City Research Online

Layer-wise dynamic stiffness solution for free vibration analysis of laminated composite plates

Boscolo, M. & Banerjee, J. R. (2014). Layer-wise dynamic stiffness solution for free vibration analysis of laminated composite plates. Journal of Sound and Vibration, 333(1), pp. 200-227. doi: 10.1016/j.jsv.2013.08.031

Abstract

The dynamic stiffness method has been developed by using a sophisticated layer-wise theory which complies with the Cz0 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.

Publication Type: Article
Additional Information: © 2013, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Dynamic stiffness method, benchmark solutions, Layer-wise theory, composites, free vibration analysis, Carrera Unified Formulation
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments: School of Science & Technology > Engineering
SWORD Depositor:
[thumbnail of JSV-2014 Layerwise paper MB-RB 2013.pdf]
Preview
Text - Accepted Version
Available under License : See the attached licence file.

Download (4MB) | Preview
[thumbnail of Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence]
Preview
Text (Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence) - Other
Download (201kB) | Preview

Export

Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login