Vector approximation of displacements of a curvilinear finite element in problems of stability of shells (Q2759542)

A technique of forming stiffness matrices for a curvilinear finite shell element is suggested. Unlike classic scheme, here Maclaurin series is used, which approximates a polynomial vector-function of element's displacements. The new approximation satisfies the condition for rigid-body displacement. The suggested scheme is tested on three simple deformations of a ring: rigid-body displacement, constant pressure and pure bending in accordance with the form of stability loss. It is shown, that the traditional non-vector approximation gives a significant error in calculation of critical force and does not satisfy condition of zero deformations in rigid-body displacement. The new technique is free of these shortcomings.