参数化水平集拓扑优化解决了传统水平集方法数值计算复杂的问题,由于水平集拓扑优化需要引入更高级别的函数来构建拓扑模型,大部分关于参数化水平集拓扑优化的研究止于二维。文章在二维参数化水平集拓扑优化的基础上拓展到三维,结合点...参数化水平集拓扑优化解决了传统水平集方法数值计算复杂的问题,由于水平集拓扑优化需要引入更高级别的函数来构建拓扑模型,大部分关于参数化水平集拓扑优化的研究止于二维。文章在二维参数化水平集拓扑优化的基础上拓展到三维,结合点云的思想解决了三维拓扑构型的表达问题,并通过悬臂梁、简支梁等典型数值算例验证了算法能解决三维水平集无法引入更高维度函数等问题,亦讨论了引入SIMP(Solid Isotropic Material with Penalization)多材料插值模型的多相材料拓扑优化方法,以供多相材料拓扑优化方面研究进行参考。展开更多
Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A bou...Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A boundary search scheme is proposed for 3D problems, by means of which the load surface can be identified effectively and efficiently, and the difficulties arising in other approaches can be overcome. The load surfaces are made up of the boundaries of finite elements and the loads can be directly applied to corresponding element nodes, which leads to great convenience in the application of this method. Finally, the effectiveness and efficiency of the proposed method is validated by several numerical examples.展开更多
文摘参数化水平集拓扑优化解决了传统水平集方法数值计算复杂的问题,由于水平集拓扑优化需要引入更高级别的函数来构建拓扑模型,大部分关于参数化水平集拓扑优化的研究止于二维。文章在二维参数化水平集拓扑优化的基础上拓展到三维,结合点云的思想解决了三维拓扑构型的表达问题,并通过悬臂梁、简支梁等典型数值算例验证了算法能解决三维水平集无法引入更高维度函数等问题,亦讨论了引入SIMP(Solid Isotropic Material with Penalization)多材料插值模型的多相材料拓扑优化方法,以供多相材料拓扑优化方面研究进行参考。
基金supported by the National Natural Science Foundation of China (90816025, 10721062)National Basic Research Program of China (2006CB601205)Program for New Century Excellent Talents in University of the Ministry of Education of China (NCET-04-0272)
文摘Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A boundary search scheme is proposed for 3D problems, by means of which the load surface can be identified effectively and efficiently, and the difficulties arising in other approaches can be overcome. The load surfaces are made up of the boundaries of finite elements and the loads can be directly applied to corresponding element nodes, which leads to great convenience in the application of this method. Finally, the effectiveness and efficiency of the proposed method is validated by several numerical examples.
