WO2021042660A1 - 一种张拉整体结构平衡形态确定方法 - Google Patents

一种张拉整体结构平衡形态确定方法 Download PDF

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WO2021042660A1
WO2021042660A1 PCT/CN2020/072245 CN2020072245W WO2021042660A1 WO 2021042660 A1 WO2021042660 A1 WO 2021042660A1 CN 2020072245 W CN2020072245 W CN 2020072245W WO 2021042660 A1 WO2021042660 A1 WO 2021042660A1
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longitudinal
length
compression member
tension
tie rod
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PCT/CN2020/072245
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English (en)
French (fr)
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陈务军
胡建辉
赵兵
杨钧
徐建东
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上海交通大学
新誉集团有限公司
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Publication of WO2021042660A1 publication Critical patent/WO2021042660A1/zh
Priority to US17/684,637 priority Critical patent/US12209999B2/en

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    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/34—Extraordinary structures, e.g. with suspended or cantilever parts supported by masts or tower-like structures enclosing elevators or stairs; Features relating to the elastic stability
    • E04B1/3408—Extraordinarily-supported small buildings
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/18—Structures comprising elongated load-supporting parts, e.g. columns, girders, skeletons
    • E04B1/19—Three-dimensional framework structures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
    • G01L5/16—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes for measuring several components of force
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/20—Investigating strength properties of solid materials by application of mechanical stress by applying steady bending forces
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/18—Structures comprising elongated load-supporting parts, e.g. columns, girders, skeletons
    • E04B1/19—Three-dimensional framework structures
    • E04B2001/1996—Tensile-integrity structures, i.e. structures comprising compression struts connected through flexible tension members, e.g. cables
    • Y—GENERAL 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • the invention relates to the field of engineering structure design analysis, and in particular to a method for determining the balance form of a tensioned overall structure.
  • the tensioning overall structure is a tension self-balancing system composed of separate compression members and continuous tension members. It has the least total number of components, the least compression components, the lowest redundancy and mechanism freedom, and the weight is ultra-light. , To give full play to the strength of materials, is currently a research hotspot in many engineering technologies and cutting-edge cross-fields such as aerospace, architectural structure, sculpture art, intelligent robots, molecular structural biology and so on.
  • the prestress calculation usually adopts the equilibrium matrix decomposition based on the equilibrium shape, solves the self-stress mode, recombines, and determines the stiffness or weight target optimization.
  • Pellegrino et al. established a more complete theoretical method of balanced matrix analysis. However, self-stress is not necessarily reasonable. Therefore, the concept of feasible pre-stress is proposed.
  • Yuan Xingfei et al. used the geometric symmetry of the structure to propose the concept of overall feasible prestress and the quadratic singular value method for solving this mode.
  • Chen Wujun et al. established a method for determining the unstressed state of cable-rod tension, and established a stress-introduction analysis method and effectiveness analysis, as well as a vector projection method based on tensor norm. However, these methods are very complicated and require specialized software to analyze.
  • Chinese patent 201910275705.7 "a large-scale semi-rigid structure airship” invented a semi-rigid structure airship with a tensioned integral keel as the main structural system.
  • Chinese patent 201910275699.5 "A compression rod contact type tensioning overall structure and integration and tension application method” proposes a tensioning overall keel composition and integration method. However, there is no clear method for calculating and determining the prestress of the equilibrium form.
  • the technical problem to be solved by the present invention is how to quickly, accurately and reasonably determine the prestress value, component positioning size, and tension introduction measures.
  • the present invention provides a method for determining the balance form of a tensioned overall structure, which includes the following steps:
  • tensioned integral structure is used as an airship keel system, and the critical bending moment is determined according to aerodynamic load, static moment, and buoyancy gradient moment.
  • calculating the tension of the longitudinal rod includes the following steps:
  • the tension of the longitudinal tie rod near the first end of the integral tension structure and the tension of the longitudinal tie rod near the second end of the integral tension structure are calculated respectively.
  • E j A j is the material elastic modulus and the cross-sectional area of the longitudinal tie rod in the j-th section
  • t j is the longitudinal tie rod of the j-th section tension
  • the unstressed length and compression of the longitudinal compression member are calculated as follows:
  • E jc A jc is the material elastic modulus and the cross-sectional area of the longitudinal compression member in the j section
  • N jc is the length of the longitudinal compression member in the j section
  • N i t i sina i -t i-1 sina i-1 formula (9)
  • N i denotes the i th of said compression force to the ring receiving member
  • N ci denotes an i-th axis of the pressure ring to the compression member
  • t i represents the i-th longitudinal tension rod
  • a is i represents the deflection angle between the longitudinal tie rod in the i-th paragraph and the longitudinal tie rod in the i-1 paragraph
  • n is the number of the longitudinal tie-rods of the circumferential compression member along the circumference.
