【摘要】 提出适用于多目标最优化问题的自适应加权系数算法,将其应用于周期性两相材料微结构拓扑优化。以具有一定体积分数实体材料和对称性的单胞微结构作为优化对象。将单胞经有限元划分,应用均匀化方法计算单胞的等效弹性模量。以材料的等效弹性模量作为目标函数,以单胞各单元的相对密度作为设计变量,并引入SIMP单元刚度插值格式对中间密度单元进行惩罚。在迭代过程中,根据目标函数的变化,自适应调节加权系数,以保证各个分目标在目标函数中的比重。应用自适应加权系数算法,对单胞等效弹性模量设定不同的加权系数组合,得到了不同的单胞微结构拓扑。数值算例验证了所提出的自适应加权系数算法可以有效地求解复合材料微结构多目标拓扑优化问题。更多还原

【Abstract】 An adaptive weighted sum algorithm proposed for multiple objective problems is presented to optimize the topology of the microstructure with periodic two-phase materials.The microstructure of porous composite with a certain volume fraction of solid materials and structural symmetry is studied.By means of the homogenization method and method of moving approximating(MMA),the equivalent elastic module of cell is calculated and maximized, based on the finite element method.The relative density of each element of the cell is defined as the design variable based on the finite element method,with SIMP density-stiffness scheme which has the effect of penalizing to elements with intermediate density.During the process of iteration,the weighing coefficient is adaptively adjusted according to the variety of the objective function.Several microstructure topologies are obtained by the adaptive weighting algorithm with different combinations of equivalent elastic module and weighing coefficients.Numerical results verify the validity of the proposed adaptive weighted sum algorithm in the multiple objective topology design of microstructures.更多还原