Justification and solvability of dynamical contact problems for generalized Marguerre–von Kármán shallow shells

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AbstractIn this work, we consider a three–dimensional dynamical model of unilateral contact problems with Signorini conditions and Coulomb friction laws for nonlinearly elastic shallow shells with a specific class of boundary conditions of generalized Marguerre–von Kármán type. Using technics from formal asymptotic analysis, we show that the scaled three–dimensional solution still leads to a two–dimensional dynamical model with frictionless contact problems. Then, we solve the last problems, using penalization method.