A 2D equivalent single-layer formulation for the effect of transverse shear on laminated plates with curvilinear fibres
A 2D equivalent single-layer formulation for the effect of transverse shear on laminated plates with curvilinear fibres
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DOI：
10.1016/j.compstruct.2013.01.014
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发表时间：
2013-06
影响因子：
6.3
通讯作者：
R. Groh;P. Weaver;S. White;G. Raju;Zhangming Wu
中科院分区：
文献类型：
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作者：
R. Groh;P. Weaver;S. White;G. Raju;Zhangming Wu
Hellinger-Reissner混合变分原理与拉格朗日乘数相结合，使用简化的二维公式来模拟变刚度层合板弯曲时的横向剪切应力。研究了横向剪应力对变角拖曳层合板弯曲挠度的影响。新公式具有多个剪切修正因子，这些剪切修正因子是弯曲刚度项Dij，它们的一阶和二阶导数以及Timoshenko剪切因子χ的函数。利用微分正交法（DQM）以强形式求解了新的控制方程组，并通过二维“厚”壳和三维高保真有限元模型验证了求解技术的准确性和鲁棒性。导出的理论在捕获横向剪切效应方面优于“厚”二维壳模型，并且与实际工程层合板厚度范围内的全三维解决方案相比具有良好的精度。对于非常薄的结构，导出的方程退化为经典层压分析，但当跨度与厚度比为10:1时，差异高达43%。最后，所研究的特定增值板比相应的均匀准各向同性层压板更受横向剪切变形的影响。
The Hellinger–Reissner mixed variational principle in conjunction with Lagrange multipliers is used to model transverse shear stresses, in bending of variable stiffness laminated plates, using a reduced two-dimensional formulation. The effect of transverse shear stresses on the bending deflection of variable angle tow (VAT) laminates is assessed. The novel formulation features multiple shear correction factors that are functions of the bending rigidity terms Dij, their first and second derivatives and the Timoshenko shear factor χ. The new set of governing equations are solved, in their strong form, using the Differential Quadrature Method (DQM) and the accuracy and robustness of the solution technique verified using a 2D “thick” shell and 3D high-fidelity finite element model. The derived theory is superior to the “thick” 2D shell model in capturing transverse shear effects and shows good accuracy compared to the full 3D solution for thicknesses within the range of practical engineering laminates. The derived equations degenerate to Classical Laminate Analysis for very thin configurations but discrepancies as large as 43% are observed for span-to-thickness ratios of 10:1. Finally, the specific VAT panels under investigation are affected more by transverse shear deformation than a corresponding homogeneous quasi-isotropic laminate.