  • the force calculation of the circumferential compression member is based on a symmetric method, and the calculation of each circumferential compression member at the first end of the tensioned overall structure and the second end of the tensioned overall structure is calculated separately. The force of each of the circumferential pressure members.
  • the minimum adjustment length of the longitudinal compression member satisfies:
  • ⁇ L jc represents the minimum adjustment length of the longitudinal compression member in the j-th stage, Indicates the amount of compression of the longitudinal compression member in the j-th stage, Is the stretching amount of the longitudinal tie rod described in section j.
  • the longitudinal tie rod, the longitudinal compression member, and the circumferential compression member are made of carbon fiber composite material.
  • the longitudinal tie rod, the longitudinal compression member, and the circumferential compression member are made of carbon fiber composite material.
  • the longitudinal tie rod is linear elastic in the tension stage, and the problems of material nonlinearity and strength failure are not considered;
  • the longitudinal compression member is in the material linear elasticity during the compression stage, and the calculation of the compression length requires consideration of geometric nonlinearity and stability.
  • the method for determining the balance form of the tensioned overall structure proposed in the present invention can quickly and effectively determine the prestressed balance form stress and the unstressed length of the tension and compression members, and provide a basis for production and installation; the prestress level is reasonable and feasible, and can meet the overall force requirements of the structure ; Determining the length and production length of the tension and compression member can easily realize the integration of the tension and overall structure, and effectively realize the introduction of prestress to ensure the mechanical properties of the prestress balance form; the method is simple, efficient, small in calculation, and easy to implement.
  • Figure 1 is a schematic diagram of the overall structure of the tensioning of a preferred embodiment of the present invention
  • FIG. 2 is a flowchart of a preferred embodiment of the present invention.
  • Figure 3 is a flow chart of the method for calculating the tension of the longitudinal tie rod
  • FIG. 4 is a schematic diagram of the tension of the first longitudinal rod of a preferred embodiment of the present invention.
  • Fig. 5 is a schematic diagram of a balanced prestress of a preferred embodiment of the present invention.
  • the overall tension structure is a tension self-balancing system composed of separate compression members and continuous tension members.
  • a typical tensioning overall structure as shown in Figure 1, includes a longitudinal tie rod, a longitudinal center shaft 2 and a pressure ring.
  • the pressure ring is a ring pressure member, and the number is multiple, including a first pressure ring 31 with the largest cross-sectional area and other second pressure rings 32 located in the middle section.
  • the number of the second pressure ring 32 can be set in multiples, not limited to the one shown in FIG. 1, and its area is gradually along the middle to the end. Decrease.
  • first longitudinal tie rod 11 located at the largest cross-section and a plurality of second longitudinal tie rods 12 located on a tapered surface.
  • a plurality of compression rings 31 and 32 are compressed in isolation, a plurality of longitudinal central shafts 2 are longitudinal compression members, and a plurality of longitudinal tie rods 11 and 12 are continuously tensioned to form a self-balancing, self-supporting tensioning overall structure.
  • the tensioning overall structure is a combined geometric body.
  • a plurality of pressure rings 31 and 32 are arranged in parallel. The diameter of the first pressure ring 31 in the middle section is the same. From the middle section to the two ends, the diameters of the plurality of second pressure rings 32 gradually change. small.
  • the first longitudinal tie rod 31 and the plurality of second longitudinal tie rods 32 located at the largest cross-sectional area are sequentially connected to the outer rings of the parallel compression rings 31 and 32 to form a closed tension ring.
  • the longitudinal tie rods 11 and 12, the longitudinal center shaft 2, the pressure rings 31 and 32 may be composed of a single rod-shaped member such as a thin-walled tube, or a truss structure, preferably made of high-performance carbon fiber conforming material (CFRP).
  • CFRP high-performance carbon fiber conforming material
  • the method for determining the equilibrium form of the tensioned overall structure includes the following steps:
  • Step 101 Determine the critical bending moment to be borne by the tensioned overall structure
  • Step 102 Calculate the tension of the longitudinal rod
  • Step 103 Calculate the pressure of the mandrel in the longitudinal direction
  • Step 104 Calculate the stretched length and the stress-free length of the longitudinal tie rod
  • Step 105 Calculate the compressed length and unstressed length of the longitudinal center shaft
  • Step 106 Calculate the force and radial deformation of the pressure ring
  • Step 107 calculates the structural dimensions of each component, including the positioning length and the manufacturing length.
  • Step 101 determines the critical bending moment M cr to be borne by the tensioned overall structure.
  • the critical bending moment M cr can be calculated according to actual application scenarios and working conditions of the tensioned overall structure.
  • the critical bending moment M cr can be calculated according to actual working conditions such as aerodynamic load, static moment, floating gradient moment, etc.
