# Numerical and Computer Methods in Structural Mechanics

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Numerical and Computer Methods in Structural Mechanics is a compendium of papers that deals with the numerical methods in structural mechanics, computer techniques, and computer capabilities. Some papers discus the analytical basis of the computer technique most widely used in software, that is, the finite element method. This method includes the convergence (in terms of variation principles) isoparametrics, hybrid models, and incompatible displacement models. Other papers explain the storage or retrieval of data, as well as equation-solving algorithms. Other papers describe general-purpose structural mechanics programs, alternatives to, and extension of the usual finite element approaches. Another paper explores nonlinear, dynamic finite element problems, and a direct physical approach to determine finite difference models. Special papers explain structural mechanics used in computing, particularly, those related to integrated data bases, such as in the Structures Oriented Exchange System of the Office of Naval Research and the integrated design of tanker structures. Other papers describe software and hardware capabilities, for example, in ship design, fracture mechanics, biomechanics, and crash safety. The text is suitable for programmers, computer engineers, researchers, and scientists involved in materials and industrial design.

## Table of Contents

List of Contributors

Preface

Part I. Finite Elements—Fundamentals

Variational Procedures and Convergence of Finite-Element Methods

References

Isoparametric and Allied Numerically Integrated Elements—A Review

1. Introduction

2. Basic Principles of Shape Function (Interpolation) Mapping

3. Uniqueness of Mapping

4. Iso-, Sub-, and Superparametric Elements

5. Evaluation of Element Properties in Curvilinear Coordinates

6. Required Accuracy of Numerical Integration

7. Some Useful Elements for Two- and Three-Dimensional Analysis

8. Degeneration of Quadrilateral or Brick Elements

9. Computation Efficiency of Numerical Integration

10. Practical Examples and Stress Computation

11. Shells and Plates as Limiting Cases of Three-Dimensional Analysis

12. Applications to Nonlinear Analysis

13. Concluding Remarks—Other Uses of Mapping

References

Incompatible Displacement Models

1. Introduction

2. Source of Errors

3. Addition of Incompatible Modes for Two-Dimensional Isoparametric Elements

4. Three-Dimensional Elements

5. Thick Shell Element

6. Thick Shell Examples

References

Hybrid Models

1. Introduction

2. Formulation of Hybrid Stress Model

3. Features of Hybrid Stress Model

4. Hybrid Displacement Models

5. Conclusion

References

Computer Implementation of the Finite-Element Procedure

1. Introduction

2. Prerequisites

3. Solution Methods for the Load-Deflection Equations

4. Incorporation of Different Finite-Element Types

5. Modular Design

6. Problem Description and Representation of the Results

References

Part II. Critical Review of General-Purpose Structural Mechanics Programs

Review of the ASKA Program

1. Introduction

2. General Information

3. Element Library

4. Preparation of an ASKA Job

5. Special Features in ASKA

6. Dynamic Analysis

7. Problems Solved with ASKA

8. Concluding Remarks

References

A Critical View of NASTRAN

1. Introduction

2. History of NASTRAN

3. Boeing Evaluation Project

4. Analytic Capability

5. Element Technology

6. Numerical Methods

7. Ease of Use

8. Problem Size

9. Performance

10. Design Criteria

11. Maintainability

12. Conclusion

Appendix A. Future NASTRAN Developments

Appendix B. Examples of Analysis

References

The DAISY Code

1. Introduction

2. Some Features of DAISY

3. Lockheed's Development of DAISY

4. Some Examples of Problems Solved with DAISY

5. Future Plans

An Evaluation of the STARDYNE System

1. Introduction

2. STARDYNE

3. Examples of Problems Solved

4. Performance

5. Conclusions

Analysis and Design Capabilities of STRUDL Program

1. Introduction

2. Definition of the Problem

