基于等效静态载荷法的非线性动态拓扑优化

Nonlinear dynamic topology optimization on equivalent static loads method

等效静态载荷法是目前解决动态拓扑优化问题的一种有效方法,但是由于未考虑塑性变形中应力应变关系的时效性,会导致等效载荷偏大和载荷方向偏差,因此无法有效处理材料的非线性问题。据此,提出一种基于模量比率因子的等效静态载荷计算方法。首先,根据结构应力、应变和杨氏模量之间的函数关系,计算各时刻的计算杨氏模量;然后,得到各时刻的模量比率因子,根据位移等效原则计算修正等效静态载荷,进而进行多工况静态拓扑优化,并更新设计变量再次进行动力学分析,重复直至收敛。数值算例表明,修正后的等效静态载荷法能够解决弹塑性材料的非线性问题,在提高等效精度的同时拓展了在非线性材料方面的应用边界。工程算例表明,在相同约束下,采用基于模量比率因子的等效静态载荷法在轻量化的同时能得到更小的塑性应变。

Equivalent static loads method (ESLM)is an effective method to solve dynamic topology optimization problems.However,when solving a dynamic topology optimization problem of elastoplastic material,plastic deformations,occurring in different directions at each moment,lead to larger equivalent static loads and direction deviations.Therefore,an ESLM based on modulus ratio coefficient (MRC-ESLM)is proposed.Based on relationships between stress,strain and Young’s modulus,calculated Young’s modulus is equated at each moment firstly.Then the modulus ratio coefficients are derived,and equivalent static loads are amended based on equivalent displacements.Static multi-condition topology optimization is performed,and then a dynamic analysis is performed again.The two cycles are repeated until convergence criterion is satisfied.Numerical examples show the modified ESLM can solve nonlinear problems of elastoplastic materials effectively,and improve accuracy,which means the application range of ESLM is expended.The numerical example of an automobile knee buffer shows that,under the same constraints,smaller plastic strain is obtained by MRC-ESLM compared with that of ESLM.