Vector approximation of displacements of a curvilinear finite element in problems of stability of shells
type: Item
instance of: scholarly article
zbMATH Open document ID: 1054.74650
author: E. O. Gotsulyak
author: N. E. Aranchij
publication date: 2001-12-12T00:00:00Z
Mathematics Subject Classification ID: 74K25
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74G60
zbMATH DE Number: 1681862
zbMATH Keywords: elastic shell
zbMATH Keywords: finite element
zbMATH Keywords: polynomial vector-function
zbMATH Keywords: Maclaurin series
zbMATH Keywords: stability
zbMATH Keywords: ring shell
MaRDI profile type: Publication
title: Vector approximation of displacements of a curvilinear finite element in problems of stability of shells
published in: Dopovidi Natsional'noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky
review text: 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.
description: scientific article; zbMATH DE number 1681862