Jump to ContentJump to Main Navigation
An Introduction to Nonlinear Finite Element Analysis$
Users without a subscription are not able to see the full content.

J. N. Reddy

Print publication date: 2004

Print ISBN-13: 9780198525295

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198525295.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 24 November 2020

Nonlinear Bending of Straight Beams

Nonlinear Bending of Straight Beams

(p.87) 4 Nonlinear Bending of Straight Beams
An Introduction to Nonlinear Finite Element Analysis


Oxford University Press

This chapter considers the application of the finite element method to the analysis of a slightly more complicated one-dimensional nonlinear problem: the bending of straight beams. When the applied loads on the beam are large, the linear load deflection relationship ceases to be valid because the beam develops internal forces that resist deformation, and the magnitude of internal forces increases with the loading as well as the deformation. This nonlinear load deflection response of straight beams is discussed. A nonlinear formulation of straight beams based on assumptions of large transverse displacements, small strains, and small to moderate rotations is presented. Two different theories to model the kinematic behavior of beams are examined: the Euler-Bernoulli beam theory that neglects the transverse shear strain, and the Timoshenko beam theory that accounts for the transverse shear strain in the simplest way. This chapter also discusses weak forms, iterative solutions of nonlinear equations, membrane locking, tangent stiffness matrix, and computer implementation of the problem.

Keywords:   finite element method, computer implementation, nonlinear bending, straight beams, load deflection, strains, kinematic behavior, Euler-Bernoulli beam theory, Timoshenko beam theory, membrane locking

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .