基于单胞代理模型的热弹性点阵结构优化方法

Optimization method of thermo-elastic lattice structure based on surrogate models of microstructures

三维点阵材料是一种具有多尺度特性的新型轻质多功能材料,其有千变万化的微结构和高孔隙率,通过设计其细观尺度特征可以获得优良的宏观性能。为了发挥材料与结构的最大设计潜力,提出一种热弹性点阵结构优化方法。在材料细观研究尺度上,实现了三维点阵材料等效热弹性性能预测,利用周期性边界条件下的代表体元法进行数值求解,利用径向基函数代理模型构建细观结构和宏观材料性能的数学关系,并进行了预测误差验证,证明了所提方法具有良好的精确度。在结构宏观研究尺度上,建立了以等效材料填充的结构优化模型,考虑了热力载荷作用,以单胞等效性能代理模型作为材料插值模型,提出最小应变能热弹性点阵结构优化数学模型。在典型三维算例中得到了细观结构变密度分布的优化结果,结构热刚度在一定体积约束下显著提高,证明了所提方法的有效性。

Lattice material is a new type of lightweight and multifunctional material,which has a variety of microstructures and high porosity.Excellent macroscopic properties can be obtained by designing its mesoscale features.To maximize the design potential of materials and structures,an optimization method for the thermo-elastic lattice structure is proposed.As for mesoscale material research,the effective thermo-elastic properties prediction of three-dimensional lattice materials is implemented.Relevant coefficients are solved using the idea of the representative volume method under periodic boundary conditions.Surrogate models are constructed to build the relationship between macroscopic responses and microstructures,and are proved to have good accuracy through error verification tests.As for macroscale material research,a structural optimization model filled with equivalent materials is established.Considering the thermal and mechanical loads,a mathematical model for structural optimization of thermo-elastic lattice structure with minimum strain energy is proposed using the surrogate models of effective properties as the material interpolation schemes.The result of an optimal spatially varying metamaterial is obtained in a typical three-dimensional structure example,and the thermal stiffness of the structure is improved under a certain volume constraint,demonstrating the effectiveness of the optimization method.