Isotropic material topology optimization method based on second-order cone programming

Abstract

The invention discloses an isotropic material topology optimization method based on second-order cone programming, and the method comprises the steps of carrying out the singular value decomposition on a unit stiffness matrix through taking the Young modulus E and the Poisson's ratio v of an isotropic material as the design variables, and building a novel decomposition representation form of the stiffness matrix; mapping the original design variables (E, v) into a group of new design variables (P, Q) through a bijection function, converting the original topological optimization problem into asecond-order cone programming problem with the (P, Q) as the design variables to thereby obtain a globally optimal (P, Q) solution, and obtaining the corresponding optimal Young's modulus and Poisson's ratio through the bijection function; and for any given target material type, carrying out hierarchical clustering on the continuous solution in (P, Q) space, so that a high-fidelity discrete solution is obtained. According to the method disclosed by the invention, the topological optimization problem of the free isotropic material is converted into the second-order cone programming problem, sothat the optimal solution of the problem can be theoretically ensured to be solved, and the high-fidelity discrete solution under any specified material type and quantity can be obtained.

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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