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Investigation on the effects of temperature dependency of material parameters on a thermoelastic loading problem. (English) Zbl 1379.35307

Summary: The present work is concerned with the investigation of thermoelastic interactions inside a spherical shell with temperature-dependent material parameters. We employ the heat conduction model with a single delay term. The problem is studied by considering three different kinds of time-dependent temperature and stress distributions applied at the inner and outer surfaces of the shell. The problem is formulated by considering that the thermal properties vary as linear function of temperature that yield nonlinear governing equations. The problem is solved by applying Kirchhoff transformation along with integral transform technique. The numerical results of the field variables are shown in the different graphs to study the influence of temperature-dependent thermal parameters in various cases. It has been shown that the temperature-dependent effect is more prominent in case of stress distribution as compared to other fields and also the effect is significant in case of thermal shock applied at the two boundary surfaces of the spherical shell.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
35A22 Transform methods (e.g., integral transforms) applied to PDEs
74B10 Linear elasticity with initial stresses
74F05 Thermal effects in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
65R10 Numerical methods for integral transforms
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