  • the calculation formula is as follows:
  • L a length of the airship D is the maximum diameter of the outer bag airship, ⁇ a is the air density, u is the wind speed, v c is the speed of the airship, V e is the volume of the outer bag.
  • Step 102 calculates the tension of the longitudinal rod.
  • the first longitudinal tie rod 11 includes a middle section of the tensioned overall structure, that is, the largest cross-sectional area, and a plurality of second longitudinal tie rods 12 form a cone-like structure.
  • step 1021 first calculate the tension of the first longitudinal rod 11
  • step 1022 then recursively push the tension of the second longitudinal rod 12 sequentially.
  • Step 1021 Calculate the tension of the first longitudinal rod 11
  • the longitudinal rods are evenly arranged along the pressure ring.
  • the number of the first longitudinal tie rods 11 is n
  • the ring radius of the pressure ring is R max
  • the first longitudinal tie rod 11 The tension of is t 0 , which can be expressed as:
  • M cr is the critical moment
  • d i is the distance of the i-th first longitudinal rod in a longitudinal mandrel 2.
  • Step 1022 Calculate the tension of the second longitudinal rod 12
  • the tension of the second longitudinal rod 12 is calculated sequentially and recursively according to the static equilibrium conditions of the tensioned overall structure separation.
  • the tension of the second longitudinal rod 12 can be expressed recursively as:
  • t j is the tension of the j-th section of the second longitudinal tie rod 12
  • t j-1 is the tension of the j-1 section of the second longitudinal tie rod 12
  • a j is the j-th section longitudinal tie rod and the j-1 section longitudinal tie rod Declination.
  • the cross-sectional diameter of the tensioned overall structure decreases from the middle section to the two ends respectively.
  • a plurality of second longitudinal tie rods 12 are respectively arranged between the middle section and one end.
  • end A in Figure 1 is defined as The head and the B end are the tail.
  • the calculation can be performed according to the symmetric method, and the subscripts can be used to distinguish the tension of the second longitudinal rod 12 near the head and the tension of the second longitudinal rod 12 near the tail.
  • the subscripts f and r in t jr , t jf , a jr , and a jf denote the head and tail, respectively.
  • Step 103 calculates the pressure of the mandrel 2 in the longitudinal direction.
  • the longitudinal center shaft 2 is a longitudinally compressed member.
  • the longitudinal center mandrel 2 is compressed, and the pressure is balanced with the tension of the longitudinal rod.
  • the pressure of the longitudinal center mandrel 2 is:
  • N cj nt j cos a j formula (4)
  • N cj is the pressure of the mandrel in the longitudinal direction of the j-th segment.
  • Step 104 Calculate the stretched length and unstressed length of the longitudinal tie rods 11 and 12
  • the stress length of the longitudinal rods 11 and 12 in the current prestressed equilibrium state, and the tensile stiffness of the longitudinal rods 11 and 12 calculate the tensile lengths of the longitudinal rods 11 and 12, and then calculate the longitudinal rods 11 and The stress-free length of 12.
  • the stress-free lengths of the longitudinal rods 11 and 12 are:
  • the current length of the rod, E j A j is the material elastic modulus and cross-sectional area of the j-th section longitudinal tie rod, and t j is the tension of the j-th section longitudinal tie rod.
  • the stretching amount of the longitudinal rods 11 and 12 is:
  • Step 105 Calculate the compressed length and unstressed length of the longitudinal center shaft 2
  • the compression length of the longitudinal center mandrel 2 is calculated, and then the longitudinal center mandrel 2 is calculated The stress-free length.
  • the stress-free length of the longitudinal center shaft 2 is:
  • the current length of the center mandrel, E jc A jc is the material elastic modulus and cross-sectional area of the mandrel in the longitudinal direction of the jth section, and N jc is the axial compressive force of the mandrel in the longitudinal direction of the jth section.
  • the compression of the mandrel 2 in the longitudinal direction is:
  • Step 106 Calculate the force and radial deformation of the pressure rings 31 and 32
  • the radius and geometric relationship of the pressure rings 31 and 32 in the current prestressed equilibrium state, the axial pressure and the radial deformation of the pressure rings 31 and 32 are calculated.
  • N i t i sina i -t i-1 sina i-1 formula (9)
  • N i denotes the i-th ring compression force
  • N 2f t 2f sina 2f -t 1f sina 1f formula (12)
  • N 2r t 2r sina 2r -t 1r sina 1r formula (13)
  • a pressure ring has n longitudinal rods along the circumference, the axial pressure of the pressure ring:
  • the axial pressure of each pressure ring on the forward head and the backward tail can be calculated.
