Abstract
In this paper a robust and effective 4-node shell element for the structural analysis of thin structures is described. A Hu–Washizu functional with independent displacements, stress resultants and shell strains is the variational basis of the theory. Based on a previous paper an additional interpolation part using quadratic shape functions is introduced for the independent shell strains. Especially for unstructured meshes this leads to an improved convergence behavior. The expanded element formulation proves to be insensitive to mesh distortion. Another well-known feature of the mixed hybrid element is the robustness in nonlinear applications with large deformations.
Highlights
Nonlinear structural analysis of thin structures requires effective and robust element formulations
A Hu–Washizu functional with independent displacements, stress resultants and shell strains is the variational basis of the theory
Based on a previous paper an additional interpolation part using quadratic shape functions is introduced for the independent shell strains
Summary
Nonlinear structural analysis of thin structures requires effective and robust element formulations. The variational formulation is based on a Hu–Washizu functional with independent displacements, stress resultants and shell strains. V = [u, φ]T contains the displacements u and rotational parameters φ, as well as ε and σ denote the independent shell strains and stress resultants, respectively. Numel denotes the total number of finite shell elements to discretize the problem and fa corresponds to the element load vector of a standard displacement method. The parameter k = 6 reduces the eigenvalues of some bending modes This is the reason for the improved convergence behavior in the subsequent depicted test examples. It holds especially for element geometries which deviate notably from a square.
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