Mathematical and Asymptotic Analysis of Thermoelastic Shells in Normal Damped Response Contact

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for this problem. Then, we study the particular case when the deformable body is, in fact, a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.This project has received funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No 823731 CONMECH and grant MTM2016-78718-P by Ministerio de Economía Industria y Competitividad of Spain with the participation of FEDE

Asymptotic Analysis of a Problem for Dynamic Thermoelastic Shells in Normal Damped Response Contact

[Abstract] The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for this problem. We then study the particular case when the deformable body is, in fact, a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.[Resumo] En termoelasticidade, dado un problema de contacto entre una lámina tipo membrana elíptica e un obstáculo, estudamos a existencia de problema bidimensional límite cando o espesor tende a cero. Preséntase un teorema de converxencia para xustificar a bondade da aproximación.This project has received funding from the European Unions Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement Nº 823731 CONMECH and grant MTM2016-78718-P by Ministerio de Economía Industria y Competitividad of Spain with the participation of FEDE