Extended Bond Graph Representation of the Traction Problem in Linear Elastodynamics

Abstract

To illustrate the use of the extended bond graph notation, a reticulation is developed for a conjugate variable approximation of the traction problem in linear elastodynamics. This reticulation is general in the sense that all vector and tensor quantities are expressed using direct notation; that is, no specific coordinate system is chosen a priori. In addition, the only limitation placed upon the elasticity tensor C(X) is that it be symmetric. This allows homogeneous and inhomogeneous isotropic, orthotropic, etc., linearly elastic bodies to be modeled using these results. The conjugate approximations used here are entirely compatible with Galerkin based finite element methods. Consequently, this extended bond graph reticulation allows well-developed approximation techniques in solid mechanics to be directly incorporated into bond graph based system models.