explicitly follow from the prior art for a person skilled in the art. This confirms the compliance of the claimed invention with the condition "inventive step".

Brief Description of Drawing Figures

FIG. 1 shows a section of the fundamental spline r (t) between the end points p _k and P _{k + 1} .

FIG. 2 shows tangent vectors at endpoints parallel to chords

FIG. 3 shows a graph of the curve in the area bounded by the control points p _{k + 1} and p _k in the OXZ plane.

FIG. 4 is a plot of the curve between control points p _k and p _k-1 in the OYZ plane.

FIG. 5 shows a mathematical model of a curved bar in the projections OXY, OXZ, OYZ.

FIG. 6 shows a curved bar 1.

FIG. 7 shows a braided polygon 2 of a building block 3.

FIG. 8 shows a panel hollow structural unit 3.

FIG. 9 shows a diagram of a hollow panel structural unit 3.

FIG. 10 shows a diagram of the frame structural unit 5.

FIG. 11 shows a schematic diagram of a combined hollow structural unit 3.

FIG. 12 shows a diagram of a communication panel structural unit 3.

FIG. 13 shows a diagram of the frame structural unit 5.

FIG. 14 shows a diagram of a communication mixed structural block 3.

FIG. 15 shows a diagram of the connection of braided polygons 2 at the vertices of the structural block 3.

FIG. 16 shows a diagram of the connection of braided polygons 2 of the building blocks 3 between the ribs.

FIG. 17 shows a diagram of the connection of the building blocks 3 between the vertices.

FIG. 18 shows a diagram of the connection of the building blocks 3 between the ribs.

FIG. 19 shows a diagram of the connection of building blocks 3 between braided polygons 2.

FIG. 20 shows a diagram of the connection of building blocks 3 between the edges of one building block 3 and the vertices of another building block 3.

FIG. 21 shows the connection diagram of the building blocks 3 between the braided polygon 2 of one building block 3 and the edge of another building block 3.

FIG. 22 shows a diagram of the connection of building blocks 3 between a braided polygon 2 of one building block 3 and the vertex of another building block 3.

FIG. 23 shows a diagram of the connection of the structural blocks 3 with the formation of a spherical shell from a woven spatial structure.

FIG. 24 shows a connection diagram of the skeleton structural blocks 3 to form a skeleton gear from a woven spatial structure.

An embodiment of the invention

The patent describes a woven spatial structure that is universally suitable for structures of any shape and size without the use of additional joints and fasteners.

A wicker spatial structure is a system of structural blocks 3 and frame structural blocks 5, each of which is woven from curved rods 1, fastened to each other by the ends 4 of curved rods 1 coming out of them, taking into account the calculation of the geometry of each curved rod 1 of this system.

Curved bar 1 is an extended element in which the axis passing through the centers of gravity of the cross sections is a curve (Fig. 6).

Curved rods 1 can be metallic and non-metallic; solid section (wire, bar, etc.) and not solid section (tube, etc.), curvilinear, describing the trajectory of a two-dimensional or three-dimensional curve.

Braided polygon 2 - a braided flat figure made of curved rods 1, having the shape of a polygon.

Structural block 3 is an elementary three-dimensional cell of a wicker spatial structure, consists of wicker polygons 2 (Fig. 8), connected to each other at nodes 6 (Fig. 12-16).

Regular structural blocks 3 can have the form of regular polyhedrons (tetrahedron, octahedron, icosahedron, hexahedron, dodecahedron, etc.).

Frame structural unit 5 (Fig. 10, 13) is an elementary three-dimensional cell of a wicker spatial structure, consisting of curved rods 1, which are connected to each other at nodes 6 to form the sides of the frame. Curved rods 1 are connected to each other to form the sides of the polygons, the connection of which forms a frame structural block 5.

Structural blocks 3 are subdivided: into panel hollow (Fig. 9), combined (Fig. 11); panel bindings (Fig. 12), mixed (Fig. 14).

