Some Results on Thermal Stress of Layered Plates and Shells by Using Unified Formulation

Abstract

This work presents some results on two-dimensional modelling of thermal stress problems in multilayered structures. The governing equations are written by referring to the Unified Formulation (UF) introduced by the first author. These equations are obtained in a compact form, that doesn't depend on the order of expansion of variables in the thickness direction or the variable description (layer-wise models and equivalent single layers models). Classical and refined theories based on the Principle of Virtual Displacements (PVD) and advanced mixed theories based on the Reissner Mixed Variational Theorem (RMVT) are both considered. As a result, a large variety of theories are derived and compared. The temperature profile along the thickness of the plate/shell is calculated by solving the Fourier's heat conduction equation. Alternatively, thermo-mechanical coupling problems can be considered, in which the thermal variation is influenced by mechanical loading. Exact closed-form solutions are provided for plates and shells, but also the applications of the Ritz method and the Finite Element Method (FEM) are presented.

Keywords:

• Coupled and uncoupled
• Finite Element Method
• Plates and shells
• Ritz formulation
• Thermal stress
• Unified Formulation

Notes

Comparison between assumed and calculated temperature profiles. for advanced mixed theories formulated on the basis of RMVT.

Comparison between assumed and calculated temperature profiles. for classical theories formulated on the basis of PVD.

Cylindrical shell (0°/90°) with thickness ratio a/h = 10. Equivalent single-layer theories. Transverse displacement .

Cylindrical shell (0°/90°) with thickness ratio a/h = 10. Layer-wise theories. Transverse displacement .

Spherical shell (0°/core/0°) with thickness ratio a/h = 4 and a/h = 100. Equivalent single-layer theories. Transverse displacement .

Spherical shell (0°/core/0°) with thickness ratio a/h = 4 and a/h = 100. layer-wise theories. Transverse displacement .

Spherical shell (0°/90°/core/90°/0°) with thickness ratio a/h = 4. Equivalent Single Layer theories. Transverse displacement .

Spherical shell (0°/90°/core/90°/0°) with thickness ratio a/h = 4. layer-wise theories. Transverse displacement .

Out of plane displacement results. Errors measured with regards to [44].

Out of plane displacement results.