Abstract:
A review of recent works on thermoelasticity is provided. It is recommended to use the boundary state method (BSM) for constructing numerical-analytical solutions of problems by means of computing systems supporting “computer algebras”. The structures of Hilbert spaces of internal and boundary states of a thermoelastostatic medium (TE) are formed and a method for describing scalar products of both isomorphic spaces is determined. A possibility of saving computational resources for performing the procedure of orthogonalization of bases of separable spaces is discovered. When solving problems of thermoelasticity coupled/uncoupled by boundary conditions (BC), one does not need to decompose them into a traditional sequence of a temperature and elastic problems. A classification of TE problems is given. Calculations are performed and the results are commented for two classes of problems.
Keywords:thermoelasticity, thermoelastostatics, boundary state method, BSM, Dirichlet problem, Neumann problem, energy methods.
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