Extended framework of Hamilton’s principle for continuum dynamics

• Published in: International journal of solids and structures Vol. 50; no. 20-21; pp. 3418 - 3429
• Main Authors: Kim, Jinkyu, Dargush, Gary F., Ju, Young-Kyu
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2013
• Subjects: Continua dynamics; Continuums; Dynamical systems; Dynamics; Hamilton's principle; Initial conditions; Mathematical analysis; Mathematical models; Mixed formulation; Non-iterative algorithm; Space–time finite element; Variational principles; Non-iterative algorithm; Initial conditions; Hamilton’s principle; Continua dynamics; Mixed formulation; Space–time finite element
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2013.06.015

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.