Progressive structure topological optimization method based on isogeometric analysis

Abstract

The invention belongs to the related technical field of structure optimization design, and discloses a progressive structure topology optimization method based on isogeometric analysis, which comprises the following steps of: (1) setting a design variable as a density value of any point in a design domain, constructing an optimization model, and dividing the design domain to obtain an isogeometric background grid; (2) respectively solving the element stiffness of each type of element by adopting a calculation rule of an extended finite element so as to obtain an overall displacement vector of the structure; (3) calculating to obtain a unit sensitivity value in combination with the set unit artificial density and the overall displacement vector; (4) fitting an NURBS sensitivity field by taking the unit sensitivity value as the unit center point sensitivity and as a sample point; (5) selecting a density threshold to intercept a current NURBS sensitivity field so as to update a design variable; and (6) judging whether the target function converges or not, and if yes, ending topological optimization; otherwise, turning to the step (2). The method is stable, effective and good in applicability.

Description

technical field [0001] The invention belongs to the related technical field of structure optimization design, and more specifically relates to a progressive structure topology optimization method based on isogeometric analysis. Background technique [0002] The isogeometric analysis (Isogeometric analysis) method is based on the isoparametric element idea of ​​the finite element analysis method, and the basis function of the non-uniform rational B-spline (NURBS) used to express the geometric model in the computer-aided geometric design (CAGD) is used as the shape function. Realized the seamless combination of computer-aided design (CAD) and computer-aided engineering (CAE). Because the NURBS basis function can construct any high-order continuous approximation function, it overcomes the disadvantages of traditional finite element analysis methods that usually only have C0 continuity, so that the isogeometric analysis method has the advantage of being convenient for solving hi...

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Problems solved by technology

[0005] Aiming at the above defects or improvement needs of the prior art, the present invention provides a progressive structure optimization method based on isogeometric analysis. The method applies the extended finite element calculation rule, and the structural structure with smooth and clear boundaries under a fixed background grid The mechanical response of the model is solved, which overcomes the defects that the traditional isogeometric topology optimization based on the variable density method is not clear and the two-way progressive optimization method cannot obtain a smooth boundary, and can easily complete the post-processing work of CAD model construction, and The method is stable and effective

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