| The problem under consideration is the representation of thermomechanical processes in continuous media in the form of discrete networks. Specifically, a generalization of the standard bond graph notation is used to reticulate the material forms of the mixed problems in nonlinear hyperelasticity, nonlinear thermoelasticity, and nonlinear thermoviscoelasticity. These generalized bond graph reticulations are developed from conjugate variable approximations of specialized forms of the constitutive relations, the field and energy relations, and the boundary and initial conditions. A number of boundary conditions are considered here so that these reticulations may be incorporated into larger overall systems that contain both continuous and inherently discrete components.;The conjugate variable approximations used to develop the generalized bond graph reticulations yield systems of state equations that are identical in form to those obtained through the use of the Ritz-method, the Galerkin method, or other types of weighted residual methods. As a consequence, the guidelines for selecting basis functions that have been developed for these other methods are also applicable to the generalized bond graph method. In particular, most of the basis selection results from the theory of Galerkin finite elements apply with equal validity to the generalized bond graph case. Several examples of the use of these results are presented for illustration.;A major advantage of the generalized bond graph technique is that complex systems consisting of both continuous and inherently discrete components can be represented in a uniform fashion. In addition, the formulation of a set of first order state equations, in terms of physically significant variables, is obtained directly from the causally assigned bond graph. Finally, rational model simplification is possible through the use of power level comparisons. |
