Variational principles, FE and MPT for analysis of nonlinear impact-contact problems
type: Item
instance of: scholarly article
title: Variational principles, FE and MPT for analysis of nonlinear impact-contact problems
zbMATH Open document ID: 0852.73070
DOI: 10.1016/0045-7825(94)00731-2
author: X. Q. He
author: Qing H. Qin
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1996-12-17T00:00:00Z
review text: We present an analysis of the impact-contact problems between elasto-plastic bodies without friction. Three pairs of extended variational complementary functionals for the impact-contact problems are presented which constitute the theoretical foundations of the ensuing numerical analysis. A general condition of non-interpenetration is suggested for general cases of two elasto-plastic solids in contact. In fact, the extended variational principles are equivalent to a stationarity of the potential energy with constraints on displacements which may be reduced to a particular case of the mathematical programming techniques (MPT). The present analysis is limited to a two-dimensional time dependent case where both geometrical and material nonlinearities are considered; an eight node plane element is used to derive the finite element (FE) formulation in the problem.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74M20
zbMATH DE Number: 881097
zbMATH Keywords: Wilson-theta scheme
zbMATH Keywords: Lamker method
zbMATH Keywords: elasto-plastic bodies without friction
zbMATH Keywords: variational complementary functionals
zbMATH Keywords: condition of non-interpenetration
zbMATH Keywords: stationarity of the potential energy
zbMATH Keywords: mathematical programming techniques
zbMATH Keywords: eight node plane element
MaRDI profile type: Publication
full work available at URL: 0045-7825(94)00731-2
OpenAlex ID: W1969308607
cites work: A finite element method for contact problems of solid bodies. I: Theory and validation. II: Application to turbine blade fastenings
cites work: Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems
cites work: Models and computational methods for dynamic friction phenomena
cites work: Q3908578
cites work: Sliding interfaces with contact-impact in large-scale Lagrangian computations
cites work: Enlarging the region of convergence of Newton's method for constrained optimization
cites work: Theory of finite element method for elastic contact problems of solid bodies
cites work: Numerical analysis of certain contact problems in elasticity with non-classical friction laws
cites work: Q3994823
cites work: Finite element formulation of large deformation impact-contact problems with friction
cites work: A mixed formulation for the finite element solution of contact problems
cites work: A nonlinear programming approach to the unilateral contact-, and friction-boundary value problem in the theory of elasticity
cites work: A mathematical programming approach to three-dimensional contact problems with friction
cites work: A mathematical programming approach to contact problems with friction and varying contact surface
cites work: Contact mechanical algorithms
cites work: Conjugate progector preconditioning for the solution of contact problems
cites work: A finite element method for elasto-plastic structures and contact problems by parametric quadratic programming
cites work: Frictionless contact of elastic bodies by finite element method and mathematical programming technique
cites work: Boundary element solution for half-plane problems
cites work: Q3670719
cites work: A complementarity problem formulation for two-dimensional frictional contact problems
cites work: An augmented lagrangian treatment of contact problems involving friction
cites work: A parallel finite element contact/impact algorithm for non‐linear explicit transient analysis: Part I—The search algorithm and contact mechanics
cites work: Nonlinear analysis of Reissner's plate by the variational approaches and boundary element methods
cites work: Nonlinear analysis of Reissner plates on an elastic foundation by the BEM
cites work: Variational principles and hybrid approach for finite deformation analysis of shells
cites work: Finite element formulations for large deformation dynamic analysis
cites work: Q5801127
description: scientific article; zbMATH DE number 881097