Effects of Transverse Normal Stress on Hygrothermomechanical Analysis of Laminated Shallow Shells

Hygrothermomechanical analysis of doubly curved laminated composite shallow shells is presented in this paper using a two-dimensional higher-order shell theory considering the effects of transverse normal stress. The present theory accounts for the fifth-order expansion of the thickness coordinates in the in-plane displacements and the fourth-order expansion in the transverse displacement. The main focus of this work is to study the effects of both transverse normal stress and the fifth-order expansion of thickness coordinates on the hygrothermomechanical responses of doubly curved laminated shallow shells. The governing equations of the theory are derived based on the principle of virtual work and solved by using Navier's method. The theory ensures traction-free boundary conditions using constitutive relations and does not require a shear correction factor. Interlaminar transverse shear stresses are recovered using the three-dimensional equilibrium equations of the theory of elasticity to ascertain the stress continuity at the layer interface. Three-dimensional elasticity solutions are taken as a basis for comparing the present results in thermal problems, whereas this study contributes some useful results to the hygrothermomechanical analysis of doubly curved laminated composite shallow shells.