Accurate recovery of 3D local field in FRP laminated beam based on asymptotic dimension reduction model

Abstract Accurate prediction of local field distribution plays an important role in failure analysis of FRP laminates. Based on the variational asymptotic method (VAM), a asymptotic dimensional reduction model (ADRM) of FRP laminated beams that can be implemented in standard finite element programs is developed, which provides a novel idea for local field recovery of FRP laminated beams. The present theory formulates the original 3D elasticity problem in a variational form, which is applicable for arbitrarily large displacement and global rotation. Then, the unknown 3D warping functions are solved asymptotically by the ADRM, resulting in the classical model (zero-order approximation) and asymptotically correct refined model (first-order approximation), respectively. Finally, the refined model is casted into a generalized Timoshenko beam model (GTM) using equilibrium equations, which can be applied conveniently in real applications. Numerical examples of FRP laminated I-beams and box-beams show that the local field distributions obtained from GTM are in good agreement with those of finite element analysis, while the computational cost and modeling effort of VAM-based analysis are significantly lower than those of direct finite element analysis.