A high-precision triangular cylindrical shell finite element

Abstract

element uses as generalized displacements the tangential displacements and their first derivatives, plus the normal displacement and its first and second derivatives at each vertex, a total of 36 in all. The transverse displacement function for the element contains a complete quartic polynomial plus some higher degree terms and allows a cubic variation of normal slope along each edge. The tangential displacement functions are complete cubic polynomials, and it is shown that this formulation leads to a consistent asymptotic strain energy convergence rate of n~6, where n is the number of elements per side of a shell. Results show that this element is exceedingly accurate and far outperforms early lower order elements in predicting stresses as well as displacements. This element may easily be converted into an efficient and useful cylindrical shell element simply by substituting cylindrical shell theory for the shallow shell theory. The purpose of this Note is to present the necessary derivations for doing this and to illustrate the element's usefulness on an example application. The problem of a cylindrical shell with a circular cut-out is analyzed, and the stress concentration results are compared with those from both an approximate analytic analysis2 and a new finite difference variational approach.3 The following presentation is necessarily brief, but more details are available in Ref . 4.