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The modified Green function technique for the exterior Dirichlet problem in linear thermoelasticity
Author(s) -
Argyropoulos Elias,
Argyropoulou Eftychia,
Kiriaki Kiriakie
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4783
Subject(s) - mathematics , thermoelastic damping , eigenvalues and eigenvectors , mathematical analysis , dirichlet problem , boundary value problem , neumann boundary condition , dirichlet distribution , dirichlet boundary condition , displacement field , spectrum (functional analysis) , linear elasticity , integral equation , displacement (psychology) , function (biology) , psychology , physics , quantum mechanics , thermal , finite element method , meteorology , psychotherapist , thermodynamics , evolutionary biology , biology
In this work, the modified Green function technique for the exterior Dirichlet problem in linear thermoelasticity is presented. Expressing the solution of the problem as a double‐layer potential of an unknown density, we form the associated boundary integral equation that describes the problem. Exploiting that the discrete spectrum of the irregular values of the associated integral equation is identified with the spectrum of eigenvalues of the corresponding interior homogeneous Neumann problem for the transverse part of the elastic displacement field, we introduce a modification of the fundamental solution of the elastic field. We establish the sufficient conditions that the coefficients of the modification must satisfy to overcome the problem of nonuniqueness for the thermoelastic problem.