Hygrothermal analysis of multilayered composite plates by variable kinematic finite elements

Advanced plate models with variable kinematics for steady state hygrothermal analysis of composite laminates are proposed. The refined models discussed include both layer-wise (LW) and equivalent single layer (ESL) models, and the Carrera Unified Formulation (CUF) is used. The mixed interpolation of tensorial component (MITC) method is applied to a nine-node element to contrast the shear locking phenomena. The governing equations are derived from the principle of virtual displacement (PVD) taking into account elastic mechanical, thermal and hygroscopic effects. Through-the-thickness variations of temperature and moisture concentration are calculated by solving the Fourier equation and the Fick law, respectively. Cross-ply plates with symmetrical lamination and simply supported edges subjected to bisinusoidal thermal/hygroscopic loads are analyzed considering various thickness ratios. Results obtained with assumed linear and calculated temperature/hygroscopic profiles are compared. Variable kinematics with a variety of thickness functions are compared regarding both accuracy and computational costs. The results show that all the kinematics proposed 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.