Vibration of thick plates using finite strip-elements
by
J. Petrolito
La Trobe University, Bendigo
Coauthors: B.W. Golley {Australian Defence Force Academy}

Finite strips have been successfully used for the analysis of plates for some thirty years. For problems which are amenable to analysis, finite strips have a number of advantages over finite elements. Originally, the method was developed for analysing thin rectangular plates with two opposite edges simply supported. In this case the global equations uncouple into a number of smaller systems of equations owing to certain orthogonality relationships resulting from the chosen displacement functions. This leads to a reduction in core requirements and an increase in computational efficiency when compared with the finite element procedure. Later work enabled other boundary conditions to be treated. However, in all other cases uncoupling of the equations does not occur, thereby reducing some of the computational efficiency of the method. In addition, the shape functions used in the finite strip method do not satisfy free edge boundary conditions.

In this paper, we consider the use of finite strip-elements for the vibration analysis of thick plates. Finite strip-elements combine shape functions of finite elements and finite strips. For a finite strip-element in the xy plane, the shape functions are obtained as the product of combined trigonometric and polynomial functios in the x direction and polynomial functions in the y direction. The simplest displacement approximation within the finite strip-element is obtained by using a linear approximation in the y direction. Higher-order approximations in the y direction can be achieved by using internal nodal lines. The formulation of the strip-element stiffness equations follows standard finite element techniques.

The advantages of this approach include the following.

1.

By using trigonometric and polynomial functions to describe displacements, computational problems associated with hyperbolic functions with large arguments that arise with conventional finite strips are avoided.

2.

Mixed boundary conditions are simply treated, with the free edge condition being approximately satisfied as a natural boundary condition.

Date received: July 23, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-39.