Skip to Main Content
Introduction to Finite Element Analysis and Design, 2nd Edition
book

Introduction to Finite Element Analysis and Design, 2nd Edition

by Nam H. Kim, Bhavani V. Sankar, Ashok V. Kumar
August 2018
Intermediate to advanced content levelIntermediate to advanced
552 pages
21h 1m
English
Wiley
Content preview from Introduction to Finite Element Analysis and Design, 2nd Edition

Chapter 3Finite Element Analysis of Beams and Frames

In chapter 1, the finite element equations of a truss were obtained using the direct stiffness method. Similar direct methods for beams are possible but quite complicated, and such methods are impossible for plates and two‐dimensional and three‐dimensional solids. In chapter 2, we introduced the Galerkin method and the principle of minimum potential energy for different engineering problems. In this chapter, we will formally derive the finite element equations for beams using the energy method. The same finite element equation can be obtained using the principle of virtual work.1

In chapter 2, we learned that in the finite element method, the displacements in an element are interpolated using an expression of the form images, in which {N(x)} is the column vector of shape functions, and {q} is the vector of nodal displacements or in general nodal degrees of freedom (DOFs). In the case of beam finite element, the nodal DOFs include the vertical (or transverse) deflection as well as the rotation (or slope). Using this interpolation scheme, the stiffness matrix and applied load vector are derived and solved for the nodal DOFs.

After a review of the elementary beam theory in section 3.1, we will first present the Rayleigh‐Ritz method in section 3.2. The formal development of the interpolation functions for the beam finite elements is ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Advanced Mechanics of Materials and Applied Elasticity, 6th Edition

Advanced Mechanics of Materials and Applied Elasticity, 6th Edition

Saul K. Fenster, Ansel C. Ugural
Technical Drawing with Engineering Graphics, 15th Edition

Technical Drawing with Engineering Graphics, 15th Edition

Frederick E. Giesecke, Alva Mitchell, Henry C. Spencer, Ivan L. Hill, John T. Dygdon, James E. Novak, R. O. Loving, Shawna E. Lockhart, Cindy Johnson
Engineering Drawing, 2nd Edition

Engineering Drawing, 2nd Edition

M. B. Shah, B. C. Rana

Publisher Resources

ISBN: 9781119078722Purchase book