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Free vibration of laminated beams and stiffened plates using a high-order element

Published online by Cambridge University Press:  04 July 2016

Abhijit Mukherjee
Abhijit Mukherjee*
Affiliation:
Institute for Computer Applications, University of Stuttgart, Germany
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Abstract

Free vibration analysis of laminated composite beams, plates and stiffened plates using the finite element method has been presented. To give due importance to the shear deformation in composite materials, a high-order element which considers the quadratic variation of shear strain along the thickness of the element has been developed. The element has been developed using the quadratic isoparametric shape functions. Therefore, it can accommodate curved boundaries. Moreover, the stiffener element can have an arbitrary planform and it need not pass through any nodal point. The stiffener element has been developed in such a fashion to make the mesh division free from the location of the stiffener. This is extremely advantageous for optimisation of the path of the stiffener in a stiffened plated structure, while it is not necessary to modify the mesh division whenever the stiffener path is modified. Two different shape functions — the eight-node Serendipity and the nine-node Lagrangian — have been employed and a comparison between their performances has been presented. Two schemes for the generation of mass matrix, namely the lumped mass scheme and the consistent mass scheme, have been developed. The elements have been implemented in the ASKA element library and they can be used along with any standard ASKA element.

Type
Research Article
Information
The Aeronautical Journal , Volume 95 , Issue 944 , April 1991 , pp. 124 - 131
Copyright
Copyright © Royal Aeronautical Society 1991 

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Footnotes

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Present address: Department of Civil Engineering, Indian Institute of Technology, Bombay, India.

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