Stress and strain energy double-constraint topological optimization method based on variable density method

Abstract

The invention discloses a variable density method-based stress and strain energy double-constraint topological optimization method. Based on a variable density method and an SIMP material interpolation model, a finite element method is utilized to calculate the strain energy of a structure and the Mises stress of a unit, the minimal structure volume is taken as an objective function, the structurewhole is taken as a constraint, a P norm method condenses the unit stress of the structure into a global stress constraint; a topological optimization model containing stress and strain energy doubleconstraints is constructed, the sensitivity of an objective function and a constraint function relative to a design variable is calculated, a topological optimization problem is solved by using a moving asymptotic line method, iteration is repeated until a convergence condition is met, and an optimal topological structure is obtained. The stress and strain energy double-constraint topological optimization method is used for topological optimization of the structure, the problem that a topological structure obtained through a traditional topological optimization method cannot meet the strengthor rigidity condition is solved, and the topological structure obtained through topological optimization meets the preset structural static strength and rigidity condition.

Description

technical field [0001] The invention relates to the field of mechanical structure topology optimization, in particular to a topology optimization method based on variable density method with dual constraints of stress and strain energy. Background technique [0002] With the increasing development of science and technology and productivity, the research on structural optimization design has become more and more important. Among them, topology optimization, as a method of mechanical structure optimization design, is generally used in the conceptual design stage of structural design. Compared with size optimization design And size optimization design, topology optimization has a greater impact on the optimization target and has greater economic benefits. It is currently widely used in aerospace engineering, automobile industry and other fields. [0003] In topology optimization, different optimization objective functions and constraint functions can be set to obtain different ...

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Problems solved by technology

[0003] Different optimization objective functions and constraint functions can be set in topology optimization, and different optimization results can be obtained. At present, most topology optimization uses structural stiffness as the objective function and volume as the constraint function to obtain the topology optimization structure. However, From practical engineering considerations, structures that only satisfy the stiffness conditions may not be able to satisfy the strength conditions, and the imposition of volume constraints requires pre-setting the optimized volume value, but this value is not a priori before topology optimization

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