A novel 'boundary layer' finite element for the efficient analysis of thin cylindrical shells

Abstract

Classical shell finite elements usually employ low-order polynomial shape functions to interpolate between nodal displacement and rotational degrees of freedom. Consequently, carefully-designed fine meshes are often required to accurately capture regions of high local curvature, such as at the ‘boundary layer’ of bending that occurs in cylindrical shells near a boundary or discontinuity. This significantly increases the computational cost of any analysis. This paper is a ‘proof of concept’ illustration of a novel cylindrical axisymmetric shell element that is enriched with rigorously-derived transcendental shape functions to exactly capture the bending boundary layer. When complemented with simple polynomials to express the membrane displacements, a single boundary layer shell element is able to support very complex displacement and stress fields that are exact for distributed element loads of up to second order. A single element is usually sufficient per shell segment in a multi-strake shell. The predictions of the novel element are compared against analytical solutions, a classical axisymmetric shell element with polynomial shape functions and the ABAQUS S4R shell element in three problems of increasing complexity and practical relevance. The element displays excellent numerical results with only a fraction of the total degrees of freedom and involves virtually no mesh design. The shell theory employed at present is kept deliberately simple for illustration purposes, though the formulation will be extended in future work.