Thermal stress analysis of laminated structures by a variable kinematic MITC9 shell element

A linear static thermal stress analysis of composite shell structures is carried out by means of a shell finite element with variable through-The-Thickness kinematic. The refined models used are both Equivalent Single Layer (ESL) and Layer Wise (LW) and they are grouped in the Unified Formulation by Carrera (CUF). These models permit the distribution of displacements, stresses and temperature along the thickness of the multilayered shell to be accurately described. The Principle of Virtual Displacement (PVD) is employed to derive the governing equations. The Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon for a nine-node shell element. Cross-ply plate, cylindrical and spherical shells with simply supported edges and subjected to bi-sinusoidal thermal load are analyzed and various thickness ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using higher-order models and Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very efficient, and its use leads to reach higher accuracy than classical models in the study of layered structures.