局域载荷作用下梁板问题微分求积法求解模式

Differential Quadrature Modeling for Beams/Plates under Local Loads

摘要: 对于若干典型局域特殊性的问题，微分求积法往往难于得到较好的计算效率和准确度。为了改善微分求积法的求解质量，本文讨论了微分求积法的应用模式，如改进节点分布、采用小波插值以及与势能原理相结合等等。结果表明，经过上述改进，微分求积法的计算收敛性和准确性得到了良好的改善，有助于解决微分求积法在处理局域问题时难收敛、结果不够准确等问题。

Abstract: For several typical local problems, the differential quadrature method is often difficult to get a better computational efficiency and accuracy. The modified models of the differential quadrature method were discussed to improve the quality of solutions of the differential quadrature method, such as, adjustment of the node distribution, adaptation of the wavelet interpolation and combination with a potential energy principle, and so on. The results show that the numerical convergence and accuracy of the solutions are ameliorated when differential quadrature method is employed to deal with local problems.