Method of fundamental solution using Erdogan's solution: Static and dynamic. (March 2023) - Wei, H.; Zheng, J.L.; Sladek, J.; Sladek, V.; Wen, P.H.
Highlights: Erdogan fundamental solutions are employed in the method of fundamental solution for cracked body. The accuracy and convergence of MFS have been observed. Dynamic problem is solved without dynamic fundamental solutions. Large integral domain technique is proposed to deal with arbitrary boundary configurations. Constant cell technique and finite block method are proposed in the domain integral. Abstract: This paper developed the method of Erdogan`s fundamental solution (MFS) for a 2D in-plane crack problem with static and dynamic loads. The analytical solutions with complex variables with a pair of static concentrated force in a cracked infinite domain were derived by Erdogan in 1965. Based on the Erdogan's fundamental solutions, the MFS is extended to 2D elasticity under static and dynamic loads. The Laplace transform technique and the Durbin inversion technique are adopted for a dynamic case to determine the time-dependent variables. The domain integrals are obtained numerically with both Constant Cell Method (CCM) and Finite Block Method (FBM). The accuracy and convergence of the MFS are demonstrated by four numerical examples. Comparisons have been implemented with both analytical solutions and the finite element method.