  • the deformation of the pressure ring 31 and 32 is the change of the radius of the pressure ring:
  • Step 107 Calculate the structural dimensions of each component, including positioning length and manufacturing length
  • the stress length of the longitudinal tie rods 11 and 12 the stress length of the longitudinal center mandrel 2, and the unstressed length of the longitudinal tie rods 11 and 12, and the unstressed length of the longitudinal center mandrel 2
  • the tension introduction method and installation according to the prestressed balance form Integrate stress-free geometric consistency, and calculate the positioning length and manufacturing length of the longitudinal rods 11 and 12 and the longitudinal center mandrel 2.
  • ⁇ L jc is the minimum adjustment length of the longitudinal compression member of the j-th segment.
  • the calculation of the compression amount of the longitudinal center mandrel 2 and the compression rings 31 and 32 can be performed by numerical analysis and calculation using structural analysis software.
  • the structural analysis software can be used for numerical nonlinear stability analysis and calculation.
  • the longitudinal tie rods 11 and 12 are linear elastic in the tension load stage, and the material nonlinearity and failure problems are not considered; the longitudinal middle mandrel 2 and the compression rings 31 and 32 are linear elastic in the compression stage, and the calculation of the compression length needs to consider the geometric non-linearity. Linearity and stability.
  • Structure size in this embodiment the airship length L a, or maximum radius R max diameter D, radius of the ring compression
  • Material and process selection (longitudinal tie rod, longitudinal center shaft, and pressure ring are made of CFRP), critical bending moment (environmental load and flight performance, structural performance requirements), prestress value (longitudinal tie rod tension t j , longitudinal
  • the pressure of the pressure member N jc and the pressure of the pressure ring axis N ci ) can be determined for specific engineering applications.

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Abstract

一种张拉整体结构平衡形态确定方法，包括：确定所述张拉整体结构承受的临界弯矩；计算纵向拉杆的张力；计算纵向受压构件的压力；计算所述纵向拉杆的拉伸长度，计算所述纵向拉杆的无应力长度；计算所述纵向受压构件的压缩长度，计算所述纵向受压构件的无应力长度；计算环向受压构件的受力和径向变形；计算所述纵向拉杆、所述纵向受压构件的定位长度和制作长度。

