Plane strain and three-dimensional analyses for thermo-mechanical behavior of multilayered transversely isotropic materials

• Thermo–mechanical behavior of layered transversely isotropic material is studied.
• An extended precise integration model is built in the transformed domain.
• The actual solutions are obtained by numerical inverse of Laplace–Fourier transform.
• The effects of heat source’s shapes, mechanical and thermal parameters are analyzed.

An extended precise integration model for analysis of thermo-mechanical behavior of multilayered transversely isotropic materials in Cartesian coordinate system is established in this paper. From the governing equations of plane strain and three-dimensional transversely isotropic thermo-elastic materials, ordinary differential equations are derived by employing Laplace–Fourier transform. An extended precise integration model is built and solved in the transformed domain by extending the precise integration method (PIM) to multilayered thermo-elastic material system, and the actual solutions are obtained by adopting numerical quadrature schemes for the Laplace–Fourier transform inversion. The accuracy and feasibility of the proposed model is demonstrated by selected numerical examples, and then the influences of heat source’s shapes, layering, mechanical and thermal parameters of the transversely isotropic material on thermo-mechanical response are investigated.