Geometric analysis method based functionally gradient material part modeling method

A technology of functionally graded materials and modeling methods, applied in special data processing applications, instruments, electrical digital data processing, etc., can solve problems such as low efficiency, and achieve the effect of improving computing efficiency, eliminating node interpolation, and strong adaptability

Active Publication Date: 2017-05-17
NORTHWESTERN POLYTECHNICAL UNIV
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Problems solved by technology

[0003] In order to overcome the inefficiency of existing functionally graded material modeling methods, the

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  • Geometric analysis method based functionally gradient material part modeling method
  • Geometric analysis method based functionally gradient material part modeling method
  • Geometric analysis method based functionally gradient material part modeling method

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Embodiment Construction

[0034] The specific steps of the functionally graded material part modeling method based on the isogeometric analysis method of the present invention are as follows:

[0035] 1. Establish a mathematical model of material distribution inside functionally graded material parts.

[0036] Taking the volume fraction f of each component material phase of the functionally graded material as the design variable, the material distribution state inside the part can be abstracted into the following mathematical model:

[0037]

[0038] Among them, A is the Laplacian differential operator matrix, f=[f 1 ,f 2 … f N ] is the corresponding volume fraction of N kinds of materials that make up functionally graded material parts, b=[b 1 ,b 2 …b N ] is the adjustment factor for the designer to control the material distribution inside the part, f 0 Represents the known material composition information at the boundary, Ω refers to the geometric space of the part, Refers to the boundary ...

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Abstract

The invention discloses a geometric analysis method based functionally gradient material part modeling method and aims to solve the technical problem of low efficiency of an existing functionally gradient material part modeling method. According to the technical scheme, the method includes: adopting a Poisson equation for precisely describing part internal material distribution; adopting a tensor product NUPBS parameter entity for coupling expression of functionally gradient material part geometry and materials; adopting material information appointed by a designer as boundary conditions; solving the Poisson equation according to an isogeometric analysis algorithm to finally realize functionally gradient material modeling. Since the Poisson equation is a partial differential equation and a computational domain of the Poisson equation can be any complicated geometric spaces, high adaptability is realized; part geometric expression and material space calculation can be brought into a unified framework according to the isogeometric analysis algorithm, so that procedures of node interpolation, model conversion and the like are avoided, and material space calculation efficiency is improved.

Description

technical field [0001] The invention relates to a modeling method of functionally graded materials, in particular to a modeling method of functionally graded material parts based on an isogeometric analysis method. Background technique [0002] The literature "Functional Gradient Material Modeling Method Based on the Idea of ​​Mapping from Material Space to Geometric Space, Computer Integrated Manufacturing System, 2009, Vol31(8), p1864-1869" aims at functionally graded material parts with complex geometry and material distribution. A modeling idea for mapping from material space to geometric space. This method first defines the gradient material space, and then, given the mapping function from the material space to the geometric space, determines the geometric space corresponding to the given material component value through the material component value and the corresponding mapping function. Then use the interpolation algorithm to calculate the material information of oth...

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/20
Inventor 杜珂万能段永吉
Owner NORTHWESTERN POLYTECHNICAL UNIV
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