Variable kinematic shell elements for composite laminates accounting for hygrothermal effects

This article presents advanced shell models for the steady-state hygrothermal analysis of composite laminates. The Carrera Unified Formulation is used to derive refined models that include both layer-wise and equivalent single layer models. The governing equations are derived from the principle of virtual displacement taking into account thermal and hygroscopic effects. The geometrical relations for the exact cylindrical geometry are here considered. Through-the-thickness variations of temperature and moisture concentration are calculated by solving the Fourier equation and the Fick law, respectively. The mixed interpolation of tensorial component method is applied to a nine-node shell element to contrast the membrane and shear locking phenomena. Simply supported cross-ply cylindrical shells with antisymmetrical lamination subjected to bisinusoidal thermal/hygroscopic loads are analyzed considering various thickness/curvature ratios. Results obtained with assumed linear and calculated temperature/hygroscopic profiles are presented. Variable kinematics are compared regarding both accuracy and computational costs. The results show that all the kinematics can approximate the transverse shear stress distribution through the thickness with satisfactory accuracy when sufficient expansion terms are adopted. In some cases, miscellaneous expansions can lead to significant reductions in computational costs. The results presented here can be used as benchmark solutions for future works.