Exact solution of thermo-mechanical analysis of laminated composite and sandwich doubly-curved shell

Abstract

This paper presents an exact solution for doubly-curved shells subjected to thermal loads. The solution is based on equilibrium equations. The through-the-thickness shell temperature is calculated using the Fourier’s heat conduction equation. The governing equations for displacement and temperature are solved using Navier method, which is valid for shell panels with constant curvature and simply-supported edges. The governing equations for temperature and displacements are in term of the thickness variable and they are solved using the differential quadrature method (DQM). The structures are discretized by each layer applying the Chebyshev-Gauss-Lobatto grid distribution. Lagrange interpolation polynomials are used as basis functions. The inter-laminar continuity of transverse stresses and displacements is imposed. The out-of-plane zero-stresses condition are imposed at the top and bottom of the shell since no mechanical loadings are considered in the presented study. The results for spherical, cylindrical and rectangular plates are presented. The results demonstrate the capability of DQM to produce 3D elasticity when compared with other highly accurate available solutions. Consequently, the method can be used to solve multifield problems in continuum mechanics.