PolyStress: a Matlab implementation for local stress-constrained topology optimization using the augmented Lagrangian method
PolyStress: a Matlab implementation for local stress-constrained topology optimization using the augmented Lagrangian method
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DOI：
10.1007/s00158-020-02760-8
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发表时间：
2021-02-10
影响因子：
3.9
通讯作者：
Paulino, Glaucio H.
中科院分区：
文献类型：
--
作者：
Giraldo-Londono, Oliver;Paulino, Glaucio H.
我们提出了PolyStress，一个Matlab实现的拓扑优化与局部应力约束，考虑线性和材料非线性问题。PolyStress的实现是建立在PolyTop的基础上的，PolyTop是一种用于非结构化多边形有限元柔度最小化的教育代码。为了解决非线性弹性问题，我们实现了一个Newton-Raphson格式，它可以处理具有给定应变能密度函数的非线性材料模型。为了解决应力约束问题，我们采用了一种基于增广拉格朗日方法的方案，该方法将问题与应力的局部定义相一致，而不采用传统的约束聚合技术。本文讨论了应力约束问题的几个理论方面，包括本文实施的增广拉格朗日为基础的方法的细节。此外，本文还详细介绍了PolyStress的Matlab实现，作为电子学的辅助材料。我们提出了几个数值例子来证明PolyStress解决应力约束拓扑优化问题的能力，并说明其模块化，以适应任何非线性材料模型。六个附录补充了论文。特别是，第一个附录提供了一个基准测试示例库，详细描述了这些示例，可以在本工作范围之外进行探索。
We present PolyStress, a Matlab implementation for topology optimization with local stress constraints considering linear and material nonlinear problems. The implementation of PolyStress is built upon PolyTop, an educational code for compliance minimization on unstructured polygonal finite elements. To solve the nonlinear elasticity problem, we implement a Newton-Raphson scheme, which can handle nonlinear material models with a given strain energy density function. To solve the stress-constrained problem, we adopt a scheme based on the augmented Lagrangian method, which treats the problem consistently with the local definition of stress without employing traditional constraint aggregation techniques. The paper discusses several theoretical aspects of the stress-constrained problem, including details of the augmented Lagrangian-based approach implemented herein. In addition, the paper presents details of the Matlab implementation of PolyStress, which is provided as electronic supplementary material. We present several numerical examples to demonstrate the capabilities of PolyStress to solve stress-constrained topology optimization problems and to illustrate its modularity to accommodate any nonlinear material model. Six appendices supplement the paper. In particular, the first appendix presents a library of benchmark examples, which are described in detail and can be explored beyond the scope of the present work.