三维弹性静力问题的无网格局部Petrov-Galerkin法  

Meshless Local Petrov-Galerkin Method in Three Dimensional Elasto-statics

作　　者：龙述尧[1] 姜琛[1] 郑娟[1] 

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2013年第12期55-61,共7页Journal of Hunan University:Natural Sciences

基　　金：汽车先进设计和制造技术国家重点实验室建设基金资助项目(60870003);国家自然科学基金资助项目(11372106);国家青年自然科学基金资助项目(11202075)

摘　　要：将二维平面问题的无网格局部Petrov-Galerkin法拓展到三维的相应理论中,编制了该法相应的三维Fortran程序.分析了均匀受拉立方体和悬臂梁两个经典算例,将所得结果与有限元法和解析解对比.结果表明了无网格局部Petrov-Galerkin法在解决三维弹性静力问题时的可行性和有效性,相对于有限元方法在位移解和应力解上也具有更好的精度.The two dimensional Meshless local Petrov-Galerkin method （MLPG） was expanded to three dimensional theory,and its codes were programmed in Fortran.Then,two classical numerical examples,the cube under uniform tension and the 3D cantilever beam,were calculated,and the results of MLPG3D were compared with the results of analytic theory and three dimensional finite element method （FEM）.The results have shown the feasibility and effectiveness of MLPG for solving three dimensional elasto-static problems,and the precision of the results is better than those of FEM.

关 键 词：无网格法 局部Petrov-Galerkin法 移动最小二乘 三维弹性静力学问题 

分 类 号：TU470.3[建筑科学—结构工程]