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An Elastic Contact Problem with Normal Compliance and Memory Term

Barboteu M., Ramadan A., Sofonea M. T., Patrulescu F.

Machine Dynamics Research

2012

Vol. 36, No. 1

24-34

We consider a history-dependent problem which describes the contact between an elastic body and an obstacle, the so-called foundation. The contact is frictionless and is modeled with a version of the normal compliance condition in which the memory effects are taken into account. The mathematical analysis of the problem, including existence, uniqueness and convergence results, was provided in (Barboteu et al., in preparation). Here we present the analytic expression of the solution and numerical simulations, in the study of one and two-dimensional examples, respectively.

A Contact Problem with Normal Compliance, Finite Penetration and Unilateral Constraint

Barboteu M., Sofonea M.

Machine Dynamics Research

2011

Vol. 35, No. 1

60-69

We consider a quasistatic problem which describes the contact between a viscoplastic body and an obstacle, the so-called foundation. The contact is frictionless and is modelled with a version of the normal compliance condition in which the penetration is restricted with unilateral constraint. The mathematical analysis of the problem, including, existence, uniqueness and convergence results, was provided by Barboteu et al. (2011). Here we present numerical simulations in the study of an academic two-dimensional contact example.

Regularity of Solutions to Dynamic Contact Problems

Barboteu M., Sofonea M.

Machine Dynamics Research

2010

Vol. 34, No. 1

5-13

We investigate the regularity in time of solutions of two dynamic frictionless contact problems. The first problem describes the vibration of a mass-spring system and the second one concerns the contact of an elastic rod. In both models the contact is described with normal compliance. We show that the regularity of the normal compliance function determines the regularity of the solution.

Contact strength of a system of two elastic half spaces with an axially symmetric recess under compression

Monastyrskyy B., Kaczyński A.

Acta Mechanica et Automatica

2010

Vol. 4, no. 4

64-70

Frictionless contact of two isotropic half spaces is considered one of which has a small smooth circular recess. A method of solving the corresponding boundary value problem of elasticity in axially symmetric case is presented via the function of gap height. The governing integral equation for this function is solved analytically by assuming a certain shape of the initial recess. On the basis of the closed-form solution obtained the strength analysis of a contact couple is performed and illustrated from the standpoint of fracture mechanics.