大变形结构无网格拓扑优化方法研究

项目名称： 大变形结构无网格拓扑优化方法研究

项目编号： No.11302208

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 李顺利

作者单位： 中国工程物理研究院总体工程研究所

项目金额： 26万元

中文摘要： 在大多数结构拓扑优化问题中都假设线弹性响应，虽然这种假设对于很大一类问题都是有效的，但是对于柔顺机构、吸能减振结构、抗撞性结构等经历大变形的结构不再有效 。有限元法在处理几何非线性问题时可能产生网格畸变现象，将降低计算精度，如果不放松收敛准则甚至可能无法得到收敛解。由于摆脱了网格的限制，在进行大变形分析时，无网格法具有天然的优势，比有限元法具有更好的精度和收敛性。本项目基于无网格自然邻接点Petrov-Galerkin法，系统研究大变形结构的拓扑优化问题。研究解决有限元法在处理这类大变形拓扑优化问题时存在的网格畸变，"不稳定单元"造成的数值不稳定性问题，"棋盘格"现象，局部模态等相关问题。建立精确、高效设计灵敏度分析的无网格数值算法；研究无网格法应用于大变形结构拓扑优化设计的有效性和稳定性。开发适合于大变形连续体结构拓扑优化设计的程序并应用于柔顺机构、吸能减振结构等工程实际的拓扑优化设计。

中文关键词： 无网格法；拓扑优化；大变形；几何非线性；

英文摘要： The linear elastic response is assumed in most structural topology optimization problems. While this assumption is valid for a wide variety of problems, it is not valid for structures undergoing large deformation, such as in the case of compliant mechanism design, energy absorbing structure design and crashworthiness design. There are some difficulties involving mesh distortion or entanglement resulting in unreliable numerical results when dealing with the geometrically nonlinear problems by finite element method (FEM). By virtue of avoiding the dependence of meshes, the meshless method reveals better accuracy and efficiency than the FEM in large deformation analyses. This project researches topology optimization of structures with large deformation based on the meshless natural neighbor Petrov-Galerkin method. We are dedicated to study and resolve the difficulties encountered by FEM in topology optimization of structures with large deformation, such as mesh distortion or entanglement, the numerical instability problems arisen by unstable elements, checkerboard phenomenon, localized modes, etc. The efficient meshless numerical method is proposed for accurate and effective design sensitivity analysis. The validity and stability of the meshless method for topology optimization of structures with large deforma

英文关键词： the meshless method；topology optimization；large deformation；geometrically nonlinear；