Analytic and finite element solutions of the power-law Euler-Bernoulli beams

Dongming Wei, Yu Liu

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

In this paper, we use Hermite cubic finite elements to approximate the solutions of a nonlinear Euler- Bernoulli beam equation. The equation is derived from Hollomon's generalized Hooke's law for work hardening materials with the assumptions of the Euler-Bernoulli beam theory. The Ritz-Galerkin finite element procedure is used to form a finite dimensional nonlinear program problem, and a nonlinear conjugate gradient scheme is implemented to find the minimizer of the Lagrangian. Convergence of the finite element approximations is analyzed and some error estimates are presented. A Matlab finite element code is developed to provide numerical solutions to the beam equation. Some analytic solutions are derived to validate the numerical solutions. To our knowledge, the numerical solutions as well as the analytic solutions are not available in the literature.

Original languageEnglish
Pages (from-to)31-40
Number of pages10
JournalFinite Elements in Analysis and Design
Volume52
DOIs
Publication statusPublished - May 2012

Keywords

  • Convergence
  • Error estimate
  • Finite element solution
  • Hermite elements
  • Hollomon's equation
  • Nonlinear Euler-Bernoulli beam
  • Power-law
  • Ritz-Galerkin method
  • Work hardening material

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

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