Description

一种张拉整体结构平衡形态确定方法 技术领域
本发明涉及工程结构设计分析领域，尤其涉及一种张拉整体结构平衡形态确定方法。
背景技术
张拉整体结构是由分离的受压构件和连续的受拉构件组成的张力自平衡系统，具有最少的总构件数、最少的受压构件、最低的冗余度和机构自由度，质量超轻，充分发挥材料强度，是目前航空航天、建筑结构、雕塑艺术、智能机器人、分子结构生物学等众多工程技术和前沿交叉领域的研究热点。
张拉整体结构的形态和刚度是靠预应力保持和产生，而平衡形态是基础，因此，平衡形态的预应力计算、确定一直就是张拉整体结构研究的核心问题，需要解决两个问题：第一，如何计算确定一组合理可行的预应力；第二，这组预应力如何可以有效产生。
预应力计算通常采用基于平衡形态的平衡矩阵分解，求解自应力模态，再组合，并经过刚度或重量目标优化确定。Pellegrino等建立了较完善的平衡矩阵分析理论方法。但是，自应力并不一定合理，因此，提出了可行预应力概念。袁行飞等利用结构的几何对称性，提出了整体可行预应力的概念和求解该模态的二次奇异值法。陈务军等建立了索杆张力的无应力状态确定方法，并建立了应力导入分析方法及有效性分析，以及基于张量范数的向量投影方法。但是，这些方法都很复杂，需要专业化的软件才能分析。
中国专利201910275705.7“一种大尺度半刚性结构飞艇”，发明了一种由张拉整体龙骨作为主要结构体系的半刚性结构飞艇。中国专利201910275699.5“一种压杆接触型张拉整体结构与集成及张力施加方法”，提出了张拉整体龙骨构成、集成方法。但是，对平衡形态预应力计算及确定方法没有明确。
因此，本领域的技术人员致力于开发一种张拉整体结构平衡形态确定方法，可以快速、准确、合理确定预应力值、构件定位尺寸、张力导入措施。
发明内容
有鉴于现有技术的上述缺陷，本发明所要解决的技术问题是如何快速、准确、合理确定预应力值、构件定位尺寸、张力导入措施。
为实现上述目的，本发明提供了一种张拉整体结构平衡形态确定方法，包括以下 步骤：
确定所述张拉整体结构承受的临界弯矩；
计算纵向拉杆的张力；
计算纵向受压构件的压力；
计算所述纵向拉杆的拉伸长度和无应力长度；
计算所述纵向受压构件的压缩长度和无应力长度；
计算环向受压构件的受力和径向变形；
计算所述纵向拉杆、所述纵向受压构件的定位长度和制作长度。
进一步地，所述张拉整体结构用作飞艇龙骨体系，所述临界弯矩根据气动载荷、静力矩、浮力梯度矩确定。
进一步地，计算所述纵向拉杆的张力，包括如下步骤：
计算第一纵向拉杆的张力，其中所述第一纵向拉杆为抵抗矩最大截面的纵向拉杆；
依次递推计算其他所述纵向拉杆的张力。
进一步地，按照对称方法，分别计算靠近所述张拉整体结构的第一端的所述纵向拉杆的张力和靠近所述张拉整体结构的第二端的所述纵向拉杆张力。
进一步地，所述纵向拉杆的无应力长度和拉伸量的计算如下：
Figure PCTCN2020072245-appb-000001
其中，
Figure PCTCN2020072245-appb-000002
为第j节段所述纵向拉杆的无应力长度，
Figure PCTCN2020072245-appb-000003
为第j节段预应力平衡形态所述纵向拉杆的当前长度，E jA j为第j节段所述纵向拉杆的材料弹性模量和截面积，t j为第j段所述纵向拉杆的张力，
Figure PCTCN2020072245-appb-000004
为第j节段所述纵向拉杆的拉伸量。
进一步地，所述纵向受压构件的无应力长度和压缩量的计算如下：
Figure PCTCN2020072245-appb-000005
其中，
Figure PCTCN2020072245-appb-000006
为第j节段所述纵向受压构件的无应力长度，
Figure PCTCN2020072245-appb-000007
为第j节段预应力平衡形态所述纵向受压构件的当前长度，E jcA jc为第j节段所述纵向受压构件的材料弹性模量和截面积，N jc为第j段所述纵向受压构件的受压轴力，
Figure PCTCN2020072245-appb-000008
表示第j阶段所述纵向受压构件的压缩量。
进一步地，所述环向受压构件的受力计算如下：
N i＝t isina i-t i-1sina i-1    公式(9)
N ci＝N i×n/2π       公式(14)
其中，N i表示第i个所述环向受压构件的受力，N ci表示第i个所述环向受压构件的轴压力，t i表示第i个所述纵向拉杆的张力，a i表示第i段所述纵向拉杆与第i-1段所述纵向拉杆的偏角，n表示所述环向受压构件沿圆周的所述纵向拉杆数量。
进一步地，所述环向受压构件的受力计算按照对称方法，分别计算所述张拉整体 结构的第一端的各所述环向受压构件和所述张拉整体结构的第二端的各所述环向受压构件的受力。
进一步地，计算所述纵向受压构件的定位长度和制作长度中，所述纵向受压构件的最少调节长度满足：
Figure PCTCN2020072245-appb-000009
其中，ΔL jc表示第j阶段所述纵向受压构件的最少调节长度，
Figure PCTCN2020072245-appb-000010
表示第j阶段所述纵向受压构件的压缩量，
