Efficient fundamental solution based finite element for 2-d dynamics. (March 2023) - Elsheikh, Elsayed M.; Naga, Taha H.A.; Rashed, Youssef F.
Abstract: In this paper, an efficient finite element is developed for the dynamic analysis of 2-D elasticity problems. Unlike the conventional direct or indirect formulations, the proposed integral equation is based on minimizing the relevant energy functional. In doing so, variational methods are used. The proposed element stiffness matrix is obtained by a modified hybrid displacement variational statement, taking the fundamental solution as a trial function. Quadratic shape functions are used for the approximation of the boundary variables. To avoid singularities, the source points are located outside the problem domain. The element mass matrix is computed using the relevant element shape functions. Only four Gauss points are needed for accurate computation of the domain integral related to the mass matrix computation. The proposed element is applicable for: free vibration, forced vibration, and harmonic analysis as demonstrated by the presented numerical examples. The obtained results are very promising, and the accuracy level is excellent.