A hygrothermal stress finite element analysis of laminated beam structures through hierarchical one-dimensional modeling

A new multi-field beam model based on Carrera’s Unified Formulation (CUF) is offered in this article to efficiently solve the hygro-thermal-mechanical problem of beam structures with high-fidelity. Several beam models have been hierarchically derived in the framework of CUF with consideration of the hygro-thermal stresses. By adopting the principle of virtual displacement, the element stiffness matrix can be derived into a compact form. The temperature and humidity profile is generated from the Fourier’s heat conduction and Fick’s law, respectively. With simply supported and cantilever configurations being adopted, hygro-mechanical and hygro-thermal-mechanical analyses are carried out for different beam slenderness ratios. Results are provided in terms of three-dimensional displacement and stress distributions. The proposed one-dimensional CUF-based beam model has been validated against traditional three-dimensional FEM-based solutions, and an excellent correlation has been achieved. It is found that an accurate result can be obtained through the proposed CUF-based beam model with reduced computational costs.