Layer-wise dynamic stiffness solution for free vibration analysis of laminated composite plates
Layer-wise dynamic stiffness solution for free vibration analysis of laminated composite plates
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DOI：
10.1016/j.jsv.2013.08.031
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发表时间：
2014-01-06
影响因子：
4.7
通讯作者：
Banerjee, J. R.
中科院分区：
文献类型：
--
作者：
Boscolo, M.;Banerjee, J. R.
动态刚度方法是利用复杂的分层理论开发的，符合 C-z(0) 要求，并为层合复合材料板的分析提供高精度。该方法用途广泛，因为它以一种新颖的方式导出任意层数板的动态刚度矩阵，而无需在层数发生变化时重新导出和重新求解运动方程。这种操纵和求解运动方程的新颖程序在本文中被称为 L 矩阵方法。卡雷拉统一公式 (CUF) 用于通过首先使用单层板的一阶逐层假设来推导运动方程。然后该方法被推广并扩展到多层。本质上，通过将单层的运动方程写成 L 矩阵形式，可以以高效且自动的方式生成任意层数层压板的运动方程组。后续工作的一个显着特点是设计一种以封闭解析形式自动求解微分方程组的方法，然后获得层合板的动刚度矩阵。所开发的动态刚度单元已尽可能通过解析解（基于所有边缘简支板的纳维解）对相同的位移公式进行了验证。此外，动态刚度理论通过 3D 解析解（文献中很少提供）以及使用 NASTRAN 的有限元方法进行评估。该结果是首次获得精确意义上的结果，因此可以用作评估近似方法的基准解决方案。动态刚度方法的这一新发展将允许对几何复杂结构进行自由振动和响应分析，其计算效率和精度水平是使用其他方法不可能实现的。 (C) 2013 Elsevier Ltd. 保留所有权利。
The dynamic stiffness method has been developed by using a sophisticated layer-wise theory which complies with the C-z(0) requirements and delivers high accuracy for the analysis of laminated composite plates. The method is versatile as it derives the dynamic stiffness matrix for plates with any number of layers in a novel way without the need to re-derive and re-solve the equations of motion when the number of layers has changed. This novel procedure to manipulate and solve the equations of motion has been referred to as the L matrix method in this paper. The Carrera unified formulation (CUF) is employed to derive the equations of motion through the use of a first-order layer-wise assumption for a plate with a single layer first. The method is then generalised and extended to multiple layers. Essentially by writing the equations of motion of one single layer in the L matrix form, the system of equations of motion of a laminated plate with any number of layers is generated in an efficient and automatic way. A significant feature of the subsequent work is to devise a method to solve the system of differential equations automatically in closed analytical form and then obtain the ensuing dynamic stiffness matrix of the laminated plate. The developed dynamic stiffness element has been validated wherever possible by analytical solutions (based on Navier's solution for plates simply supported at all edges) for the same displacement formulation. Furthermore, the dynamic stiffness theory is assessed by 3D analytical solutions (scantly available in the literature) and also by the finite element method using NASTRAN. The results have been obtained in an exact sense for the first time and hence they can be used as benchmark solutions for assessing approximate methods. This new development of the dynamic stiffness method will allow free vibration and response analysis of geometrically complex structures with such a level of computational efficiency and accuracy that could not be possibly achieved using other methods. (C) 2013 Elsevier Ltd. All rights reserved.