Topology optimization based on finite strain plasticity
Topology optimization based on finite strain plasticity
复制标题
DOI：
10.1007/s00158-016-1435-0
复制
发表时间：
2016-04
影响因子：
3.9
通讯作者：
M. Wallin;Viktor Jönsson;Eric Wingren
中科院分区：
文献类型：
--
作者：
M. Wallin;Viktor Jönsson;Eric Wingren
本文将基于无穷小弹塑性的拓扑优化方法推广到有限应变情况。所采用的模型是基于率无关各向同性硬化塑性和分离的弹性变形和塑性变形，使用的变形梯度的乘法分裂。机械平衡法求解使用隐式总拉格朗日公式。使用移动渐近线的方法来解决优化问题，并使用路径相关的伴随策略导出形成凸可分近似所需的灵敏度。使用PDE型滤波器对优化问题进行正则化。一个简单的边界值问题，其中塑性功最大化是用来证明所提出的模型的能力。数值算例表明，有限应变塑性理论可以成功地与拓扑优化相结合。
In this paper infinitesimal elasto-plastic based topology optimization is extended to finite strains. The employed model is based on rate-independent isotropic hardening plasticity and to separate the elastic deformation from the plastic deformation, use is made of the multiplicative split of the deformation gradient. The mechanical balance laws are solved using an implicit total Lagrangian formulation. The optimization problem is solved using the method of moving asymptotes and the sensitivity required to form convex separable approximations is derived using a path-dependent adjoint strategy. The optimization problem is regularized using a PDE-type filter. A simple boundary value problem where the plastic work is maximized is used to demonstrate the capability of the presented model. The numerical examples reveal that finite strain plasticity successfully can be combined with topology optimization.