Lagrangian Bond Graphs for Solid Continuum Dynamics Modeling

Abstract

The limitations of existing continuum bond graph modeling techniques have effectively precluded their use in large order problems, where nonrepetitive graph structures and causal patterns are normally present. As a result, despite extensive publication of bond graph models for continuous systems simulations, bond graph methods have not offered a viable alternative to finite element analysis for the vast majority of practical problems. However, a new modeling approach combining Lagrangian (mass fixed) bond graphs with a selected finite element discretization scheme allows for direct simulation of a wide range of large order solid continuum dynamics problems. With appropriate modifications, including the use of Eulerian (space fixed) bond graphs, the method may be extended to include fluid dynamics modeling.