Two-dimensional elastodynamic and free vibration analysis by the method of fundamental solutions. (English) Zbl 1464.74397

Khoshroo, M.; Hematiyan, M. R.; Daneshbod, Y.

Eng. Anal. Bound. Elem. 117, 188-201 (2020).

Summary: In this paper we will present a formulation for solving elastodynamic problems in 2D using the method of fundamental solutions (MFS). The governing equation for the displacement in the elastodynamic problem is expressed by the Navier equation with an additional non-homogeneous inertial term, which involves the second derivative of displacement with respect to time. The inertial term is approximated by the Houbolt finite difference formula. In each time step, the solution for the displacement is separated into a homogeneous solution and a particular solution. The homogeneous solution is constructed in terms of the fundamental solutions of the elastostatic problem. The particular solution corresponds to the non-homogeneous inertial term, which is obtained by approximating the inertial term with radial basis functions (RBFs). In addition, a formulation based on the MFS for free vibration analysis of 2D bodies is presented in this paper. By solving several numerical examples, we have demonstrated that the proposed methods are robust and accurate. The convergence of the results with respect to the number of collocation points, the number of internal points, the value of the RBF parameter, and the time step size is also studied.

MSC:

74S99	Numerical and other methods in solid mechanics
65N80	Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
74B05	Classical linear elasticity
74H45	Vibrations in dynamical problems in solid mechanics

Keywords:

elastodynamic; free vibration; method of fundamental solutions; particular solution; location of source points

Software:

SERBA

References:

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