Computer algebra for the formation of structural matrices of piezoceramic finite elements

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. The efficiency of computer algebra application was compared here with the numerical integration methods of forming the structural matrices of the finite elements. To this end, the computer algebra system VIBRAN was used. Two popular finite elements for modelling piezoceramic actuators of the sector-type and the triangular one are discussed. All structural matrices of the elements were derived, using the computer algebra technique with the following automatic program code generation.