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Abstract: In this paper, we consider a mathematical model which describes the dynamic contact between an elastic body and an obstacle. The process is assumed to be dynamic and the contact is modeled with the normal compliance. We present a variational formulation of the problem and prove the existence and the uniqueness of a weak solution. An efficient numerical method is presented to analyze this dynamic contact. This approach exploits the augmented Lagrangian concept and a special time integration algorithm. This is exploited to study the dynamic contact between the rotor and the stator inside an ultrasonic motor SHINSEI USR 60. Numerical results are presented and show the interest of this method to forecast the origin of the principal failure mode of this motor. [Copyright &y& Elsevier]

Abstract: In this paper, we are interested in the simulation of prepreg composite deformation by deep-drawing and laying-up. It uses new bi-component finite elements made of woven material in which the nodal interior loads are deduced from fibre tensile strain energy and not polymerized resin membrane energy. Specific treatment is used to analyze the frictional-contact problem between the deformable prepreg composite and the steel rigid tools. The frictional-contact method is based on the Lagrangian formulation and the preconditioned conjugate gradient method. Some numerical tests are given to investigate the performance of the numerical strategies. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a reliability–mechanical study combination for treating the metal forming process. This combination is based on the augmented Lagrangian method for solving the deterministic case and the response surface method. Our goal is the computation of the failure probability of the frictionless contact problem. Normally, contact problems in mechanics are particularly complex and have to be solved numerically. There are several numerical techniques available for computing the solution. However, some design parameters are uncertain and the deterministic solutions could be unacceptable. Thus, a mechanical contact study is an important subject for reliability analysis: the augmented Lagrangian method coupled with the first order reliability method, and we use the Monte Carlo method to obtain the founding results. The metal forming process is treated numerically to validate the new approach. [Copyright &y& Elsevier]