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

Dongming Wei, Yu Liu

Research output: Contribution to journalArticle

5 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
Externally publishedYes

Fingerprint

Euler-Bernoulli Beam
Finite Element Solution
Strain hardening
Beam Equation
Power Law
Numerical Solution
Finite Element
Analytic Solution
Hooke's law
Conjugate Gradient
Finite Element Approximation
Hardening
Hermite
Minimizer
Galerkin
MATLAB
Error Estimates

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

Cite this

Analytic and finite element solutions of the power-law Euler-Bernoulli beams. / Wei, Dongming; Liu, Yu.

In: Finite Elements in Analysis and Design, Vol. 52, 05.2012, p. 31-40.

Research output: Contribution to journalArticle

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