Published: 30 June 2011

Formation of structural matrices for finite elements of piezoceramic structures

R. Bansevicius1
A. Cepulkauskas2
R. Kulvietiene3
G. Kulvietis4
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Abstract

This paper deals with the description of a theoretical background of systematic computer algebra methods for the formation of structural matrices of piezoceramic finite elements. Piezoceramic actuators are widely used for high-precision mechanical systems such as positioning devices, manipulating systems, control equipment, etc. In this paper, the efficiency of computer algebra application was compared with the numerical integration methods of formation of the structural matrices of the finite elements. Two popular finite elements are discussed for modeling piezoceramic actuators: sector type and the triangular one. All structural matrices of the elements were derived using the computer algebra technique with the following automatic program code generation. Due to smaller floating point operations, the computer time economy is followed by an increased accuracy of computations, which is the most important gain achieved in many cases.

About this article

Received
24 April 2011
Accepted
15 May 2011
Published
30 June 2011
Keywords
computer algebra
structural matrices
piezoactive materials
piezoceramic structures