Analysis of Thin Shells by the Element-Free Galerkin Method

A meshless approach to the analysis of arbitrary Kirchhoff shells by the Element-Free Galerkin (EFG) method is presented. The shell theory used is geometrically exact and can be applied to deep shells. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisfaction of the C1 continuity requirements are easily met by EFG since it requires only C1 weights; therefore, it is not necessary to resort to Mindlin-Reissner theory or to devices such as discrete Kirchhoff theory. The requirements of consistency are met by the use of a polynomial basis of quadratic or higher order. A subdivision similar to finite elements is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers. Membrane locking, which is due to different approximation order for transverse and membrane displacements, is removed by using larger domains of influence with the quadratic basis, and by using quartic polynomial basis, which can prevent membrane locking completely. It is shown on the obstacle course for shells that the present technique performs well.