The structural block 3 is hollow (Fig. 9) is a structural block in the form of a polyhedron, formed by braided polygons 2 in the form of its faces. Braided polygons 2, braided from curved rods 1. Braided polygons 2 are made in the form of a triangle in this case. The formation of the braided polygon 2 of full filling is carried out in various ways of weaving the curved rods 1, which maximally fill the area of the formed braided polygon 2.

The hollow combined structural block (Fig. 11) is a structural block 3 formed from a set of braided polygons 2, and curved rods 1 in the form of the sides of the polygons of the frame structural block 5. In this case, braided polygons 2 are made in the shape of a triangle.

Structural block connected panel (Fig. 12) is a structural block formed by connecting braided polygons 2. In this case, braided polygons 2 are made in the form of triangles connected on two sides 7 and 8. The remaining sides of braided polygons 2 form the sides of structural block 3.

Structural block connected mixed (Fig. 14) - structural block 3 connected, formed from braided polygons 2, a connected panel block and a frame structural block 5.

When forming structural blocks 3 and frame structural blocks 5, combinations of curved rods 1 are used that are different in material, section, thickness, depending on their purpose.

From each side or braided polygon 2, which are the faces of the structural blocks 3 and the edges of the frame structural blocks 5, at least one end 4 of the curved bar 1 emerges (Fig. 8). They serve to connect braided polygons 2 at nodes 6 (Fig. 9) using known weaving methods, twisting, tying, bending, etc., with adjacent vertices, or edges or sides or edges of structural blocks 3 to form structural blocks 3 and frame building blocks 5.

Next will be described one of the embodiments of the invention - the creation of a panel hollow structural block 3 of a cubic shape (Fig. 8). A curved bar 1 is used as a building element.

Before performing the structural block 3, a mathematical calculation is carried out using methods based on the principle of tangential movement of the final shape of the curved bar 1 after its bending.

Geometric modeling of curved rods 1 can be based on known and applied in practice design methods, such as methods based on the principle of tangential motion, methods of "free geometry" using the theory of splines.

The principle of tangential traverse is that a polyline is drawn in three-dimensional space through a set of coordinates of points. Then, circular curves or circular curves conjugated with straight inserts - transition curves, for example, clothoid ones, are inscribed into its kinks. Line segments are tangent to curves, i.e. the broken line is a tangential path. Errors possible when entering certain curves do not affect the reliability of the calculations of subsequent curves. The roundings represented by circular curves with transition curves can be symmetrical (with equal lengths of the input and output curves), asymmetric (if the input and output transition lengths are not equal), biclotoid (if there is no circular insertion between the circular curves) symmetric and asymmetric, respectively.

Bezier curves are promising geometric elements for designing curved curves as part of a tangential traverse. Bézier curves are generally spatial functions and are capable of providing spatial modeling of curved members.

The Bezier formula for a cubic polynomial (n = 3) is as follows:

Let i = 0, 1, 2, 3, then for 0 <t <1

In addition to the third-order (cubic) Bezier curve, you can use second, fourth, and fifth-order Bezier curves to design rounding of curved bars.

The construction of a Bezier curve is based on a characteristic polyline, which predetermines its properties:

- a Bezier curve is a smooth curve;

- tangents at the beginning and at the end of the curve coincide in direction with the first and last segments of the polyline;

- the Bezier curve lies in the convex hull generated by the array of points (support vertices) of the polyline;

- the curve is symmetric (retains its shape when the order of the polyline vertices is changed);

- if the vertices of the polyline lie in the same plane, then the curve lies in the same plane;

- the degree of the functional coefficients of the curve is one less than the number of vertices of the polyline;

- changing the position of at least one of the vertices of the polyline leads to a change in the outlines of the Bezier curve.

Curved rods in a structural block are threadlike objects bent in three-dimensional space. The mathematical model of a curved bar in space is a spline.

In the context of computer-aided design for the formalized representation of information about a curved rod in a numerical or analytical form, the question arises of the choice of suitable interpolating and approximating functions. The most suitable functions for this are splines as a universal mathematical apparatus for describing, storing, transforming, analyzing and representing the geometric shapes of elements.

