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On the dynamical theory of thermoelastic simple shells
Author(s) -
Bîrsan M.,
Altenbach H.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201000057
Subject(s) - thermoelastic damping , uniqueness , orthotropic material , simple (philosophy) , boundary value problem , mathematical analysis , reciprocity (cultural anthropology) , equations of motion , shell (structure) , classical mechanics , mathematics , thermal , physics , materials science , thermodynamics , finite element method , psychology , social psychology , philosophy , epistemology , composite material
Abstract In this paper we present a mathematical study of the equations of motion for orthotropic thermoelastic simple shells. We use a direct approach to the mechanics of thin shells, in which the shell‐like body is modeled as a deformable surface endowed with a triad of orthonormal vectors connected with each material point. The thermal effects are described by introducing two temperature fields which represent the temperature on the two major faces of the three‐dimensional shell. In the framework of the linear theory, we establish first the uniqueness of solution to the associated boundary–initial–value problem. Then we prove the properties of reciprocity, we give a variational characterization, and we investigate the continuous dependence of solutions on the external data. Finally, we present an existence result for the weak solutions to the equations of motion of thermoelastic simple shells.