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Beam element deformation decomposition method based on orthogonal decomposition theory

A technology of orthogonal decomposition and deformation decomposition, applied in the field of mechanical analysis

Active Publication Date: 2020-07-03
ZHENGZHOU UNIV
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  • Application Information

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Problems solved by technology

At present, the deformation decomposition method of beam elements based on the orthogonal decomposition theory has not been reported yet.

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  • Beam element deformation decomposition method based on orthogonal decomposition theory
  • Beam element deformation decomposition method based on orthogonal decomposition theory
  • Beam element deformation decomposition method based on orthogonal decomposition theory

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Embodiment 1

[0153] Such as Figure 19 As shown, taking the three-story three-span frame structure as an example, the span in the x direction is 6.0m, the span in the y direction is 6.0m, the floor height of the ground floor is 4.5m, and the floor height of the second and third floors is 3.0m. is 0.5m×0.5m, the thickness of the floor is 0.1m, and the modulus of elasticity is 3.2×10 4 N / mm 2 , Poisson's ratio is 0.2, and the density of reinforced concrete is 2500kg / m 3 .

[0154] Uniformly distributed loads are applied in the x and y directions, and the basis vectors of the basic displacement and basic deformation of the beam-forming unit are constructed using the orthogonal decomposition theory, and the complete coordinate basis matrix U of the beam unit and the nodal displacement vector d of the No. 1 beam unit are obtained e for: d e =(6.5477E-01, 8.3658E-01, -3.4239E-02, 1.3429E-04, -4.0308E-05, 4.1888E-07, 6.5405E-01, 8.3703E-01, 1.9997E-02, - 1.3452E-04, -4.4904E-05, 3.2666E-07)....

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Abstract

The invention belongs to the technical field of mechanical analysis, and discloses a beam element deformation decomposition method based on an orthogonal decomposition theory, which comprises the following steps of: constructing space deformation of a beam element under a space rectangular coordinate system, and constructing basic displacement of the beam element and a basic vector of the basic deformation by adopting the orthogonal decomposition theory so as to obtain a complete coordinate basis matrix of the beam element; establishing a three-dimensional space structure model, dividing the structure by adopting a beam unit to obtain a node coordinate displacement vector of the beam unit after any displacement and deformation are generated under any load working condition, and projectingthe node coordinate displacement vector to the complete coordinate basis matrix of the beam unit to obtain a projection coefficient vector of the beam unit; and obtaining basic displacement information and basic deformation information of the beam unit according to the projection coefficient vector of the beam unit, judging main displacement or deformation and secondary displacement or deformationof the beam unit, and so on, thereby realizing deformation decomposition and vibration mode identification of all the beam units in the space structure.

Description

technical field [0001] The invention belongs to the technical field of mechanical analysis, and relates to a beam element deformation decomposition method based on orthogonal decomposition theory. Background technique [0002] The beam element has been widely used in engineering analysis and design because of its advantages of few degrees of freedom and simple modeling. The current structural design method is to design separately for its macroscopic deformation, such as bending resistance, shear resistance, torsion resistance, etc. How to effectively identify the basic deformation types of the beam-column structure is of great significance for the performance analysis and optimal design of the structure. [0003] At present, the data given by the beam element analysis results based on finite elements are all microscopic information, such as stress and strain, while the beam-column structure undergoes comprehensive deformation under external effects, and a single basic deform...

Claims

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Application Information

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IPC IPC(8): G06F30/23G06F30/17G06F119/14
CPCY02T90/00
Inventor 王东炜梁开轩孙攀旭吴垒赵瑞青刘玉森刘雨桐
Owner ZHENGZHOU UNIV
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