Convergences and numerical analysis of a contact problem with normal compliance and unilateral constraint
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Date
2021-01-05
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African Journal of Mathematics and Computer Science Research
Abstract
This paper represents a continuation of a previous study on “Analysis of a Sliding Frictional Contact
Problem with Unilateral Constraint”. This study considers a mathematical model which describes the
equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled
with a multivalued normal compliance condition with unilateral constraints, associated to a sliding
version of Coulomb’s law of dry friction. After a description of the model, the variational formulation
was presented. Then, the dependence of the solution was studied with respect to the data and a
convergence result was proven. Regularization method was also used to study the existence and
uniqueness of the contact problem for which a convergence result was presented. Finally, a semidiscrete
scheme was introduced for the numerical approximation of the sliding contact problem. Under
certain solution regularity assumptions, an optimal order error estimate was derived
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Keywords
Elastic material, frictional contact, normal compliance, unilateral constraint, variational formulation, weak solution, regularization method, finite element, error estimate, UD College of Engineering, CoE_Djibouti, Université de Djibouti, Djibouti, Engineering