Refined shell elements for the analysis of functionally graded structures

The present paper considers the static analysis of plates and shells made of Functionally Graded Material (FGM), subjected to mechanical loads. Refined models based on the Carrera's Unified Formulation (CUF) are employed to account for grading material variation in the thickness direction. The governing equations are derived from the Principle of Virtual Displacement (PVD) in order to apply the Finite Element Method (FEM). A nine-nodes shell element with exact cylindrical geometry is considered. The shell can degenerate in the plate element by imposing an infinite radius of curvature. The Mixed Interpolation of Tensorial Components (MITC) technique is extended to the CUF in order to contrast the membrane and shear locking phenomenon. Different thickness ratios and orders of expansion for the displacement field are analyzed. The FEM results are compared with both benchmark solutions from literature and the results obtained using the Navier method that provides the analytical solution for simply-supported structures subjected to sinusoidal pressure loads. The shell element based on refined theories of the CUF turns out to be very efficient and its use is mandatory with respect to the classical models in the study of FGM structures

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 nite element with variable through-the-thickness kinematic. The re- ned models used are both Equivalent Single Layer (ESL) and Layer Wise (LW) and they are grouped in the Unied Formulation by Carrera (CUF). These models permit the distribution of displacements, stresses and temperature along the thickness of the multi- layered 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 phe- nomenon 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 dierent theories con- tained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using higher-order models and the Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very ef- cient, and its use leads to reach higher accuracy than classical models in the study of layered structures