#### Document Type

Article

#### Publication Date

5-2012

#### 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.

#### Journal Name

Finite Elements in Analysis & Design

#### Recommended Citation

Dongming Wei, Yu Liu, Analytic and finite element solutions of the power-law Euler–Bernoulli beams, Finite Elements in Analysis and Design, Volume 52, May 2012, Pages 31-40, ISSN 0168-874X, 10.1016/j.finel.2011.12.007. (http://www.sciencedirect.com/science/article/pii/S0168874X1100237X)

#### Included in

Applied Mathematics Commons, Engineering Science and Materials Commons, Mathematics Commons

## Comments

pre-print