A physical model, called the mechanical analogy of a spline, is a multi-support beam that does not undergo an external load, and whose deformations are caused by internal reactions to the given reactions of the supports to fixed nodes. Mathematically, this model is described by the differential equation of the deformation of the beam and is a multi-point boundary value problem, for the solution of which grid methods are used, as a result of which solutions are obtained in the form of splines.

Splines have good approximation properties and at the same time are simple and convenient for constructing on a computer computational algorithms derived from them. In this case, the algorithms for constructing splines coincide with the algorithm of the finite element method, which is the main industrial method of strength analysis in computer-aided design systems.

Of all the variety of splines, algebraic splines of the first and third degrees - interpolation and smoothing, are the most economical from a computational point of view and have sufficient approximation and smoothness properties.

First degree (linear) splines serve, firstly, a good and accessible illustration for understanding the processes of constructing spline algorithms, and secondly, they are sufficient for describing geometric structural elements represented in the form of broken lines.

Smooth curves are constructed using third-degree (cubic) splines, which, together with their first and second derivatives, provide the designer with the necessary quantitative and qualitative information about the projected curve.

Splines can be defined in two ways:

The first grid method: based on the mutual agreement of simple functions (polynomials of low degree);

Second grid method: from the minimization solution.

The splines determined by the first method include interpolation splines, which are necessary for the analytical representation of discretely given information.

Smoothing splines are defined more often on the basis of the second method. It is smoothing splines that are most widely used to optimize those design solutions that, at the initial stage of consideration, are, as a rule, approximate.

Cubic spline interpolation can be used to obtain a structural element, and can also be used to design the shapes of objects (structures). Cubic splines offer a reasonable trade-off between flexibility and computational speed. Compared to polynomials of higher orders, cubic splines require less calculations and memory, they are more stable. Higher order polynomials may not be accurate enough. Parametric cubic curves are curves of the lowest order that can take an arbitrary position (not on a plane) in three-dimensional space.

The construction of cubic splines is reduced to solving a system of linear equations with a diagonal matrix with a dominant main diagonal. The solution of such systems is easily implemented numerically.

To interpolate a given set of control points with cubic splines, a piecewise cubic polynomial curve passing through all control points is fitted from the input data.

Let n + 1 control points given by coordinates be given.

The parametric cubic polynomial connecting each pair of control points is described by the system of equations:

and the three derivatives define the coordinates of the corresponding tangent vector at the point.

For example, for the x coordinate:

для каждого из n участков кривой, при этом общее количество искомых коэффициентов полиномов будет 4n. Для этого задается достаточное число граничных условий в контрольных точках между участками кривой, на основе которых находятся численные значения всех коэффициентов.The problem of constructing a polynomial is reduced to finding four coefficients

for each of the n sections of the curve, while the total number of the required coefficients of the polynomials will be 4n. For this, a sufficient number of boundary conditions are set at the control points between the sections of the curve, on the basis of which the numerical values of all coefficients are found.

There are many ways to define a parametric spline. These are natural cubic, Hermitian, fundamental splines, Cohanen-Bartels splines, Bezier splines and β-splines, etc.

A spline consists of fragments of the same type, however, there are combined splines, consisting of fragments of different splines. In addition to fragments of splines in the form of algebraic polynomials, exponential splines, splines of variable stiffness described in the works of V.F. Snigirev can be used. and Pavlenko A.P., trigonometric and rational splines.

The expediency of using fragments of a certain type is based on the specific conditions of the problem and implementation constraints. The main requirement is to achieve a given interpolation accuracy with an acceptable investment of time and resources for implementation.

It is known that interpolation splines are not a mathematical apparatus for optimal modeling, but only a convenient tool for computer processing of sketched design solutions. Thus, the formulation of the spline-based modeling problem should assume the following: the interpolation vertices of the sketch curve of the curved bar are assigned approximately (with a tolerance) and, more precisely, their location will need to be calculated according to certain patterns.

