Extended framework of Hamilton’s principle for continuum dynamics

Abstract

Hamilton’s principle is the variational principle for dynamical systems, and it has been widely used in mathematical physics and engineering. However, it has a critical weakness, termed end-point constraints, which means that in the weak form, we cannot use the given initial conditions properly. By utilizing a mixed formulation and sequentially assigning initial conditions, this paper presents a novel extended framework of Hamilton’s principle for continuum dynamics, to resolve such weakness. The primary applications lie in an elastic and a J2-viscoplastic continuum dynamics. The framework is simple, and initiates the development of a space–time finite element method with the proper use of initial conditions. Non-iterative numerical algorithms for both elasticity and J2-viscoplasticity are presented.