Figure PCTCN2020072245-appb-000011
为第j节段所述纵向拉杆的拉伸量。
进一步地，所述纵向拉杆、所述纵向受压构件、所述环向受压构件由碳纤维复合材料制成。
进一步地，所述纵向拉杆、所述纵向受压构件、所述环向受压构件由碳纤维复合材料制成。
其中，所述纵向拉杆在受拉阶段处于线弹性，不考虑材料非线性和强度破坏问题；
所述纵向受压构件在受压阶段处于材料线弹性，计算压缩长度，需要考虑几何非线性和稳定性。
本发明提出的张拉整体结构平衡形态确定方法，可以快速有效确定预应力平衡形态应力、拉压构件无应力长度，为制作和安装提供依据；预应力水平合理可行，可满足结构整体受力要求；确定拉压构件长度和制作长度，容易实现张拉整体结构集成，且有效实现预应力导入，保证预应力平衡形态力学特性；所述方法简洁、高效、计算量小、容易实现。
以下将结合附图对本发明的构思、具体结构及产生的技术效果作进一步说明，以充分地了解本发明的目的、特征和效果。
附图说明
图1是本发明的一个较佳实施例的张拉整体结构示意图；
图2是本发明的一个较佳实施例的方法流程图；
图3是计算纵向拉杆张力的方法流程图；
图4是本发明的一个较佳实施例的第一纵向拉杆的张力示意图；
图5是本发明的一个较佳实施例的平衡形态预应力示意图。
具体实施方式
以下参考说明书附图介绍本发明的一个优选实施例，使其技术内容更加清楚和便于理解。本发明可以通过许多不同形式的实施例来得以体现，本发明的保护范围并非仅限于文中提到的实施例。
在附图中，结构相同的部件以相同数字标号表示，各处结构或功能相似的组件以相似数字标号表示。附图所示的每一组件的尺寸和厚度是任意示出的，本发明并没有 限定每个组件的尺寸和厚度。为了使图示更清晰，附图中有些地方适当夸大了部件的厚度。
张拉整体结构是由分离的受压构件和连续的受拉构件组成的张力自平衡系统。一种典型的张拉整体结构，如图1所示，包括纵向拉杆、纵向中芯轴2和受压环。其中，受压环为环受压构件，其数量为多个，包括位于中段的截面积最大的第一受压环31和其他的第二受压环32。在张拉整体结构的中部分别与两端形成的区域中，第二受压环32的数量均可设置多个，而不仅局限于图1中的一个，而且其面积沿着中部往端部逐渐减小。纵向拉杆数量为多个，包括位于最大截面处的第一纵向拉杆11和位于锥形面上的多个第二纵向拉杆12。多个受压环31和32孤立受压，多个纵向中芯轴2为纵向受压构件，若干个纵向拉杆11和12连续受拉，组成自平衡、自承力的张拉整体结构。张拉整体结构为组合几何体，多个受压环31和32平行设置，位于中段的第一受压环31的直径相同，从中段往两端，多个第二受压环32的直径逐渐变小。位于截面积最大处的第一纵向拉杆31以及多个第二纵向拉杆32依次连接平行的受压环31和32的外环，形成闭合拉力环。
纵向拉杆11和12、纵向中芯轴2、受压环31和32可以由单个杆状件例如薄壁管构成，也可以是桁架结构，优选采用高性能碳纤维符合材料(CFRP)制成。本发明的目的在于提供一种确定张拉整体结构平衡形态的方法，无论张拉整体结构由单个杆状件构成，还是由桁架结构构成，均能适用本发明的方法。
如图2所示，本发明一个优选实施例中，确定张拉整体结构的平衡形态的方法包括如下步骤：
步骤101确定张拉整体结构承受的临界弯矩；
步骤102计算纵向拉杆的张力；
步骤103计算纵向中芯轴的压力；
步骤104计算纵向拉杆的拉伸长度和无应力长度；
步骤105计算纵向中芯轴的压缩长度和无应力长度；
步骤106计算受压环的受力和径向变形；
步骤107计算各构件的结构尺寸，包括定位长度、制作长度。
下面结合图1所示的实施例，详细说明确定张拉整体结构的平衡形态的方法。
步骤101确定张拉整体结构承受的临界弯矩M cr。
根据张拉整体结构实际运用的场景和工况来确定临界弯矩M cr。例如，当张拉整体结构作为飞艇龙骨体系时，临界弯矩M cr可以根据气动载荷、静力矩、浮动梯度矩等实际工况参数进行计算，计算公式如下：
Figure PCTCN2020072245-appb-000012
其中，L a为飞艇长度，D为飞艇外气囊最大直径，ρ a为空气密度，u为风速，v c为 飞艇速度，V e为外气囊体积。
步骤102计算纵向拉杆的张力。
如图1所示，第一纵向拉杆11包括位于张拉整体结构的中段，即截面积最大处，多个第二纵向拉杆12形成类似锥面的结构。在计算纵向拉杆的张力时，计算步骤如图3所示，步骤1021：先计算第一纵向拉杆11的张力；步骤1022：然后再依次递推第二纵向拉杆12的张力。
步骤1021计算第一纵向拉杆11的张力
按照预张力抵抗临界弯矩M cr，且以预张力失效作为临界条件，即弯矩作用下张拉整体结构受压侧张力为零，计算抵抗矩最大截面的第一纵向拉杆11的张力。
在每个受压环处，纵向拉杆沿着受压环均匀设置。以最大截面处的第一受压环31和第一纵向拉杆11为例，如图4所示，第一纵向拉杆11的数量为n，受压环环形半径为R max，第一纵向拉杆11的张力为t 0，可表达为：
Figure PCTCN2020072245-appb-000013
其中，M cr为临界弯矩，d i为第i根第一纵向拉杆与纵向中芯轴2的距离。
步骤1022计算第二纵向拉杆12的张力
根据张拉整体结构分离静力学平衡条件，依次递推计算第二纵向拉杆12的张力。
如图5所示，根据平衡条件，第二纵向拉杆12张力可递推表达为：
t j＝t j-1/cos a j       公式(3)
