| 求解变分型积分方程的一种新型数值方法——有限变分法 |
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| 引用本文： | 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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| 作者姓名： | 卢炎麟 周国斌 贾虹 应富强 傅建钢 |
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| 作者单位： | 浙江工业大学,机械制造及自动化教育部重点实验室,杭州,310014 |
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| 基金项目： | 国家自然科学基金(50675206,10972198)资助项目. |
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| 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。
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| 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 |
| 收稿时间： | 2008/10/26 0:00:00 |
Finite variation method: a new numerical method for solving variational integral equations |
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| LU Yan-lin,ZHOU Guo-bin,JIA Hong,YING Fu-qiang and FU Jian-gang.Finite variation method: a new numerical method for solving variational integral equations[J].Chinese Journal of Computational Mechanics,2010,27(5):801-808. |
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| Authors: | LU Yan-lin ZHOU Guo-bin JIA Hong YING Fu-qiang and FU Jian-gang |
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| Institution: | The MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310014, China;The MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310014, China;The MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310014, China;The MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310014, China;The MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310014, China |
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| Abstract: | 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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| Keywords: | finite variation method variational integral equations stress intensity factor 3-D general weight function method multiple virtual crack extension method |
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