Coupled thermo-mechanical finite element models with node-dependent kinematics for multi-layered shell structures

Node-dependent Kinematic (NDK) shell finite element (FE) formulations are presented for the steady-state thermo-mechanical analysis of laminated structures. The displacements and temperature change are treated as primary variables in the FE models and are directly solved through the coupled thermo-mechanical models. The enforcement of distributed temperature boundary conditions on the top or the bottom surface of hierarchical shell elements is conducted through the Linear Least Squares. The effectiveness of the proposed FE approaches is verified by comparing the results against those from the literature. The application of adaptive refinement approach based on the hierarchical elements and NDK to build FE models with optimal efficiency is demonstrated through numerical examples

Heat conduction and thermal stress analysis of laminated composites by a variable kinematic MITC9 shell element

The present paper considers the linear static thermal stress analysis of composite structures by means of a shell finite element with variable through-thethickness kinematic. The temperature profile along the thickness direction is calculated by solving the Fourier heat conduction equation. The refined models considered are both Equivalent Single Layer (ESL) and Layer Wise (LW) and are grouped in the Unified Formulation by Carrera (CUF). These permit the distribution of displacements, stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes, and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the Principle of Virtual Displacement (PVD). Cross-ply plate, cylindrical and spherical shells with simply-supported edges and subjected to bi-sinusoidal thermal load are analyzed.Various thickness ratios and curvature 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 the CUF and the Navier’s method. Finally, plates and shells with different lamination and boundary conditions are analyzed using high-order theories in order to provide FEM benchmark solutions