基于变密度法的多材料与结构一体拓扑优化研究

Integrated topology optimization of materials andstructures based on variable density method

针对多材料连续体结构拓扑优化问题,基于3D打印技术的发展,将材料可由多种不同材料按任意比例混合组成的技术应用于多材料拓扑优化问题中。在变密度法结构拓扑优化方法基础上,提出了一种双材料混合结构拓扑优化模型及其计算方法;在该模型中以单元密度作为设计变量,同时增加单元中两种材料混合比例为设计变量;最后通过两个算例对所提出方法的有效性进行了验证。研究结果表明:采用该方法进行结构拓扑优化的同时,可以得到两种材料的混合比例,实现基于各向同性固体材料插值模型(SIMP)的多材料与结构一体拓扑优化。

Aiming at topology optimization of multi-material continuum structures,based on the development of 3D printing technology,the technology of material made up of a variety of different materials mixed in any proportion was investigated.Based on the topological optimization method of variable density method,a topological optimization model and its calculation method for two-material hybrid structure was proposed.In this model,the elements densities were used as the design variables,and the mixing ratios of two materials in the elements were added as the design variables.The developed method was verified by two examples.The results indicate that this method can optimize the structure topology and obtain the mixture ratios of two materials,so as to realize the material and structure integrated topology optimization based on the interpolation model for solid isotropic material with penalization.