M. Kögl, L. Gaul²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 27-44, 2000, DOI:10.3970/cmes.2000.001.479

Abstract A Boundary Element formulation is presented for the solution of three-dimensional problems of anisotropic elastodynamics. Due to the complexity of the dynamic fundamental solutions for anisotropic materials and the resulting high computational costs, the approach at hand uses the fundamental solution of the static operator. This leads to a domain integral in the representation formula which contains the inertia term. The domain integral can be transformed to the boundary using the Dual Reciprocity Method. This results in a system of ordinary differential equations in time with time-independent matrices. Several general questions concerning the anisotropic solutions, the use of DRM, and… More >

Chia-Cheng Tsai ¹

CMC-Computers, Materials & Continua, Vol.22, No.3, pp. 197-218, 2011, DOI:10.3970/cmc.2011.022.197

Abstract This paper describes the combination of the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method to solve problems of Kirchhoff plates under arbitrary loadings. In the solution procedure, a arbitrary distributed loading is first approximated by either the multiquadrics (MQ) or the augmented polyharmonic splines (APS), which are constructed by splines and monomials. The particular solutions of multiquadrics, splines and monomials are all derived analytically and explicitly. Then, the complementary solutions are solved formally by the MFS. Furthermore, the boundary conditions of lateral displacement, slope, normal moment, and effective shear force are… More >