Topology optimization method for isotropic materials based on second-order cone programming

Abstract

The invention discloses a topology optimization method for isotropic materials based on second-order cone programming. The method takes Young's modulus E and Poisson's ratio v of isotropic materials as design variables, and performs singular value decomposition on the unit stiffness matrix. Construct a new decomposition representation of the stiffness matrix; and map the original design variables (E,v) to a new set of design variables (P,Q) through a bijective function, take (P,Q) as the design variables, and convert the original The topology optimization problem is transformed into a second-order cone programming problem, so as to obtain the global optimal (P, Q) solution, and obtain the corresponding optimal Young's modulus and Poisson's ratio through the bijective function; for any given target material category, the continuous solution is hierarchically clustered in (P,Q) space to obtain a high-fidelity discrete solution. By transforming the topology optimization problem of free isotropic materials into a second-order cone programming problem, the method of the invention can theoretically ensure the optimal solution of the problem and can obtain high-fidelity discrete solutions under any specified number of materials.

Description

technical field [0001] The invention relates to the technical field of structure optimization, in particular to a topology optimization method for isotropic materials based on second-order cone programming. Background technique [0002] In recent years, with the development of computer technology, more and more engineering and product design fields use topology optimization methods to obtain structures with ideal and optimal performance. Topology optimization aims to find the best solid distribution in the field of discrete design to improve structural performance. After decades of tremendous development, topology optimization has designed a variety of new structures with extreme properties and has been widely used in industry . [0003] In traditional topology optimization studies, the Young's modulus of each design element is directly or implicitly used as a design variable, ignoring other important material parameters such as Poisson's ratio or general anisotropy. There...

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Problems solved by technology

For the discrete dimensionality reduction problem of topology optimization continuous solution, there is still no good solution, and most of the existing methods cannot reduce the types of materials while maintaining structural properties

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