其中，t j为第j段第二纵向拉杆12的张力，t j-1为第j-1段第二纵向拉杆12的张力，a j为第j段纵向拉杆与第j-1段纵向拉杆偏角。
如图1和5所示，张拉整体结构的截面直径从中段分别往两端递减，多个第二纵向拉杆12分别设置在中段与一个端部之间，这里定义图1中的A端为头部，B端为尾部。在递推计算第二纵向拉杆12的张力时，可以按照对称方法进行计算，并使用下标来区分靠近头部的第二纵向拉杆12的张力和靠近尾部的第二纵向拉杆12的张力，具体为，如图5所示，t jr、t jf、a jr、a jf中的下标f和r分别表示头部和尾部，同样地，N cjf、N cjr、N jf、N if中，其下标f和r也表示头部和尾部，后面就不在赘述，其中，j＝0，1，2，…。
步骤103计算纵向中芯轴2的压力。
纵向中芯轴2纵向受压构件。纵向中芯轴2受压，压力与纵向拉杆的张力平衡，纵向中芯轴2的压力为：
N cj＝nt jcos a j       公式(4)
其中，N cj为第j节段纵向中芯轴的压力。
步骤104计算纵向拉杆11和12的拉伸长度和无应力长度
根据纵向拉杆11和12的张力、当前预应力平衡态纵向拉杆11和12的应力长度、纵向拉杆11和12的抗拉刚度，计算纵向拉杆11和12的拉伸长度，进而计算纵向拉杆11和12的无应力长度。
纵向拉杆11和12的无应力长度为：
Figure PCTCN2020072245-appb-000014
杆的当前长度，E jA j为第j节段纵向拉杆的材料弹性模量和截面积，t j为第j段纵向拉杆的张力。
纵向拉杆11和12的拉伸量为：
Figure PCTCN2020072245-appb-000015
其中，
Figure PCTCN2020072245-appb-000016
为第j节段纵向拉杆的拉伸量，
Figure PCTCN2020072245-appb-000017
步骤105计算纵向中芯轴2的压缩长度和无应力长度
根据纵向中芯轴2的压力、当前预应力平衡态纵向中芯轴2的应力长度、纵向中芯轴2的抗压刚度，计算纵向中芯轴2的压缩长度，进而计算纵向中芯轴2的无应力长度。
纵向中芯轴2的无应力长度为：
Figure PCTCN2020072245-appb-000018
中芯轴的当前长度，E jcA jc为第j节段纵向中芯轴的材料弹性模量和截面积，N jc为第j段纵向中芯轴的受压轴力。
纵向中芯轴2的压缩量为：
Figure PCTCN2020072245-appb-000019
其中，
Figure PCTCN2020072245-appb-000020
表示第j节段纵向中芯轴的压缩量，
Figure PCTCN2020072245-appb-000021
步骤106计算受压环31和32的受力和径向变形
根据纵向拉杆11和12的张力、当前预应力平衡态受压环31和32的半径和几何关系，计算受压环31和32的轴压力和径向变形。
受压环的受力N i为：
N i＝t isina i-t i-1sina i-1      公式(9)
其中，N i表示第i个受压环的受力；
如图5所示，在本实施例中，头部和尾部各有2个受压环，计算受压环的受力如 下：
N 1f＝t 1fcos a 1f      公式(10)
N 1r＝t 1rcos a 1r       公式(11)
N 2f＝t 2fsina 2f-t 1fsina 1f       公式(12)
N 2r＝t 2rsina 2r-t 1rsina 1r       公式(13)
一个受压环沿圆周有n个纵向拉杆，则受压环的轴压力：
N ci＝N i×n/2π       公式(14)
按照对称方法，可计算前向头部和后向尾部的各受压环的轴压力。
受压环31和32的变形为受压环半径变化：
Figure PCTCN2020072245-appb-000022
其中，
Figure PCTCN2020072245-appb-000023
为第i个受压环平衡形态当前半径，
Figure PCTCN2020072245-appb-000024
为第i个受压环无应力状态半径。
步骤107计算各构件的结构尺寸，包括定位长度、制作长度
根据预应力平衡形态纵向拉杆11和12应力长度、纵向中芯轴2的应力长度，以及纵向拉杆11和12的无应力长度、纵向中芯轴2的无应力长度，考虑张拉导入方法和安装集成无应力几何一致性，计算纵向拉杆11和12、纵向中芯轴2的定位长度和制作长度。
纵向中芯轴2的最少调节长度：
Figure PCTCN2020072245-appb-000025
其中，ΔL jc为第j节段纵向受压构件最少调节长度。
纵向中芯轴2以及受压环31和32的压缩量计算，可采用结构分析软件进行数值分析计算。
纵向中芯轴2以及受压环31和32的稳定性分析，可采用结构分析软件进行数值非线性稳定分析计算。
纵向拉杆11和12在受拉载荷阶段处于线弹性，不考虑材料非线性和破坏问题；纵向中芯轴2以及受压环31和32在受压阶段处于线弹性，计算压缩长度需要考虑几何非线性和稳定性。
本实施例中的结构尺寸：飞艇长度L a、最大半径R max或直径D、受压环半径
Figure PCTCN2020072245-appb-000026
受压环纵向拉杆数量n、节段数、纵向受压构件长度
Figure PCTCN2020072245-appb-000027
纵向拉杆长度
