Element free analyses of shell and spatial structures

Abstract

The element free analyses of shell and spatial structures are conducted. The original element free Galerkin method proposed by Belytschko et al. is enhanced to analyse three-dimensional thin structures. By using the mapping technique the geometry of arbitrary curved surface is expanded in the two-dimensional space, and the bases of convected co-ordinate system are utilized for the expression of strain and stress components in the virtual work principle. Only nodal data are generated on this two-dimensional space and the convected co-ordinates are used in the moving least-squares interpolation method for the approximation of displacement field. For shell, the formulation allows transverse shear strain, therefore, it results in the Mindlin plate when the surface is flat and membrane state is negligible. In order to avoid shear and membrane locking, bi-cubic and quartic basis functions are adopted for the interpolation. For membrane structure, as geometrical stiffness to support the structure cannot be negligible, geometrically non-linear analysis is essential and the total Lagrangian method is adopted for the formulation. Several numerical examples are demonstrated to show the validity of the proposed method and the satisfactory results are obtained in comparison to the theoretical or the finite element results. Copyright © 2000 John Wiley & Sons, Ltd.