Numerical Analysis of Cross-Laminated Timber Panels Under Three-Point Bending Using Laminate Theory

Cross-laminated timber (CLT) panels, composed of orthogonally bonded layers, are often used in civil engineering and tall constructions owing to their sustainability, prefabrication advantages and favourable mechanical performance. However, their multilayered, anisotropic and shear-compliant nature presents significant challenges for accurate structural modelling and performance prediction. This study presents an advanced numerical approach to analysing the bending behaviour of CLT panels using the finite element method (FEM) in combination with the classical laminate theory. The proposed plate model was implemented in FlexPDE and validated through a series of three-point bending experiments on three-layer spruce panels. Further verification was conducted using commercial FEM software-Dlubal, incorporating both linear elastic and non-linear damage models, and Abaqus, where a three-dimensional solid model with a cohesive zone formulation captured progressive delamination and local failure in the glued layers. Comparison of the experimental data and numerical simulations revealed strong agreement in load-deflection behaviour, stiffness evolution and damage localisation. The framework we developed accurately reproduces both the global and the local mechanical responses of CLT panels while maintaining computational efficiency. Our results confirm the reliability of laminate theory-based FEM formulations in the design, optimisation and safety assessment of cross-laminated timber structures in building applications.