Comparison of Numerical Differentiation Solution and Finite Element Analysis for Axisymmetric Bulged Thin Metal Shells

Abstract-Based on large deformation geometrical relationship, a mathematical model described with differential algebraic equations (DAEs) is presented for axisymmetric thin metal shells with variable curvature and thickness under internal pressure. Numerical differentiation solutions are carried out using Klopfenstein-Shampine numerical differentiation formulas with varying step size and variable order. The distribution of stresses, strains, and displacements of metal shells at specific loads can be obtained. Elasto-plastic finite element method (FEM) is also used to study the nonlinear mechanical behavior of bulged shells. Simulated results by numerical differentiation formulas (NDFs) and FEM are verified with the test data of vertical deflections, and then both numerical results are compared and discussed.