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Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials

机译：基于Chebyshev多项式的精细理论的层合梁静，自由振动分析。

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摘要

This paper presents a new class of refined beam theories for static and dynamic analysis of composite structures. These beam models are obtained by implementing higher-order expansions of Chebyshev polynomials for the three components of the displacement field over the beam cross-section. The Carrera Unified Formulation (CUF) is adopted to obtain higher-order beam models. The governing equations are written in terms of fundamental nuclei, which are independent of the choice of the expansion order and the interpolating polynomials. Static and free vibration analysis of laminated beams and thin-walled boxes has been carried out. Results obtained with the novel Chebyshev Expansion (CE) model have been compared with those available in the literature. For comparison, Taylor-like Expansion (TE) and Lagrange Expansion (LE) CUF models, commercial codes, analytical and experimental data are exploited. The performances of refined beam models in terms of computational cost and accuracy in comparison to the reference-solutions have been assessed. The analysis performed has pointed out the high level of accuracy reached by the refined beam models with lower computational costs than 2D and 3D Finite Elements. (C) 2015 Elsevier Ltd. All rights reserved.
机译：本文提出了一种用于组合结构静力和动力分析的新型细化梁理论。这些梁模型是通过对梁截面上的位移场的三个分量实施切比雪夫多项式的高阶展开而获得的。采用Carrera统一公式（CUF）获得高阶光束模型。控制方程是根据基本核写的，基本核与展开阶数和插值多项式的选择无关。进行了层合梁和薄壁箱的静，自由振动分析。使用新颖的Chebyshev扩展（CE）模型获得的结果已与文献中的结果进行了比较。为了进行比较，利用了泰勒式膨胀（TE）和拉格朗日膨胀（LE）CUF模型，商业代码，分析和实验数据。与参考解决方案相比，已评估了精化光束模型在计算成本和准确性方面的性能。进行的分析指出，精简的光束模型可以以比2D和3D有限元更低的计算成本达到很高的精度。 （C）2015 Elsevier Ltd.保留所有权利。

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