One-Dimensional Finite Elements: An Introduction to the FE Method

✍ Scribed by Andreas Öchsner, Markus Merkel (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2013
• Tongue: English
• Leaves: 407
• Edition: 1
• Category: Library

✦ Synopsis

This textbook presents finite element methods using exclusively one-dimensional elements. The aim is to present the complex methodology in an easily understandable but mathematically correct fashion. The approach of one-dimensional elements enables the reader to focus on the understanding of the principles of basic and advanced mechanical problems. The reader easily understands the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. But although the description is easy it remains scientifically correct.

The approach using only one-dimensional elements covers not only standard problems but allows also for advanced topics like plasticity or the mechanics of composite materials. Many examples illustrate the concepts and problems at the end of every chapter help to familiarize with the topics.

✦ Table of Contents

Front Matter....Pages i-xxiii
Introduction....Pages 1-4
Motivation for the Finite Element Method....Pages 5-32
Bar Element....Pages 33-50
Torsion Bar....Pages 51-56
Bending Element....Pages 57-110
General 1D Element....Pages 111-128
Plane and Spatial Frame Structures....Pages 129-153
Beam with Shear Contribution....Pages 155-207
Beams of Composite Materials....Pages 209-231
Nonlinear Elasticity....Pages 233-271
Plasticity....Pages 273-311
Stability (Buckling)....Pages 313-325
Dynamics....Pages 327-358
Back Matter....Pages 359-398

✦ Subjects

Structural Mechanics; Computational Mathematics and Numerical Analysis; Mechanical Engineering