Abstract

The smoothed finite element methods (S-FEMs) have been found capable of producing softer models whose “stiffness” is closer to the true continuous model. This paper explores, for the first time, this unique feature of S-FEMs to develop a complete formulism and procedure to study free vibration and forced vibration of solid structures, via 1) solving eigenvalue problems that produces vibration modes of a given structure; 2) using model superimposition techniques and the Lanczos algorithm to obtain transient dynamic solution for structures subjected to arbitrary dynamics forces. The present S-FEM modeling takes the advantageous of the so-called softening effects achieved by establishing proper types of smoothing domains based on edges and faces of the mesh known as ES/FS-FEM, so as to obtain accurate modes for both free and forced vibration analysis. For easy automation in creating 3D solids, we use only the automatically generatable tetrahedral mesh, while to ensure excellent stress solution using the ES/FS-FEM models. A 3D code has been developed in the framework of S-FEMs, and applied to solve a number of 3D solid structures. The results are compared with those from the commercial finite element analysis software ABAQUS in terms of accuracy and convergence. The results shows that S-FEMs have better accuracy and convergence than ABAQUS.

Keywords: Smoothed finite element method; Free vibration; Forced vibration; Lanczos algorithm; Mode superposition method; ABAQUS;