A variational‐inequality approach to stochastic boundary value problems with inequality constraints and its application to contact and elastoplasticity | Zendy

Arnst M. | Zendy; Ghanem R. | Zendy

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A variational‐inequality approach to stochastic boundary value problems with inequality constraints and its application to contact and elastoplasticity

Author(s) -

Arnst M.,

Ghanem R.

Publication year - 2011

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.3307

Subject(s) - mathematics , discretization , variational inequality , inequality , boundary value problem , projection (relational algebra) , mathematical optimization , boundary (topology) , class (philosophy) , mathematical analysis , computer science , algorithm , artificial intelligence

SUMMARY This paper is concerned with stochastic boundary value problems (SBVPs) whose formulation involves inequality constraints. A class of stochastic variational inequalities (SVIs) is defined, which is well adapted to characterize the solution of specified inequality‐constrained SBVPs. A methodology for solving such SVIs is proposed, which involves their discretization by projection onto polynomial chaos and collocation of the inequality constraints, followed by the solution of a finite‐dimensional constrained optimization problem. Simulation studies in contact and elastoplasticity are provided to demonstrate the proposed framework. Copyright © 2011 John Wiley & Sons, Ltd.

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