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 6Finite Elements for Two‐Dimensional Solid Mechanics

6.1 INTRODUCTION

All real‐life structures are three–dimensional. It is engineers who make the approximation as a one‐dimensional (e.g., beam) or a two‐dimensional structure (e.g., plate or plane solid). In chapter 5 we explained in detail the conditions under which such approximation could be made. When the stresses on a plane normal to one of the axes are approximately zero, then we say that the solid is in the state of plane stress. Similarly, when the corresponding strains are zero, the solid is in the state of plane strain. A two‐dimensional solid is also called a plane solid. Some examples of plane solids are: (1) a thin plate subjected to in‐plane forces; or (2) a very thick solid with a constant cross‐section in the thickness direction. In this chapter, we will discuss when an engineering problem can be assumed to be two‐dimensional and how to solve such a problem using two‐dimensional finite elements. We will introduce three different types of two‐dimensional problems and corresponding two‐dimensional elements. Every element has its own characteristics. In order to use the finite element method appropriately, a thorough understanding of the capabilities and limitations of each element is required.

In general, two‐dimensional elasticity problem can be expressed by a system of coupled second‐order partial differential equations. Based on the constraints imposed in the thickness direction, a two‐dimensional problem ...

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