As a mathematical apparatus for solving the problem of generating a geometric shape from their rough (approximate) descriptions, it is necessary to consider the use of smoothing splines that minimize the functional of I.Ya. Schoenberg:

(х) - сплайн; S

(x) - spline;

where q = 1, 2;

p _i is the weighting factor of the interpolation node;

f ₀ (x _i ) - initial approximation function.

Restrictions can be on the permissible radius, the direction of the curve, the slope in the longitudinal profile, etc. In this case, for splines of the third degree (q = 2), boundary conditions must be added at the points x ₀ = a , x _n = b, ensuring the uniqueness of the construction of the spline. These can be conditions of a given initial and final direction of the projected section of the curve S '(x _a ), S' (x _b ).

The above functionality well simulates the task of constructing a curve, which consists in achieving the minimum deviation of the projected curve from the existing (original) sketch, with simultaneous conditions for the slope and curvature in the longitudinal profile and for the curvature and rate of increase in curvature. The minimum deviation is achieved due to the second term of the functional, and the curvature condition - due to the first term.

Calculation of smoothing splines of the first and third degree is carried out by coordinate descent, by the method of penalty functions.

A three-dimensional vector representation of points on a curve with respect to the X, Y, Z axes is mathematically described by a set of parametric splines:

- текущая длина кривой. Значение параметра

задает координатный вектор точки на кривой.where parameter

is the current length of the curve. Parameter value

specifies the coordinate vector of a point on the curve.

The shape of a plane curve is determined by the function of its curvature, the shape of a space curve is uniquely determined by the combination of two functions: curvature and torsion.

Curvature (r) and radius of curvature (R = 1 / r) of a spatial curve have the same geometric meaning as for a plane curve, but are calculated using a more complex relationship:

S (x) - spline;

where q = 1, 2;

p _i - weighting factor of the interpolation node

f ₀ (x _i ) - initial approximation function.

Restrictions can be on the allowable radius, the direction of the curve, the slope in the longitudinal profile, etc. In this case, for splines of the third degree (q = 2), boundary conditions must be added at the points x ₀ = a , x _n = b, ensuring the uniqueness of the construction of the spline. These can be conditions of a given initial and final direction of the projected section of the curve S '(x _a ), S' (x _b ).

The above functionality well simulates the task of constructing a curve, which consists in achieving the minimum deviation of the projected curve from the existing (original) sketch, with simultaneous conditions for the slope and curvature in the longitudinal profile and for the curvature and rate of increase in curvature. The minimum deviation is achieved due to the second term of the functional, and the curvature condition - due to the first term.

Calculation of smoothing splines of the first and third degree is carried out by coordinate descent, by the method of penalty functions.

A three-dimensional vector representation of points on a curve with respect to the X, Y, Z axes is mathematically described by a set of parametric splines:

- текущая длина кривой. Значение параметра

задает координатный вектор точки на кривой.where parameter

is the current length of the curve. Parameter value

specifies the coordinate vector of a point on the curve.

The shape of a plane curve is determined by the function of its curvature, the shape of a space curve is uniquely determined by the combination of two functions: curvature and torsion.

Curvature (r) and radius of curvature (R = 1 / r) of a spatial curve have the same geometric meaning as for a plane curve, but are calculated using a more complex relationship:

where x ', x "are the first and second derivatives of x with respect to l.

The torsion (T) of the space curve at the point of contact is determined by the formula:

Spatial modeling of curves can be performed on the basis of tangential traverse with inscribed rounds in the form of Bezier curves. The reference points of the characteristic Bezier polyline (tangential path), in the general case, are specified by the points of the three-dimensional space P _i (x _i , y _i , x _i ), i = 0, 1,…, m. Then the spatial Bezier curve is determined by the equation:

- многочлены Бернштейна. Матричная запись параметрических уравнений, описывающих пространственную кривую Безье:

are Bernstein polynomials. Matrix notation of parametric equations describing the spatial Bezier curve:

If the measurement interval of the parameter is arbitrary, and≤t≤b, the Bezier curve equation has the following form:

The resulting representation is used when specifying a single parameterization of the composite Bezier curve as a whole:

R = R (t), t ₀ ≤t≤t _i , where

R = R ⁽ⁱ⁾ (t), t _i-1 ≤t≤t _i , i = 1, 2,…, l - parametric vector equation of the th elementary Bezier curve.

