3D semi-analytical solution of hygro-thermo-mechanical multilayered doubly-curved shells

In this paper, a three-dimensional bending solution of doubly-curved shells subjected to mechanical, thermal and hygrothermal load is studied. Through-the-thickness temperature of the shell is modeled by Fourier's heat conduction equation. Fick's moisture diffusion law equation is used to determine the hygro-thermal profile through-the-thickness. The partial differential equations are solved by using the Navier closed form summations which are valid only for shells with constant radii of curvature among the midsurface and with simply supported boundary conditions on its shell's edges. The shell governing equations are solved by discretizing the thickness profile via Legendre's grid distribution and by using the Differential Quadrature Method (DQM). The Layerwise capabilities of the method is guaranteed by imposing the inter-laminar continuity of out-of-the-plane stresses, displacements, temperature and hygrothermal load thickness profile. The zero-stress condition for the transverse shear stresses is imposed due to the fact that no mechanical loads are applied in those directions. Results for cylindrical, spherical panels and rectangular plates are presented. Comparisons are made with Layerwise and three-dimensional solutions available in literature. The results have strong accuracy and a benchmark problem is delivered.