Weak solvability of antiplane frictional contact problems for elastic cylinders

We consider a class of quasi-variational inequalities arising in a large number of mathematical models, which describe quasi-static processes of contact between a deformable body and an obstacle, the so-called foundation. The novelty lies in the special structure of these inequalities that involve a history-dependent term as well as in the fact that the inequalities are formulated on the unbounded interval of time [0, +∞). We prove an existence and uniqueness result of the solution, then we complete it with a regularity result. The proofs are based on arguments of monotonicity and convexity, combined with a fixed point result obtained in [22]. We also describe a number of quasi-static frictional contact problems in which we model the material's behaviour with an elastic or viscoelastic constitutive law. The contact is modelled with normal compliance, with normal damped response or with the Signorini condition, as well, associated to versions of Coulomb's law of dry friction or to the frictionless condition. We prove that all these models cast in the abstract setting of history-dependent quasi-variational inequalities, with a convenient choice of spaces and operators. Then, we apply the abstract results in order to prove the unique weak solvability of each contact problem.

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Contact problems for nonlinearly elastic materials: weak solvability involving dual Lagrange multipliers

ANZIAM Journal ◽

10.21914/anziamj.v52i0.2212 ◽

2011 ◽

Vol 52 ◽

pp. 160

Author(s):

Andaluzia Matei ◽

Raluca Ciurcea

Keyword(s):

Lagrange Multipliers ◽

Contact Problems ◽

Elastic Materials ◽

Nonlinearly Elastic ◽

Weak Solvability

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Elastoplastic Frictional Contact Study on Interference Fits of Compressor

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.211-212.535 ◽

2011 ◽

Vol 211-212 ◽

pp. 535-539

Author(s):

Ai Hua Liao

Keyword(s):

Stress Distribution ◽

Contact Stress ◽

Frictional Contact ◽

Contact Problems ◽

Boundary Problems ◽

Interference Fit ◽

Parametric Variational Principle ◽

Design And Manufacturing ◽

Contact Stress Distribution ◽

Fit Tolerance

The impeller mounted onto the compressor shaft assembly via interference fit is one of the key components of a centrifugal compressor stage. A suitable fit tolerance needs to be considered in the structural design. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading was considered in the numerical analysis. The FE parametric quadratic programming (PQP) method which was developed based on the parametric variational principle (PVP) was used for the analysis of stress distribution of 3D elastoplastic frictional contact of impeller-shaft sleeve-shaft. The solution of elastoplastic frictional contact problems belongs to the unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. The effect of fit tolerance, rotational speed and the contact stress distribution on the contact stress was discussed in detail in the numerical computation. The study play a referenced role in deciding the proper fit tolerance and improving design and manufacturing technology of compressor impellers.

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CONTACT PROBLEMS FOR NONLINEARLY ELASTIC MATERIALS: WEAK SOLVABILITY INVOLVING DUAL LAGRANGE MULTIPLIERS

The ANZIAM Journal ◽

10.1017/s1446181111000629 ◽

2010 ◽

Vol 52 (2) ◽

pp. 160-178 ◽

Cited By ~ 15

Author(s):

A. MATEI ◽

R. CIURCEA

Keyword(s):

Lagrange Multipliers ◽

Variational Equation ◽

Small Deformation ◽

Contact Problems ◽

Point Theory ◽

The Body ◽

Elastic Materials ◽

Weak Formulation ◽

Nonlinearly Elastic ◽

Weak Solvability

AbstractA class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

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