Volume 20, Issue 4, 2011

FULL ARTICLE: ANALYTICAL AND FINITE ELEMENT MODELLING OF CIRCULAR GLARE PLATES UNDER INDENTATION LOADING AND UNLOADING

George J. Tsamasphyros and George S. Bikakis*

Strength of Materials Laboratory, National Technical University of Athens, 9 Iroon Polytechniou, Zographou, GR 157 73, Athens, Greece

*Author to whom correspondence should be addressed, e-mail: bikakis.george@yahoo.com

Received 5 February 2011; accepted 28 July 2011

ABSTRACT

In this paper, analytical expressions are derived and a finite element modelling procedure is proposed in order to predict the static load-indentation curves of circular GLARE fibre-metal laminates during loading and unloading by a hemispherical indentor. Analytical formulas have been recently published for the static indentation of circular GLARE plates which are now used during the loading stage. Here, considering that aluminum layers are in a state of membrane yield and employing energy balance during unloading, the unloading path is determined. Using this unloading path, an algebraic equation is derived and solved for calculating the permanent dent depth of the GLARE plate after the indentor’s withdrawal. ANSYS software is used and a non-linear analysis is employed with geometric and material non-linearities for FEM calculations. The derived formulas and the proposed finite element modelling procedure are applied to GLARE 2-2/1-0.3 and to GLARE 3-3/2-0.4 circular plates. The analytical results are compared with corresponding FEM results and a good agreement is found. The analytically calculated permanent dent depth is within 6 % for the GLARE 2 plate, and within 7 % for the GLARE 3 plate, of the corresponding numerically calculated result. No other solution of this problem is known to the authors.

Keywords:GLARE, fibre-metal laminate, indentation, FEM, circular plate, unloading, dent.