Thus, parametric splines and Bezier curves allow mathematical modeling of a curved bar in space.

An example of geometric modeling of a section of a curved bar. To obtain an analytical expression describing a section of a curved bar, we use fundamental splines.

Fundamental splines are interpolating piecewise cubic polynomials with specified tangents at the endpoints. However, you do not need to enter tangent values at the endpoints. Formulation of the problem:

Suppose given n + 1 control points given by coordinates:

для каждого из n участков кривой. Для этого задается достаточное количество граничных условий в контрольных точках между участками кривой, на основе которых находятся численные значения всех коэффициентов.It is necessary to determine the values of four coefficients

for each of the n sections of the curve. For this, a sufficient number of boundary conditions are set at the control points between the sections of the curve, on the basis of which the numerical values of all coefficients are found.

и

(на фиг. 2)The section of the fundamental spline r (t) by the plane is specified by the positions of four successive control points. The two middle control points p _k and p _{k + 1} are the end points of the section, the other two p _k-1 and p _{k + 2} are used when calculating the tangents at the end points (in Fig. 1). The tangent vectors at the endpoints are parallel to the chords

and

(in fig. 2)

Let given:

и

I - производные по параметру (наклон кривой) в контрольных точках p_k и p_k+1 соответственно.where

and

I - derivatives with respect to the parameter (slope of the curve) at the control points p _k and p _{k + 1,} respectively.

Let us write the form of the functions r (t) and r '(t) in matrix form:

Подставив вместо параметра t значения конечных точек t_k и t_k+1, фундаментальные граничные условия можно выразить в матричной форме:

Substituting the values of the end points t _k and t _{k + 1} instead of the parameter t, the fundamental boundary conditions can be expressed in matrix form:

Solving this equation for the coefficients of the polynomials, for t _k = 0 and t _{k + 1} = 1, we obtain:

We get the polynomial form:

Let there be given four control points, given with coordinates:

p ₀ = (x ₀ , y ₀ , z ₀ ), p ₁ = (x ₁ , y ₁ , z ₁ ), p ₂ = (x ₂ , y ₂ , z ₂ ), р ₃ = (x ₃ , y ₃ , z ₃ ). We interpolate a given set of control points with fundamental splines.

The parametric cubic polynomial describing the fundamental spline connecting each pair of control points at u = 0 (s = 0.5) has the form:

The solution of the resulting system of equations in the area bounded by the control points p _{k + 1} and p _k are the coordinates of the points given in table 1.

From the values of the coordinates in Table 1, a curve was plotted in the area bounded by the control points p _{k + 1} and p _k , shown in FIG. 3. This curve corresponds to the bending of a curved bar at a specific section in the OXZ plane.

The solution of the resulting system of equations in the area bounded by the control points p _k and p _k-1 are the coordinates of the points given in table 2.

From the values of the coordinates in Table 2, a curve was plotted in the area bounded by the control points p _k and p _k-1 , shown in FIG. 4. This curve corresponds to the bending of the curved bar 1 at a specific section in the OYZ plane.

As a result of calculations, a solution is obtained in the form of a spline, which is a mathematical model of a curved bar 1. Curved bar 1, bent in accordance with the calculation, is a wire bent in three-dimensional space (Fig. 6).

According to the calculated mathematical model of the curved rod 1, the wire is given the calculated shape bent in space, shown in the projections OXY, OXZ, OYZ in Fig. 5.

FIG. 6 shows a curved bar 1 bent in three-dimensional space along a curve representing a third-order interpolation passing through the given calculated coordinates. In this case, the formation of a curved rod 1 in space is carried out by bending the wire. The depicted version of the bent curved bar 1 is not the only possible one, but is one of the many bending options.

