一种基于修正SSPH近似的无网格局部Petrov-Galerkin法  

A MESHLESS LOCAL PETROV-GALERKIN METHOD BASED ON MODIFID SSPH APPROXIMATION METHOD

作　　者：肖毅华[1] 胡德安[1] 韩旭[1] 龙述尧[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：《工程力学》2012年第1期32-38,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10902038;10972075);湖南大学汽车车身先进设计制造国家重点实验室自主课题项目(60870003);教育部长江学者与创新团队发展计划项目(531105050037)

摘　　要：首先采用奇异权函数对对称光滑粒子流体动力学(SSPH)近似进行了修正,使其构造的形函数近似满足函数性质,方便无网格法中本质边界条件施加;然后应用修正的SSPH近似法构造试函数,结合以Heaviside函数为权函数的局部弱形式,提出了一种新的求解弹性静力问题的无网格局部Petrov-Galerkin法;最后应用新的无网格法计算了一系列数值算例,结果表明:该方法具有良好的精度和收敛性。In this paper, the singular weight function is introduced to modify the symmetric smoomeu hydrodynamics （SSPH） approximation method firstly, which makes the shape functions constructed satisfy the Dirac delta function properties approximatively and the enforcement of essential boundary conditions become easier. Then, a new meshless Petrov-Galerkin method is proposed for solving elasticity problems by using the modified SSPH approximation method to construct trial function in local weak form with Heaviside weight function. Finally, several plane problems are calculated with the presented method. Numerical results demonstrate that the new method can achieve quite good accuracy and convergence.

关 键 词：弹性力学 无网格局部Petrov-Galerkin法 SSPH近似 奇异权函数 Heaviside函数 

分 类 号：O343[理学—固体力学]