Three-dimensional stress analysis for laminated composite and sandwich structures

Accurate stress prediction in composite laminates is crucial for safe design under different loading conditions. Classical laminated theory, i.e. those based on the Euler-Bernoulli and Kirchhoff hypotheses, respectively for beams and plates/shells are inaccurate for relatively thick laminates as three-dimensional (3D) effects such as transverse shear and normal deformations are neglected. Therefore, 3D finite element models are often employed for accurate stress analysis. However, these models are computationally expensive when used for laminates with a large number of layers, in optimisation studies, or for non-linear analyses. To address this issue, a Unified Formulation approach is presented for the analysis of laminated, slender beam-like structures. To define the kinematic field over the beam's cross-section, a recently developed hierarchical set of expansion functions, based on Serendipity Lagrange expansions, are employed and adapted to the layer-wise approach. The present formulation, which has displacements as degrees of freedom, does not ensure continuous transverse stresses across layer interfaces. Thus, an extra post-processing step is required to capture these stresses accurately. The proposed model is benchmarked against a 3D closed-form solution, 3D finite elements, and results available in the literature by means of static analyses of highly heterogeneous, laminated composite and sandwich beams. A key advantage of the present model is its ability to predict accurate 3D stress fields efficiently, including boundary layer regions, i.e. towards clamped ends. As a result, global analyses (e.g. overall displacements, buckling, etc.) and local analyses (e.g. stress concentrations) are combined within a single, computationally efficient model. The performance of the proposed approach, in terms of computational cost and precision, is assessed. Significant computational efficiency gains over 3D finite elements are observed for similar levels of accuracy.