A direct minimization technique for finding minimum energy configurations for beam buckling and post-buckling problems with constraints

Zhujiang Wang, Annie Ruimi, A. R. Srinivasa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We present a novel technique to simulate the deformation of a cantilever elastic beam constrained in a curved solid channel subject to end forces. We pose this as the minimization of an energy functional and solve it by a variant of a dynamic programming approach called the Viterbi algorithm. The core idea of this approach is to discretize the variables describing the potential energy and to construct a set of admissible configurations of the beam. The Viterbi algorithm is then employed to search through the set of possible beam configurations and locate the one with the minimum potential energy in a very computationally efficient way. The new approach does not require any gradient computations and could be considered as a direct search method, and thus can be guaranteed to find the global minimum potential energy. Also the constraints can be automatically satisfied by constructing the proper set of all the possible configurations. The approach can also be used to find feasible starting configurations associated with conventional minimizing algorithms.

Original languageEnglish
Pages (from-to)165-173
Number of pages9
JournalInternational Journal of Solids and Structures
Volume72
DOIs
Publication statusPublished - 15 Oct 2015
Externally publishedYes

Fingerprint

Postbuckling
buckling
Potential energy
Buckling
Viterbi algorithm
Viterbi Algorithm
Configuration
optimization
potential energy
configurations
Energy
Direct Search Method
Dynamic programming
dynamic programming
energy
Cantilever
Global Minimum
Energy Functional
Dynamic Programming
Gradient

Keywords

  • Beam
  • Buckling
  • Constraints
  • Post-buckling
  • Viterbi algorithm

ASJC Scopus subject areas

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

Cite this

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