Analytical Solutions for Thermo-Mechanical Coupling Bending of Cross-Laminated Timber Panels

Abstract

This study presents analytical solutions grounded in three-dimensional (3D) thermo-elasticity theory to predict the bending behavior of cross-laminated timber (CLT) panels under thermo-mechanical conditions, incorporating the orthotropic and temperature-dependent properties of wood. The model initially utilizes Fourier series expansion based on heat transfer theory to address non-uniform temperature distributions. By restructuring the governing equations into eigenvalue equations, the general solutions for stresses and displacements in the CLT panel are derived, with coefficients determined through the transfer matrix method. A comparative analysis shows that the proposed solution aligns well with finite element results while offering superior computational efficiency. The solution based on the plane section assumption closely matches the proposed solution for thinner panels; however, discrepancies increase as panel thickness rises. Finally, this study explores the thermo-mechanical bending behavior of the CLT panel and proposes a modified superposition principle. The parameter study indicates that the normal stress is mainly affected by modulus and thermal expansion coefficients, while the deflection of the panel is largely dependent on thermal expansion coefficients but less affected by modulus.