弹性地基上正交各向异性板的无网格局部Petrov-Galerkin法分析

Analysis for orthotropic plate on elastic foundation by meshless local Petrov-Galerkin(MLPG) method

基于经典板理论和对挠度函数采用移动最小二乘近似函数进行插值,进一步研究无网格局部Petrov-Galerkin(MLPG)方法在弹性地基上正交各向异性板弯曲问题中的应用。分析中,本质边界条件采用罚因子法施加,离散的线性方程从Winkler弹性基支正交各向异性板控制方程的局部积分对称弱形式中得到。通过两个数值算例,表明用MLPG法求解弹性地基上正交各向异性板弯曲具有分析简便和计算精度高等优点。

The meshless local Petrov-Galerkin（MLPG） method applied to the bending problem of orthotropic plate on elastic foundation was investigated. The method was based on classical plate theory and used the moving least-squares approximation to interpolate the deflection function. In the analysis, the essential boundary condition was applied by the penalty method. The discrete linear equation employed a local symmetric weak form of control differential equation of orthotropic plate on the elastic foundation. Two numerical examples illustrated that the meshless local Petrov-Galerkin（MLPG） method was easy to use and with high accuracy for solving the bending problem of orthotropic plate on elastic foundation.