Analytical layer-element method for 3D thermoelastic problem of layered medium around a heat source.

*(English)*Zbl 1329.74067Summary: This paper presents a numerically efficient and stable method to study the thermoelastic problem of layered medium containing a heat source. Based on the governing equations of 3D thermoelasticity, the relationship between generalized displacements and stresses of a single layer is described by an analytical layer-element, which is obtained in the Laplace-Fourier transformed domain by using the eigenvalue approach. Considering the continuity conditions between adjacent layers, the global stiffness matrix of layered medium is gotten by assembling the interrelated layer-elements. Once the solution in the transformed domain is obtained, the actual solution can be recovered by an inverse transformation. Finally, numerical examples are given to study the influence of the layered medium’s properties on the behavior of thermoelastic problems.

##### MSC:

74F05 | Thermal effects in solid mechanics |

74B05 | Classical linear elasticity |

74G15 | Numerical approximation of solutions of equilibrium problems in solid mechanics |

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