Abstract
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.
Highlights
Multi-layered composite structures are widely used in engineering fields such as the automotive, aerospace, marine, sports and health sectors
Providing a robust and efficient tool, with advanced modelling and numerical techniques, is one of the major challenges in the field of computational mechanics, as the following issues must be addressed: 1. Severe transverse shear deformations due to high orthotropy ratio (E11/G13), which increases the channelling of axial stresses [1], a phenomenon not captured by models with simple kinematics assumptions
From the results presented it is evident that the UFSLE model is capable of accurate stress predictions compared to the HR3-RZT
Summary
Multi-layered composite structures are widely used in engineering fields such as the automotive, aerospace, marine, sports and health sectors. For a model to be suitable, it must be able to analyse structures subjected to a variety of realistic loads and boundary conditions It is because of the aforementioned complexities, amongst others, that high-fidelity finite element methods (FEM) are often employed to obtain reliable three-dimensional (3D) stress analyses with the desired level of accuracy. They are inadequate for capturing accurate three-dimensional ply-level stresses This shortcoming is due to the displacement field approximation, which predicts continuous transverse strains across the interface of different material laminates. Employing zig-zag functions within the ESL model yields fairly accurate global stress results It fails to predict accurate ply level stress responses when employed for sandwich structures with large face-tocore stiffness ratios and thick laminates with general layups [13]. Let θ denote the fibre orientation angle and the subscript k be used to refer to layer k
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