可商业化光滑有限元分析软件的研发

项目名称： 可商业化光滑有限元分析软件的研发

项目编号： No.11472184

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 刘桂荣

作者单位： 太原理工大学

项目金额： 85万元

中文摘要： 近年来，无网格法已引起人们的广泛关注。但由于计算速度的瓶颈，它并没有像FEM那样大规模的商业化。因此将无网格和FEM相结合，刘桂荣提出了光滑有限元法S-FEM，它兼有无网格法的健壮性和FEM的高效性等优点。而且S-FEM能有效解决FEM不能解决的许多复杂问题，同时也证明了FEM是S-FEM的一个特例。由于S-FEM使用弱弱形式，较FEM等使用弱形式方法具有突出优势：①S-FEM模型比FEM 模型软，因此可给出问题的上界解和超精确解；②S-FEM采用能自动生成的T-mesh，从而可用于自动建模和自适应分析；③S-FEM对网格质量要求很低；④S-FEM的计算效率比FEM高得多。本项目拟将开发一套可商业化的S-FEM软件来解决科学和工程中的固体力学和结构力学问题，包括静动态、非线性、大变形和断裂问题等。希望通过该软件的开发改变中国在工程分析软件上的落后局面，占领下一代工程软件开发的至高点。

中文关键词： 软件开发；光滑有限元；建模和模拟；结构分析软件；有限元

英文摘要： The meshfree methods (championed by Belytchko, G.R. Liu and many others) have attracted attentions in the area of computational methods in the past 20 years, due to the excellent features of robustness. The meshfree methods have not been widely commercialized due to the bottleneck problem of computation speed, compared to the well-established finite element method (FEM). The recent S-FEM (Smoothed Finite Element Methods)developed by G.R. Liu at el. possesses features of both meshfree (robustness) and FEM (speed), and has been widely applied to solve various complicated problems in science and engineering. With the rapid development of S-FEM and the proven fact the FEM is in theory a special case of S-FEM, it is believed that the S-FEM will be soon in place of the widely used FEM. This project aims to develop a set of commercial S-FEM software package that consists of a number of modules including edge-based S-FEM (ES-FEM), node-based S-FEM (NS-FEM), cell-based S-FEM (CS-FEM), and the combined NS-FEM and FEM modules. It should be capable of solving mechanics problems of solids and structures including statics, dynamics, linear, nonlinear, large deformation and contact problems. It will be fully comparable to the existing commercial software packages in the market in the capability regards. Because the S-FEM is based on the Weakened Weak (W2) formulation, it should be superior to its FEM counterpart in the following aspects: 1) The S-FEM model is proven in theory always softer than the FEM model, and hence can produce upper bound and ultra-accurate solutions; 2) It works well with the T-mesh (Triangle for 2D, Tetrahedron and Triangular-prism for 3D), hence it is ideal for the full-automation in computation and adaptive analysis, and the volumetric locking problems can be conveniently overcome; 3) It does not demand for high quality mesh as its FEM counterpart, and hence facilitate easy local mesh refinements in automatic fashions; 4) The computational efficiency can be up to one order of magnitude higher, due to the ultra-accuracy, simplicity in the formulation and implementation, and much better conditioning in the discretized system equations. Upon successful, the developed S-FEM can strategically change the current under-developed situation in China in terms of engineering software development, and compete with the international major software packages.

英文关键词： Software Development;Smoothed Finite Element Methods;Modeling and Simulation;Structural Analysis Software;Finite Element Method