Thermo-Mechanical analysis of laminated Doubly-Curved Shells: Higher order Equivalent Layer-Wise formulation

Abstract

The paper presents a refined two-dimensional formulation for the thermo-mechanical analysis of laminated doubly-curved shell structures under thermodynamic equilibrium conditions. Both the kinematic configuration variables and the temperature variation with respect to the natural equilibrium state are described with a generalized formulation, following the Equivalent Layer-Wise (ELW) approach employing higher order polynomials, along with some proper zigzag functions. The governing equations are derived from the stationary configuration of the Helmholtz free energy of the system, and a semi-analytical solution is found. In the post-processing phase, the Fourier-based Generalized Differential Quadrature (F-GDQ) is applied to recover the actual three-dimensional response of the doubly-curved shell solid, and very accurate results are obtained for the quantities of both mechanical and heat conduction problems. In addition, the integrals occurring in the theory are performed numerically with the Taylor-based Generalized Integral Quadrature (GTIQ), showing a high level of accuracy with a reduced number of sample points. The model is validated in some case studies, where the accuracy of the model is shown, and the numerical predictions are successfully compared with those ones from refined three-dimensional numerical simulations. After that, an extensive set of parametric investigations is reported, pointing out the effects of the panel curvature, lamination schemes and different levels of coupling on the thermo-mechanical structural behavior of the investigated panels.