| 卢炎麟,周国斌,贾虹,应富强,傅建钢.求解变分型积分方程的一种新型数值方法——有限变分法[J].计算力学学报,2010,27(5):801~808 |
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| 求解变分型积分方程的一种新型数值方法——有限变分法 |
| Finite variation method: a new numerical method for solving variational integral equations |
| 投稿时间：2008-10-26 |
| DOI：10.7511/jslx20105010 |
| 中文关键词: 有限变分法 变分型积分方程 应力强度因子 三维通用权函数法 多虚拟裂纹扩展法 |
| 英文关键词:finite variation method variational integral equations stress intensity factor 3-D general weight function method multiple virtual crack extension method |
| 基金项目:国家自然科学基金(50675206,10972198)资助项目. |
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| 摘要点击次数: 2213 |
| 全文下载次数: 1422 |
| 中文摘要: |
| 将作者提出的多虚拟裂纹扩展法(MVCE法)拓展为求解变分型积分方程问题的一种新型数值方法——有限变分法(FVM)。它的基本思想是,给定有限个(N个)局部变分模式,将所求解的未知量用适当的方法离散化,针对这N个局部变分模式列出N个方程,求解N个未知系数,从而求得未知量。单一未知变量FVM的最终方程组的系数矩阵通常是一个对称的窄带矩阵,对角元是大数,有很好的数值计算性能。用FVM求解了三维I型裂纹前缘的应力强度因子(SIF)分布。利用基于FVM的通用权函数法计算程序,可以高精度和高效率地求解表面力、体积力和温度载荷共同作用情况下三维裂纹前缘SIF的分布及其时间历程。FVM可以被推广到更广泛的领域,是一个求解变分型积分方程问题的普遍适用的新型数值方法。 |
| 英文摘要: |
| The multiple virtual crack extension (MVCE) method proposed by authors is extended to a new general numerical method-finite variation method (FVM). Giving finite (N) local variation modes, discretizing the solved variables, writing out the N equations for N local variation modes, the N unknown coefficients in discretization and thus the unknown variables can be solved. The coefficient matrix of the final equations in FVM is usually a symmetrical matrix with small band-width and major diagonals, which has good numerical properties. The distributions of SIFs along 3-D mode I crack fronts are solved by FVM. By means of the programs using the general weight function method based on FVM, the histories of distributions of SIFs along 3-D crack fronts of a body subjected to surface tractions, volume forces and thermal loadings can be determined with high accuracy and efficiency. FVM can be extended to more general areas, which is a widely suitable numerical method for solving the variational integral equations. |
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