Extended framework of Hamilton's principle for continuum dynamics

Jinkyu Kim, Gary F. Dargush, Young Kyu Ju

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)3418-3429
Number of pages12
JournalInternational Journal of Solids and Structures
Issue number20-21
Publication statusPublished - 2013 Oct 1


  • Continua dynamics
  • Hamilton's principle
  • Initial conditions
  • Mixed formulation
  • Non-iterative algorithm
  • Space-time finite element

ASJC Scopus subject areas

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


Dive into the research topics of 'Extended framework of Hamilton's principle for continuum dynamics'. Together they form a unique fingerprint.

Cite this