On displacement-based and mixed-variational equivalent single layer theories for modelling highly heterogeneous laminated beams

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:59

Article

Groh, R. M. J.¹  Weaver, P. M.¹ 

[1] Univ Bristol, Adv Composites Ctr Innovat & Sci, Bristol BS8 1TR, Avon, England

关键词: Laminated structures;    Sandwich beams;    Zig-zag theory;    Transverse shear and normal deformation;   

DOI  :  10.1016/j.ijsolstr.2015.01.020

来源: Elsevier

【 摘 要 】

The flexural response of laminated composite and sandwich beams is analysed using the notion of modelling the transverse shear mechanics with an analogous mechanical system of springs in series combined with a system of springs in parallel. In this manner a zig-zag function is derived that accounts for the geometric and constitutive heterogeneity of the multi-layered beam similar to the zig-zag function in the refined zig-zag theory (RZT) developed by Tessler et al. (2007). Based on this insight a new equivalent single layer formulation is developed using the principle of virtual displacements. The theory overcomes the problem in the RZT framework of modelling laminates with Externally Weak Layers but is restricted to laminates with zero B-matrix terms. Second, the RZT zig-zag function is implemented in a third-order theory based on the Hellinger-Reissner mixed variational framework. The advantage of the Hellinger-Reissner formulation is that both in-plane and transverse stress fields are captured to within 1% of Pagano's 3D elasticity solution without the need for additional stress recovery steps, even for highly heterogeneous laminates. A variant of the Hellinger-Reissner formulation with Murakami's zig-zag function increases the percentage error by an order of magnitude for highly heterogeneous laminates. Corresponding formulations using the Reissner Mixed Variational Theory (RMVT) show that the independent model assumptions for transverse shear stresses in this theory may be highly inaccurate when the number of layers exceeds three. As a result, the RMVT formulations require extra post-processing steps to accurately capture the transverse stresses. Finally, the relative influence of the zig-zag effect on different laminates is quantified using two non-dimensional parameters. (C) 2015 The Authors. Published by Elsevier Ltd.

【 授权许可】

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