Curved rods 1 are interconnected by weaving, as a result of which a braided polygon 2 of the structural block 3 is formed. Braided polygon 2 in FIG. 7 is presented in the form of a quadrangle and is not the only possible shape of a polygon, but one of many options. These options are not discussed in detail.

Braided polygons 2 are connected by connected ends 4 (Fig. 8) of curved rods 1 at nodes 6 (Fig. 9) to form a polyhedron in the form of a structural block 3. The structural block 3 consists of braided polygons 2, in the form of faces, each of which lies in its plane as shown in FIG. 8, 9.

The connection of the braided polygons 2 of the structural block 3 is carried out by tying the nodes 6 according to the calculated bent shapes of the ends 4 of the curved rods 1. The connection of all braided polygons 2 with the ends 4 of the curved rods 1 form the structural block 3.

Thus, the forces of interaction of the curved rods 1 inside the structural block 3 with each other are balanced. Building block 3 - an elementary three-dimensional wicker cell of a wicker spatial structure.

The representation of the structural blocks 3 of a wicker spatial structure in the form of a polyhedron ensures the minimization of the computing resources of a computer, simplification of the presentation of the structural block 3 in the further design of the wicker spatial structure.

Building block 3 is performed in the following sequence:

1. Determine the size, shape, type and purpose of the structural unit 3;

2. Determine the shape of each braided polygon 2 of the considered structural block 3.

3. Determine the curved rods 1 to build a braided polygon 2 of the structural block 3.

4. Calculate the mathematical model of each curved bar 1.

5. Build a braided polygon 2 of the structural block 3 by joining the curved rods 1.

6. A structural block 3 is formed by connecting braided polygons 2, by tying in nodes 6 with the ends of the curved rods 1 emerging from the vertices of the braided polygons (Fig. 15), or the ends of the curved rods 1 extending from the sides of the braided polygons (Fig. 16). Tying the ends of the curved rods 1 emerging from the connected braided polygons 2 in the form of faces is carried out according to the calculated mathematical model.

As shown in FIG. 17, the connection of the structural blocks 3 at the nodes 6 can be carried out by twisting, or weaving, or tying the ends of the curved rods 1 extending from the vertices of the structural blocks 3.

As shown in FIG. 18, the connection of the structural blocks 3 at the nodes 6 can be carried out by twisting, or weaving, or tying the ends 4 of the curved rods 1 (Fig. 8) extending from the ribs of the structural blocks 3.

As shown in FIG. 19, the connection of the structural blocks 3 at the nodes 6 can be carried out by twisting, or weaving, or tying the ends 4 of the curved rods 1 (Fig. 8) coming out of the mating braided polygons 2 of the structural blocks 3.

The connection of the structural blocks 3 at the nodes 6 can be carried out by twisting, or weaving, or tying the ends 4 of the curved rods 1 coming out of the mating edges of one structural block 3 with the vertices of another structural block 3 (Fig. 20); linking the ends 4 of the curved rods 1 coming out of the mating braided polygon 2 of one structural block 3 and the edges of another structural block 3 (Fig. 21); by tying the ends 4 of the curved rods 1 emerging from the mating braided polygon 2 of one structural block 3 and the vertices of another structural block 3 (Fig. 22).

The listed connections are carried out by weaving according to the calculated mathematical models of the ends of 4 curved rods 1, emerging from the structural blocks 3.

Methods of connecting the structural blocks 3 were considered here. Variants of connecting the frame structural blocks 5 to each other and connecting them with the structural blocks 3 are based on the same principles.

FIG. 23 shows a woven spatial structure in the form of a spherical shell of combined structural blocks. FIG. 24 shows a schematic diagram of a wicker spatial structure in the form of a gear made of frame structural blocks 5. These examples are not the only possible ones, but are one of numerous variants of execution.

The formation of wicker spatial structures is carried out by connecting structural blocks 3 and frame structural blocks 5 in such a way that the ends of the curved rods 1 emerging from the interconnected blocks 3 and 5 are bent and articulated with each other according to their calculated mathematical models.

