Adaptive mesh refinement for shells with modified Ahmad elements

This paper presents a simple scheme for the generation of a quadrilateral element mesh for shells with arbitrary three-dimensional geometry. The present mesh generation scheme incorporates a normal mesh generator for generating a mesh in the two-dimensional plane and a specific mapping technique which maps the two-dimensional mesh onto the three-dimensional curved surface. As the mapping is a one-to-one mapping between the mesh in the plane and that on the curved surface, the resulting surface discretization is compatible with the local mesh parameters in two dimensions. This scheme is further combined, both with a sophisticated error estimate determined by using the best guess values of bending moments and membrane and transverse shear forces obtained from a previous solution, and an effective mesh refinement strategy established at an element level in order to complete an adaptive analysis for shell structures. Numerical examples are shown to illustrate the principles and procedure of the present adaptive analysis.