Finite Element local structure assembly and shape functions influence on bond graph modelling

摘要

Among the distributed parameters systems (DPS) modelling methods the finite elements methods (FEM) are nowadays the most used. This preference is mainly due to their simplicity and their easy implementation to most of the applications. The aim of this paper is to study the impact of the choice of the mesh functions and of the modelling procedure on the Bond Graph representation of a distributed parameter system. It is shown that the structure of the bond graph representation using FEM the structure is unchanged if the shape functions are changed. The difference is only visible in the form of the constitutive matrix of the multi-ports of the Bond Graph representation. Since the Bond Graph approach presents the advantage to ease the structural study of a system using the causality or bicausality concepts, our goal is here to investigate the consequence of the shape functions choice and of the modelling procedure when inverse problems of systems including distributed parameter systems are considered. A new modelling procedure is introduced that focuses on the elementary cell analysis and on the bond graph representation before assembling the whole mesh and applying the boundary conditions. The impact of the different choices are then discussed considering commonly used polynomial shape functions.