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Phase-field based topology optimization with Drucker-Prager yield stress constraints[J].计算力学学报,2020,37(6):670~676

Phase-field based topology optimization with Drucker-Prager yield stress constraints
Phase-field based topology optimization with Drucker-Prager yield stress constraints

DOI：10.7511/jslx20191119002

 作者 单位 E-mail 张晓鹏 大连理工大学 工程力学系, 工业装备结构分析国家重点实验室, 大连 116024 zhangxiaopeng@dlut.edu.cn 康柯 大连理工大学 工程力学系, 工业装备结构分析国家重点实验室, 大连 116024 杨东生 中国运载火箭技术研究院, 北京 100076

运用了基于相场描述的拓扑优化方法，来寻找在拉伸和压缩中表现出不对称强度行为的连续体结构的最优布局。依据Drucker-Prager屈服准则和幂率插值方案，优化问题可以描述为在局部应力约束下的最小化结构的体积。用qp放松法来解决应力约束的奇异性，并采用基于P-norm函数的聚合方法对应力约束进行凝聚，该方法实现了约束个数的降低，同时引入了稳定转化法来处理大量的局部应力约束和高度非线性的应力行为，以修正应力，提高优化收敛的稳定性。在优化问题求解时，使用拉格朗日乘子法对目标函数和应力约束进行处理。利用伴随变量法进行灵敏度分析，并通过求解Allen-Cahn方程更新相场函数设计变量。数值算例证明了该优化模型和相应数值技术的有效性，相关算例还揭示了考虑拉压不同强度和考虑同拉压强度约束时得到的结构优化拓扑构型具有显著的差异。

Phase-field based topology optimization method is employed for finding the optimal layout of continuum structures exhibiting asymmetric strength behaviors in tension and compression.According to the Drucker-Prager yield criterion and the power rate interpolation scheme,the topology optimization problem is formulated to minimize the total material volume under the stress constraints.The qp relaxation method is used to solve the singularity problem of local stress constraints,and the stress constraints are condensed by the P-norm function.This method realizes the reduction of the number of the stress constraints.The STM(stability transformation method)is adopted to correct the highly nonlinear stress behavior and improve the convergence stability of optimization process.In the real application,the objective function and stress constraint are processed using the Lagrange multiplier method.Sensitivity analysis is performed with the adjoint variable method,and the design variables are updated by solving the Allen-Cahn equation.Numerical examples demonstrate the effectiveness of the proposed optimization model.The numerical examples also show that the design obtained with topology optimization considering Drucker-Prager yield constraints is obviously different from that obtained with topology optimization considering von-Mises strength constraints.