A kinematically exact finite element formulation of planar elastic-plastic frames
type: Item
instance of: scholarly article
title: A kinematically exact finite element formulation of planar elastic-plastic frames
zbMATH Open document ID: 0892.73070
DOI: 10.1016/S0045-7825(96)01172-3
author: Igor Planinc
author: B. Vratanar
author: Miran Saje
author: G. Turk
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1997-10-26T00:00:00Z
review text: A finite element formulation of finite deformation static analysis of plane elastic-plastic frames subjected to static loads is presented, in which the only function to be interpolated is the rotation of the centroid axis of the beam. One of the advantages of such a formulation is that the problem of the field-consistency does not arise. Exact nonlinear kinematic relationships of the finite-strain beam theory are used, which assume the Bernoulli hypothesis of plane cross-sections. Finite displacements and rotations as well as finite extensional and bending strains are accounted for. Because the potential energy of internal forces does not exist with elastic-plastic material, the principle of virtual work is introduced as the basis of the finite element formulation. A generalized principle of virtual work is proposed in which the displacements, rotation, extensional and bending strains, and the Lagrangian multipliers are independent variables. The theoretical findings and the performance of the derived finite elements are illustrated by numerical examples.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74C99
zbMATH DE Number: 1079167
zbMATH Keywords: interpolation polynomials
zbMATH Keywords: Lobatto rule
zbMATH Keywords: discontinuous integrands
zbMATH Keywords: finite deformation static analysis
zbMATH Keywords: finite-strain beam theory
zbMATH Keywords: Bernoulli hypothesis of plane cross-sections
zbMATH Keywords: generalized principle of virtual work
zbMATH Keywords: Lagrangian multipliers
MaRDI profile type: Publication
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full work available at URL: s0045-7825(96)01172-3
OpenAlex ID: W2081191355
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description: scientific article; zbMATH DE number 1079167