Structure topology optimization technology based on meshless EFGM and isogeometric analysis coupling method

Abstract

The invention discloses a structure topology optimization technology based on a meshless EFGM and isogeometric analysis coupling method, which establishes an EFGM-IGA coupling total stiffness matrix by using shape function consistency, and comprises the following steps: (1) modeling according to an isogeometric analysis method to obtain discrete point information; (2) calculating a shape function of an EFGM-IGA coupling method according to a consistency condition, a meshless EFGM shape function and an IGA primary function; (3) solving the relative density of each discrete point according to an SIMP material interpolation model; (4) searching all Gaussian points in the design domain and calculating the relative density, the geometric matrix and the EFGM-IGA coupling sub-stiffness matrix of the Gaussian points; (5) assembling an EFGM-IGA coupling total stiffness matrix; and (6) establishing a topological optimization mathematical model, and programming and solving by using an OC method. According to the invention, the structure topology optimization is performed based on the meshless EFGM and isogeometric analysis coupling method, the result is accurate, the convergence is stable, and the calculation efficiency is high.

Description

technical field [0001] The invention belongs to the field of optimal design in computer-aided engineering, in particular to a structural topology based on the coupling method of Element-free Galerkin Method (EFGM) and Iso-Geometric Analysis (IGA) optimization technology. Background technique [0002] The meshless method is a numerical calculation method that uses randomly distributed nodes to construct interpolation functions and discretize the control equations to simulate the physical fields of various complex shapes and structures; the main advantage of the meshless method is to discretize the entire design domain into field nodes The formal representation of the shape function does not need to consider the grid, which can avoid the calculation non-convergence caused by grid distortion or distortion, and can effectively suppress the numerical instability such as grid dependence and checkerboard in topology optimization. At the same time, when higher calculation accuracy ...

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Problems solved by technology

[0005] In order to solve the low calculation efficiency caused by only using meshless EFGM for structural topology optimization and the grid dependence problem caused by only relying on IGA method for structural topology optimization, the present invention proposes a method based on meshless EFGM and isogeometric Structural topology optimization technology of the analytical coupling method divides the initial design domain into two design domains: meshless EFGM design domain and isogeometric analysis design domain, and constructs meshless EFGM area, isogeometric analysis area, and EFGM-IGA coupling area Three calculation areas; according to the isotropic material penalty model (Solid Isotropic Material with Penalization Model, SIMP) in the variable density method, a hypothetical material with a variable relative density between 0 and 1 is introduced; for the convenience of description, no The nodes in the grid EFGM area, the control points in the isogeometric analysis area, and the nodes / control points in the EFGM-IGA coupling area are collectively referred to as discrete points in the design domain; the relative density of the discrete points is selected as the design variable, and the relative density field is constructed , taking the minimum structural flexibility as the objective function of topology optimization, and taking the structural volume as the constraint condition, a structural topology optimization mathematical model based on meshless EFGM and isogeometric analysis coupling method is established, and a computer program is written according to the coupling algorithm and optimization method to obtain Optimal topology under different loads and constraints

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