1st Edition

# Nonlinear Problems in Machine Design

By Eliahu Zahavi, David M. Barlam Copyright 2000
434 Pages 100 B/W Illustrations
by CRC Press

440 Pages
by CRC Press

Also available as eBook on:

Modern machine design challenges engineers with a myriad of nonlinear problems, among them fatigue, friction, plasticity, and excessive deformation. Today's advanced numerical computer programs bring optimal solutions to these complex problems within reach, but not without a trained and experienced overseer.

Nonlinear Problems in Machine Design provides that training and experience. It acquaints readers with the modern analytical methods of machine design and enables them to use those methods in daily applications. The authors first build the theoretical foundation, then focus on the application of the finite element method to machine design problems. They offer practical examples with solutions generated using both the ANSYS and MSC.NASTRAN finite element programs, demonstrating the reliability of the results, offering readers experience with the two most widely used programs in industry.

Developed through the authors' extensive knowledge of engineering theory and their experience in verifying the accuracy and applicability of computer generated solutions, this book helps ensure foolproof results when designing machine parts. Nonlinear Problems in Machine Design is unique in its focus, will prove equally valuable to students and practitioners, and appears destined to become a standard in its field.

PART I: THEORETICAL FUNDAMENTALS
BASICS OF SOLID MECHANICS
Stress
Linear Strain
Stress-Strain Relationship
Variational Principles
Solution of the Boundary Value Problem
FINITE ELEMENT METHOD
Introduction to Finite Element Theory
Isoparametric Elements
Hierarchical Functions
Bending Elements: Beams and Plates
Accuracy of FE Solution
NONLINEAR PROBLEMS
Introduction
Example: Two-Spar Frame
Iterative Methods
PLASTICITY
One-Dimensional Theory
Yield Criteria for Multi-Axial Stresses
Constitutive Theories of Plasticity
Finite Element Implementation
LARGE DISPLACEMENTS
Tensor Analysis of a Deformed Body
Deformation and Strain
Stress
Constitutive Equations
Finite Element Implementation
CONTACT PROBLEMS
Introduction
Penalty Method
Lagrange Multiplier Method
Critical Review
FATIGUE-FAILURE PREDICTION METHODS
Strain Method
Cumulative Damage
Fracture Mechanics
PART II: DESIGN CASES
DESIGN OF MACHINE PARTS
Nonlinear Behavior of Machine Parts
Failure of Machine Parts under Static Load
Fatigue of Machine Parts under Fluctuating Load
LEAF SPRING
Introduction
Design Fundamentals
FE Analysis of Leaf-Spring
Conclusions
Introduction
Forces in Bolt Connection
Stresses
Nonlinear Analysis using FE method
Conclusions
FLANGE CONNECTION
Introduction
One-Dimensional Analysis
FE Analysis
Conclusions
FRETTING FATIGUE IN AN AXLE
Introduction
Case Study: Axle Failure Due to Fretting
Design Improvement
Conclusions
APPENDIX A: Basics of Tensor Calculus
APPENDIX B: Basics OF Matrix Calculus
APPENDIX C: Tables

Note: Each chapter also includes references

### Biography

Eliahu Zahavi, David M. Barlam