Implementation of shear-locking-free triangular refined zigzag element for structural analysis of multilayered plates with curvilinear fibers

Modeling and analysis of composites with curvilinear fiber reinforcement is rather challenging in terms of ac-curacy and computational cost associated with variable material stiffness. In this study, to reduce the compu-tational cost drastically without sacrificing the numerical accuracy, variable stiffness composite laminate (VSCL) is modelled as a single layer based on the refined zigzag theory (RZT). To this end, a three-node triangle RZT element formulation is adopted and effectively implemented for static analysis of multilayer composites and sandwich plates with curvilinear fiber paths. Moreover, to accurately model the strains in VSCL, the derivatives of the zigzag functions with respect to planar coordinates are considered for each ply within the laminate in the RZT kinematic-strain relations. Enhanced capability of the present model is verified by performing compre-hensive numerical investigation on several benchmark cases. The obtained results are compared with those present in the literature and three-dimensional elasticity solutions. Hence, it is demonstrated that the triangular RZT element is a fast, robust, and accurate structural analysis platform that can potentially lend itself to the optimization of curvilinear fiber angles of VSCL.

Automated summary

In this study, a single-layer model based on the refined zigzag theory (RZT) is proposed to model variable stiffness composite laminates with curvilinear fiber reinforcement, which significantly reduces the computational cost while maintaining numerical accuracy. A three-node triangle RZT element formulation is adopted to accurately simulate the static analysis of multilayer composites and sandwich plates. The derivatives of the zigzag functions with respect to planar coordinates are considered to accurately model the strains in the variable stiffness composite laminate.