Robustness of hierarchical elements formulated by integrals of legendre polynomials

Abstract

The purpose of this study is to ascertain the robustness of p-version models with hierarchic integrals of Legendre shape functions in various applications including plane stress/strain, axisymmetric and shell problems. The most important symptoms of accuracy failure in modern finite elements are spurious mechanisms and a phenomenon known as locking which are exhibited for incompressible materials and irregular shapes which contain aspect ratios ( R/ t, a/ b), tapered ratio ( d/ b), and skewness. The condition numbers and energy norms are used to estimate numerical errors, convergence characteristics and algorithmic efficiencies for verifying the aforementioned symptoms of accuracy failure. Numerical results from p-version models are compared with those from NASTRAN, SAP90, and Cheung's hybrid elements.