大变形问题分析的局部Petrov-Galerkin法

在微机电系统(MEMS)的建模和模拟研究中,大变形或大移动要充分予以考虑.用有限元法分析这类问题,由于难以避免的网格畸变,使模拟效率精度降低甚至失效,无网格方法(Meshless Method)则能在分析这类问题时显示出明显的优势,无网格局部Petrov-Galerkin(MLPG)法被誉为是一种有发展前景的真正无网格法.本文进一步发展了MLPG法,通过对任意的离散分布节点采用局部径向基函数构造插值形函数和Heaviside权函数,分析方程采用局部加权弱形式离散,建立了变量仅依赖于初始构型的完全Lagrange分析格式,最后用Newton-Raphson法迭代求解.文中分析了悬臂梁典型算例和微机电开关非线性大变形问题,通过与有限元结果的比较,表明本文提出的大变形问题无网格局部Petrov-Galerkin法具有稳定性好及收敛性快等优点.

Meshless local petrov-galerkin method for large deformation analysis

In the modeling and simulation of the micro-electronic mechanical systems (MEMS) devices, the large deformation or the geometrical nonlinearity must be considered. Due to the issue of mesh distortion, the finite element method is ineffective for this large deformation analysis. However the meshless method shows its potential in this area because no mesh is need. In all the existent methods, the local Petrov-Galerkin (MLPG) method is an ideal mesh free methods. In this paper, a local meshless formulation is developed for large deformation analysis. The local radial point interpolation (RPIM) approximation is employed to construct the shape functions based on the arbitrarily distributed field nodes and the Heaviside weight function. The discrete system equation is obtained using the weighted local weak form and based on the total Lagrangian (TL) approach, which refers all variables to the initial configuration. The Newton-Raphson iteration technique is used to get the final results. Examples show the local Petrov-Galerkin method is effective for large deformation analysis.