基本解是边界元法、基本解法和无网格法等数值方法的重要理论基础.在断裂问题中,采用含裂纹的基本解可以避免将裂纹表面作为边界条件,从而大大简化问题的求解.在复变函数表示的含裂纹平面问题Erdogan基本解的基础上,对Erdogan基本解的...基本解是边界元法、基本解法和无网格法等数值方法的重要理论基础.在断裂问题中,采用含裂纹的基本解可以避免将裂纹表面作为边界条件,从而大大简化问题的求解.在复变函数表示的含裂纹平面问题Erdogan基本解的基础上,对Erdogan基本解的使用条件进行了注解,修正了Erdogan基本解的一些错误,并推导出Erdogan基本解中位移函数解答的显式表达形式.编写了基于Erdogan基本解显式表达的样条虚边界元法(spline fictitious boundary element method,SFBEM)计算程序,计算了具有复合边界条件平面问题的位移、应力和应力强度因子.数值算例结果表明了该文提出的Erdogan基本解显式表达形式的正确性.展开更多
It is well known that the boundary element method (BEM) is capable of converting a boundary- value equation into its discrete analog by a judicious application of the Green’s identity and complementary equation. Howe...It is well known that the boundary element method (BEM) is capable of converting a boundary- value equation into its discrete analog by a judicious application of the Green’s identity and complementary equation. However, for many challenging problems, the fundamental solution is either not available in a cheaply computable form or does not exist at all. Even when the fundamental solution does exist, it appears in a form that is highly non-local which inadvertently leads to a sys-tem of equations with a fully populated matrix. In this paper, fundamental solution of an auxiliary form of a governing partial differential equation coupled with the Green identity is used to discretize and localize an integro-partial differential transport equation by conversion into a boundary-domain form amenable to a hybrid boundary integral numerical formulation. It is observed that the numerical technique applied herein is able to accurately represent numerical and closed form solutions available in literature.展开更多
文摘基本解是边界元法、基本解法和无网格法等数值方法的重要理论基础.在断裂问题中,采用含裂纹的基本解可以避免将裂纹表面作为边界条件,从而大大简化问题的求解.在复变函数表示的含裂纹平面问题Erdogan基本解的基础上,对Erdogan基本解的使用条件进行了注解,修正了Erdogan基本解的一些错误,并推导出Erdogan基本解中位移函数解答的显式表达形式.编写了基于Erdogan基本解显式表达的样条虚边界元法(spline fictitious boundary element method,SFBEM)计算程序,计算了具有复合边界条件平面问题的位移、应力和应力强度因子.数值算例结果表明了该文提出的Erdogan基本解显式表达形式的正确性.
文摘It is well known that the boundary element method (BEM) is capable of converting a boundary- value equation into its discrete analog by a judicious application of the Green’s identity and complementary equation. However, for many challenging problems, the fundamental solution is either not available in a cheaply computable form or does not exist at all. Even when the fundamental solution does exist, it appears in a form that is highly non-local which inadvertently leads to a sys-tem of equations with a fully populated matrix. In this paper, fundamental solution of an auxiliary form of a governing partial differential equation coupled with the Green identity is used to discretize and localize an integro-partial differential transport equation by conversion into a boundary-domain form amenable to a hybrid boundary integral numerical formulation. It is observed that the numerical technique applied herein is able to accurately represent numerical and closed form solutions available in literature.