Figure PCTCN2020072245-appb-000028
材料及工艺选择(纵向拉杆、纵向中芯轴、受压环采用CFRP制成)，以及临界弯矩(环境载荷与飞行性能能、结构性能要求)、预应力值(纵向拉杆张力t j、纵向受压构件压力N jc、受压环轴压力N ci)可针对具体工程应用确定。
以上详细描述了本发明的较佳具体实施例。应当理解，本领域的普通技术无需创造性劳动就可以根据本发明的构思作出诸多修改和变化。因此，凡本技术领域中技术 人员依本发明的构思在现有技术的基础上通过逻辑分析、推理或者有限的实验可以得到的技术方案，皆应在由权利要求书所确定的保护范围内。

Claims (10)

  1. 一种张拉整体结构平衡形态确定方法，其特征在于，包括以下步骤：
    确定所述张拉整体结构承受的临界弯矩；
    计算纵向拉杆的张力；
    计算纵向受压构件的压力；
    计算所述纵向拉杆的拉伸长度和无应力长度；
    计算所述纵向受压构件的压缩长度和无应力长度；
    计算环向受压构件的受力和径向变形；
    计算所述纵向拉杆、所述纵向受压构件的定位长度和制作长度。
  2. 如权利要求1所述的张拉整体结构平衡形态确定方法，其特征在于，所述张拉整体结构用作飞艇龙骨体系，所述临界弯矩根据气动载荷、静力矩、浮力梯度矩确定。
  3. 如权利要求1所述的张拉整体结构平衡形态确定方法，其特征在于，计算所述纵向拉杆的张力，包括如下步骤：
    计算第一纵向拉杆的张力，其中所述第一纵向拉杆为抵抗矩最大截面的纵向拉杆；
    依次递推计算其他所述纵向拉杆的张力。
  4. 如权利要求3所述的张拉整体结构平衡形态确定方法，其特征在于，按照对称方法，分别计算靠近所述张拉整体结构的第一端的所述纵向拉杆的张力和靠近所述张拉整体结构的第二端的所述纵向拉杆张力。
  5. 如权利要求1所述的张拉整体结构平衡形态确定方法，其特征在于，所述纵向拉杆的无应力长度和拉伸量的计算如下：
    Figure PCTCN2020072245-appb-100001
    Figure PCTCN2020072245-appb-100002
    其中，
    Figure PCTCN2020072245-appb-100003
    为第j节段所述纵向拉杆的无应力长度，
    Figure PCTCN2020072245-appb-100004
    为第j节段预应力平衡形态所述纵向拉杆的当前长度，E jA j为第j节段所述纵向拉杆的材料弹性模量和截面积，t j为第j段所述纵向拉杆的张力，
    Figure PCTCN2020072245-appb-100005
    为第j节段所述纵向拉杆的拉伸量。
  6. 如权利要求1所述的张拉整体结构平衡形态确定方法，其特征在于，所述纵向受压构件的无应力长度和压缩量的计算如下：
    Figure PCTCN2020072245-appb-100006
    Figure PCTCN2020072245-appb-100007
    其中，
    Figure PCTCN2020072245-appb-100008
    为第j节段所述纵向受压构件的无应力长度，
    Figure PCTCN2020072245-appb-100009
    为第j节段预应力平衡形态所述纵向受压构件的当前长度，E jcA jc为第j节段所述纵向受压构件的材料弹性模量和截面积，N jc为第j段所述纵向受压构件的受压轴力，
    Figure PCTCN2020072245-appb-100010
    表示第j阶段所述纵向受压构件的压缩量。
  7. 如权利要求1所述的张拉整体结构平衡形态确定方法，其特征在于，所述环向受压构件的受力计算如下：
    N i＝t isina i-t i-1sina i-1  公式(9)N ci＝N i×n/2π  公式(14)
    其中，N i表示第i个所述环向受压构件的受力，N ci表示第i个所述环向受压构件的轴压力，t i表示第i个所述纵向拉杆的张力，a i表示第i段所述纵向拉杆与第i-1段所述纵向拉杆的偏角，n表示所述环向受压构件沿圆周的所述纵向拉杆数量。
  8. 如权利要求7所述的张拉整体结构平衡形态确定方法，其特征在于，所述环向受压构件的受力计算按照对称方法，分别计算所述张拉整体结构的第一端的各所述环向受压构件和所述张拉整体结构的第二端的各所述环向受压构件的受力。
  9. 如权利要求1所述的张拉整体结构平衡形态确定方法，其特征在于，计算所述纵向受压构件的定位长度和制作长度中，所述纵向受压构件的最少调节长度满足：
    Figure PCTCN2020072245-appb-100011
    其中，ΔL jc表示第j阶段所述纵向受压构件的最少调节长度，
    Figure PCTCN2020072245-appb-100012
    表示第j阶段所述纵向受压构件的压缩量，
    Figure PCTCN2020072245-appb-100013
    为第j节段所述纵向拉杆的拉伸量。
  10. 如权利要求1所述的张拉整体结构平衡形态确定方法，其特征在于，所述纵向拉杆、所述纵向受压构件、所述环向受压构件由碳纤维复合材料制成。
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