Application of Discrete Hamilton's Equation for Parallel Processing of Impact Problems

Abstract

Application of Hamilton’s theorem is limited to rigid body dynamics problems in spite of its benefit that always yield a set of first order differential equations as a model. From the fundamental formulation procedure, introduction of Hamilton’s principle to continuum problems differs from the traditional continuum modeling methodology that relies upon partial differential field equation. For the analysis of impact problems where highly nonlinear coupled models are norm, massively distributed computation schemes are usually employed and they significantly reduce computational cost and improve accuracy. With the parallel resources in mind, the present work applies Hamiltonian modeling approach to a shock propagation problem in continuous media. The formulated model which is in first order ordinary differential equations is efficiently calculated on a Beowulf based Linux parallel machines.