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. © 2013 Elsevier Ltd. All rights reserved.
Kim, J., Dargush, G. F., & Ju, Y. K. (2013). Extended framework of Hamilton’s principle for continuum dynamics. International Journal of Solids and Structures, 50(20–21), 3418–3429. https://doi.org/10.1016/j.ijsolstr.2013.06.015