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A membrane structure deformation decomposition method based on an orthogonal theory

A technology of deformation decomposition and orthogonal theory, applied in the field of mechanical analysis, it can solve the problems that cannot be directly separated, not found, and the membrane structure cannot bear out-of-plane bending moments.

Active Publication Date: 2019-05-28
ZHENGZHOU UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0003] The membrane structure cannot bear the out-of-plane bending moment, so conventional mechanical methods cannot effectively identify its deformation. At the same time, the membrane structure shows a comprehensive deformation form under external effects, and the information of a single basic deformation is included in the comprehensive deformation, which cannot was directly separated
At present, the deformation decomposition method of membrane structure based on orthogonal theory has not been found

Method used

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  • A membrane structure deformation decomposition method based on an orthogonal theory
  • A membrane structure deformation decomposition method based on an orthogonal theory
  • A membrane structure deformation decomposition method based on an orthogonal theory

Examples

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Embodiment 3

[0156] Example 3: Application Example (1)

[0157] Such as Figure 16 As shown, take the four-sided fixed-supported tensile membrane structure as an example, in which the length and width of the membrane structure are 0.4m, the thickness of the membrane is 0.5mm, the length and width directions are the X and Y axes, and the thickness direction is the Z axis; The elastic modulus of the membrane structure is 150MPa, the Poisson's ratio is 0.38, and the initial prestress applied to the membrane surface is 2Mpa;

[0158] Apply a vertical uniform load on the surface of the membrane structure to obtain the nodal displacement vector d of the No. 1 four-node square element e for:

[0159] d e = (0.0298 0.0456 -95.1160 0.0258 0.0412 -74.5370 0.0286 0.0323 -80.1270 0.0372 0.0375 -102.3500)×10 -5 m

[0160] Carry out the rigid-flexible separation of the element rigid body displacement and basic deformation on formula (3.2); the projection coefficient vector p is transformed into the following fo...

Embodiment 4

[0174] Example 4: Application Example (2)

[0175] Such as Figure 17 As shown, take the four-sided fixed hard film structure as an example, in which the length and width of the film structure are 0.4m, the thickness of the film is 2mm, the length and width directions are the X and Y axes, and the thickness direction is the Z axis; the film structure The modulus of elasticity is 300,000 MPa, and the Poisson's ratio is 0.3.

[0176] A vertical uniform load is applied to the surface of the membrane structure, where the nodal displacement vector d of the No. 2 four-node square element e for:

[0177] d e =(-0.0121 -0.0121 -0.6779 -0.0109 -0.0038 -0.2189 -0.0036 -0.0036-0.0717 -0.0038 -0.0109 -0.2189)×10 -3 m

[0178] The deformation decomposition results of the comprehensive deformation on the 12 complete orthogonal mechanical bases are shown in Table 2 (excluding the 6 basic rigid body displacements).

[0179] Table 2 Deformation decomposition results of No. 2 four-node square element

[...

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Abstract

The invention provides a membrane structure deformation decomposition method based on an orthogonal theory, which comprises the following steps of 1, constructing spatial deformation of a four-node square unit, and obtaining a complete orthogonal coordinate basis matrix P; 2, dividing the membrane structure by adopting a four-node square unit, and forming a node coordinate displacement deformationvector d e of the four-node square unit; 3, obtaining a projection coefficient vector p of a node coordinate displacement deformation vector d e projected to the complete orthogonal coordinate basismatrix P; and 4, judging the main deformation of the four-node square unit according to the size of the projection coefficient vector p so as to carry out deformation decomposition on the membrane structure system. According to the method, the stress deformation conditions of the whole and local parts of the membrane structure can be reflected more accurately and more perfectly.

Description

Technical field [0001] The invention belongs to the technical field of mechanical analysis, and particularly relates to a membrane structure deformation decomposition method based on an orthogonal theory. Background technique [0002] Membrane structure has been widely used in engineering structure due to its advantages of light weight, easy installation, energy saving and environmental protection. Membrane structure is a spatial overall tensioning system formed by different types of high-strength films and auxiliary structures by applying prestress in a certain way, and has sufficient rigidity to resist external loads. There are two common failure types of membrane structure: 1) The in-plane deformation of the membrane structure reaches the limit failure state due to the dislocation of the support and the excessive air pressure, resulting in the tensile and shear damage of the membrane structure; 2) The out-of-plane non-uniform load will It can cause depression of the membrane ...

Claims

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Application Information

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IPC IPC(8): G06F17/50
Inventor 王东炜孙攀旭梁开轩刘玉森刘雨桐李大望
Owner ZHENGZHOU UNIV
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