Computationally efficient beam elements for accurate stresses in sandwich laminates and laminated composites with delaminations

Laminated composites are prone to delamination failure due to the lack of reinforcement through the thickness. Therefore, during the design process the initiation and propagation of delaminations should be accounted for as early as possible. This paper presents computationally efficient nine degree-of-freedom (dof) and eight-dof shear locking-free beam elements using the mixed form of the refined zigzag theory (RZT(m)). The corresponding nine-dof and eight-dof elements use the anisoparametric and constrained anisoparametric interpolation schemes, respectively, to eliminate shear locking in slender beams. The advantage of the present element over previous RZT beam elements is that no post-processing is required to accurately model the transverse shear stress while maintaining the computational efficiency of a low-order beam element. Comparisons with high-fidelity finite element models and three-dimensional elasticity solutions show that the elements can robustly and accurately predict the displacement field, axial stress and transverse shear stress through the thickness of a sandwich beam or a composite laminate with an embedded delamination. In fact, the accuracy and computational efficiency of predicting stresses in laminates with embedded delaminations make the present elements attractive choices for RZT-based delamination initiation and propagation methodologies available in the literature.