The woven spatial structure can be used in the production of structures without the use of additional fasteners. The building material is supplied to the assembly site in the form of linear materials such as rope or wire from a reel. Linear materials are cut into linear elements of the required length. Curved rods 1 are formed from the cut linear elements, then braided polygons 2 of the structural block 3 and the sides of the frame structural block 5 are weaved. block 5. Manufactured structural blocks 3 and frame structural blocks 5 are interconnected by weaving the ends 4 of the curved rods 1 coming out of blocks 3 and 5.

In addition to the specified technical result, welding, glue and other structural joints are excluded in the manufacture of a wicker spatial structure. This makes the production of structures cheaper, and makes it possible to deliver building material and create structures of any size in hard-to-reach places, such as underground, underwater, at high altitudes or in the absence of the earth's atmosphere.

Industrial applicability

This technical solution can be used for domestic and industrial purposes as a method of forming structures, which is an alternative to casting, turning, molding, additive technologies (three-dimensional printing of structures) and other known technologies. This technology makes it possible to create functional structures for a wide range of applications.

The proposed technical solution can be applied in structures that are subject to high requirements for the independence of the integrity of the structure of the structure from the integrity of a single element, simplification and cheapening of the manufacture and delivery of single elements to the place of assembly of the structure, also where there is a need to connect single structural elements in the structure of the structure. structures made of dissimilar materials in the absence of fastening elements.

In general, the discussed embodiment of the invention can be implemented on existing equipment using existing materials. This shows its performance and confirms its industrial applicability.

Claims (12)

1. Woven spatial structure containing nodes and linear elements, characterized in that each linear element is made of finite length and bent in space to obtain a shape corresponding to a previously calculated mathematical model using spline theories, while the curved element is a curved bar, curved rods are intertwined with each other and connected to each other to form a braided polygon, with the ends of curved rods emerging from it, braided polygons are interconnected by connected ends of curved rods to form a structural block in the form of a polyhedron, structural blocks are interconnected by the ends of curved rods with the formation of a wicker spatial structure. 2. Woven spatial structure containing nodes and linear elements, characterized in that each linear element is made of finite length and bent in space to obtain a shape corresponding to a pre-calculated mathematical model using spline theories, while the curved element is a curved bar, Curved rods are connected to each other to form a contour of polygons, which are interconnected to form a frame structural block, frame structural blocks are interconnected by the ends of curved rods to form a braided spatial structure. 3. Spatial construction according to PP. 1 and 2, characterized in that the frame structural and structural blocks are interconnected by the ends of curved rods, which are calculated by mathematical models on the principles of tangential motion, "free geometry" using spline theories. 4. Spatial design according to PP. 1 and 2, characterized in that each curved bar is calculated by methods based on the principles of tangential motion, "free geometry" using spline theories. 5. The spatial structure according to claim 1, characterized in that the braided polygons are interconnected by the ends of the curved rods extending from the vertices of the braided polygons. 6. The spatial structure according to claim 1, characterized in that the braided polygons are interconnected by the ends of the curved rods extending from the sides of the braided polygons. 7. Spatial design according to PP. 1 and 2, characterized in that the structural blocks and frame blocks are interconnected by the ends of curved rods extending from adjacent vertices of these blocks. 8. Spatial design according to PP. 1 and 2, characterized in that the structural blocks and frame blocks are interconnected by the ends of curved rods extending from the adjacent edges of these blocks. 9. Spatial design according to PP. 1 and 2, characterized in that the structural blocks and frame blocks are interconnected by the ends of curved rods extending from the edges of one block and the vertices of another block adjacent to it. 10. The spatial structure of claim. 1, characterized in that the structural blocks are interconnected by the ends of the curved rods emerging from adjacent braided polygons forming the edges of the structural blocks. 11. The spatial structure according to claim 1, characterized in that the structural blocks are interconnected by the ends of the curved rods emerging from the braided polygon forming the face of one structural block and from the edge of the adjacent structural block. 12. The spatial structure of claim. 1, characterized in that the structural blocks are interconnected by the ends of curved rods emerging from the braided polygon forming the face of one structural block and from the vertex of the adjacent structural block.

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