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Strong and weak formulations based on differential and integral quadrature methods for the free vibration analysis of composite plates and shells: Convergence and accuracy

机译：基于微分和积分求积分法的强弱公式用于复合板和壳的自由振动分析：收敛性和准确性

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摘要

The aim of this work is to investigate and compare the accuracy and convergence behavior of two different numerical approaches based on Differential Quadrature (DQ) and Integral Quadrature (IQ) methods, respectively, when applied to the free vibration analysis of laminated plates and shells. The numerical methods at issue allow to solve the strong and the weak forms of the governing equations of these structural elements. A completely general approach is presented to evaluate numerically derivatives and integrals by using several basis functions (polynomial approximation) and grid distributions (discretization). The convergence analyses are performed for three different approaches: Strong Formulation (SF), Weak Formulation (WF) withC1continuity conditions, and Weak Formulation (WF) withC0continuity conditions. For each approach, a set of convergence graphs is shown, by varying both basis functions and discrete grids, in order to define the combinations that provide the best accuracy with reference to the exact solutions available in the literature.
机译：这项工作的目的是研究和比较两种分别基于差分正交（DQ）和积分正交（IQ）方法的不同数值方法在层压板和壳体的自由振动分析中的准确性和收敛性。所讨论的数值方法可以解决这些结构要素的控制方程的强形式和弱形式。通过使用几个基函数（多项式逼近）和网格分布（离散化），提出了一种完全通用的方法来评估数值导数和积分。对三种不同的方法执行了收敛性分析：强公式（SF），具有C1连续性条件的弱公式（WF）和具有C0连续性条件的弱公式（WF）。对于每种方法，都通过改变基函数和离散网格来显示一组收敛图，以便参考文献中提供的确切解决方案来定义提供最佳精度的组合。

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