Penalty/finite-element approximations of a class of unilateral problems in linear elasticity
- 1 January 1981
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 39 (1) , 1-22
- https://doi.org/10.1090/qam/613950
Abstract
The present paper is concerned with a development of a penalty/finite-element approximation of a class of unilateral problems in linear elasticity. A penalty method is applied to resolve the inequality constraint due to contact, and convergence with respect to the penalty parameter is discussed. Then finite-element approximations are introduced to the penalized formulation with a priori error estimates in terms of the penalty and mesh parameters. Several numerical examples are also given in the end of the paper.Keywords
This publication has 14 references indexed in Scilit:
- Contact problems involving forces and moments for incompressible linearly elastic materialsInternational Journal of Engineering Science, 1980
- The Finite Element Method for Elliptic ProblemsJournal of Applied Mechanics, 1978
- Variational Principles of Contact ElastostaticsIMA Journal of Applied Mathematics, 1977
- Inequalities in Mechanics and PhysicsJournal of Applied Mechanics, 1977
- A finite element method for a class of contact-impact problemsComputer Methods in Applied Mechanics and Engineering, 1976
- Error Estimates for the Approximation of a Class of Variational InequalitiesMathematics of Computation, 1974
- Error estimates for the approximation of a class of variational inequalitiesMathematics of Computation, 1974
- A finite element method for contact problems of solid bodies—Part I. Theory and validationInternational Journal of Mechanical Sciences, 1971
- Non-Linear Programming Via Penalty FunctionsManagement Science, 1967
- Variational methods for the solution of problems of equilibrium and vibrationsBulletin of the American Mathematical Society, 1943