Geometrical super-elements for elasto-plastic shells with large deformation
type: Item
instance of: scholarly article
title: Geometrical super-elements for elasto-plastic shells with large deformation
zbMATH Open document ID: 0626.73035
DOI: 10.1016/0168-874X(87)90024-2
published in: Finite Elements in Analysis and Design
publication date: 1987-01-01T00:00:00Z
review text: This paper presents the application of the so-called geometrical elements method to the solution of elasto-plastic problems of shells. The approach is based on the observation that, during large deformations, the shell structure deforms in a nearly isometrical manner. Therefore, its deformed shape can be determined and analysed making use of the Gauss theorem according to which the Gaussian curvature of the isometrically deformed surface remains unchanged. The shell structure is subdivided into elements of two kinds: purely-isometrically deformed elements and quasi- isometrically deformed elements. The equilibrium of the whole structure is defined by the stationary value of the Hamiltonian function which requires the calculation of the strain energy in the elements. This can easily be obtained if we recognize that the isometrically deformed elements contain only bending energy. Using the method described, we are able to significant the number of unknown values defining the shape of the deformed structure. The problem is reduced to the numerical evaluation of the minimum of a function of many variables. The elasto- plastic state of stress of the plastic material in the structure can be determined by using the deformation theory of plasticity or the theory of plastic flow. Also, the strains and stresses in the plastic regions are the only functions of the assumed displacements field. The corresponding energy of the plastic deformation can easily be evaluated and added to the minimized functionals. For example, the elasto-plastic behaviour of a spherical shell under a concentrated load is studied. The solution obtained defines the large deformation behaviour and the motion of the plastic zones on the surface of the shell.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74D99
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 4018486
zbMATH Keywords: post-buckling
zbMATH Keywords: very large deflections
zbMATH Keywords: topology represented by small number of unknown parameters
zbMATH Keywords: geometrical elements method
zbMATH Keywords: Gauss theorem
zbMATH Keywords: Gaussian curvature
zbMATH Keywords: isometrically deformed surface
zbMATH Keywords: unchanged
zbMATH Keywords: purely- isometrically deformed elements
zbMATH Keywords: quasi-isometrically deformed elements
zbMATH Keywords: stationary value
zbMATH Keywords: Hamiltonian function
zbMATH Keywords: strain energy
zbMATH Keywords: minimum of a function of many variables
author: Stanislaw A. Lukasiewicz
MaRDI profile type: Publication
full work available at URL: 0168-874x(87)90024-2
OpenAlex ID: W4233431707
description: scientific article; zbMATH DE number 4018486