3. Analysis Facilities

4. Design Facilities

5. Save/Restore and Graphic/Output

6. Maintenance, Improvements, and Implementation

7. Machine Configuration

8. Computer Cost

9. Conclusion

References

Elastic-Plastic and Creep Analysis via the MARC Finite-Element Computer Program

1. Introduction

2. Example 1—Plasticity Analysis

3. Example 2—Primary Creep Analysis

4. Other Examples

5. The Merits of MARC

6. Conclusions

References

Part III. Finite Difference/Finite Elements—A Merging of Forces

A Survey of Finite-Difference Methods for Partial Differential Equations

1. Introduction

2. General Discussion

3. Hyperbolic Systems

4. Parabolic Systems

5. Elliptic Systems

6. Tensor Product—Fast Fourier Transform Methods

7. Implicit versus Explicit Methods—Flexibility Concept

8. The Method of Fractional Steps

9. Stability and the Energy Method

References

Finite-Difference Energy Models Versus Finite-Element Models : Two Variational Approaches in One Computer Program

Nomenclature

1. Introduction

2. Analysis

3. Numerical Results

4. Comments on Application to Two-Dimensional Problems

5. Conclusions

Appendix

References

Comparison of Finite-Element and Finite-Difference Methods

1. Introduction

2. A Problem in Wave Mechanics

3. Early Literature

References

Incremental Stiffness Method for Finite Element Analysis of the Nonlinear Dynamic Problem

1. Introduction

2. Review of Literature

3. Theoretical Considerations

4. Solution Procedure

5. Note on Solution Convergence

6. Computer Program

7. Case Studies

8. Discussion and Conclusions

References

The Lumped-Parameter or Bar-Node Model Approach to Thin-Shell Analysis

1. Introduction

2. Shallow Shell Equations

3. Lumped-Parameter Model

4. Boundary Conditions

5. Selection of Proper Model

6. Conclusions

Appendix A. Lumped-Parameter Element Stiffness Matrices

References

Part IV. Large Interactive Data Bases

Design Philosophy of Large Interactive Systems

1. Introduction

2. Components of Data Base

3. Program Design

4. Data Structure Design

5. Control System Design

6. Who Will Do It

7. Conclusions

References

Integrated Design of Tanker Structures

1. Introduction

2. Presentation of the Structural Problem

3. Design Procedure

4. Synthesis

5. Software System

6. Concluding Remarks

Appendix I. Automated Design and Optimization Programs

Appendix II. Example of BOSS Session

References

The STORE Project (The Structures Oriented Exchange)

1. Introduction

2. Basic Concepts of STORE

3. Description of the STORE System

4. Use of the STORE System

5. Costs

6. Distinguishing Characteristics of the STORE System

7. Illustrative Example—Typical STORE Program Documentation

8. Present Status, Conclusions, and Recommendations

Appendix A. List of Programs in Project STORE

References

Part V. New Capabilities for Computer-Based Analysis

Symbolic Computing

1. Introduction

2. Organization of Data and Data Processors

3. The Role of Symbolic Computation in Mechanics

4. Discussion and Conclusion

References

A Review of the Capabilities and Limitations of Parallel and Pipeline Computers

1. Introduction

2. The Parallel Computer

3. The Pipeline Processor

4. Parallel and Pipeline

5. Parallel and Pipeline Execution Times

6. Parallel Versus Pipeline: Efficiency

7. Languages for the Parallel and Pipeline Computers

8. Application Programming

9. Performance on Large Problems

10. Conclusion

References

Equation-Solving Algorithms for the Finite-Element Method

1. Introduction

2. Types of Record Encountered

3. Principal Types of Organization

4. Gaussian Reduction

5. Error Diagnostics

6. The Conjugate Gradient Algorithm

7. The Alternating-Direction Approach

8. Multivector Iteration

9. Conclusions

Appendix I. The Prefront with Variable Numbers of Degrees of Freedom at Different Nodes

Appendix II. Avoidance of Zeros within the Front

References

FLING—A FORTRAN Language for Interactive Graphics

1. Introduction

2. Basic Graphic Subroutines

3. Example Problems

Appendix A. IBM 360 Interface Package

Part VI. Numerical Methods for a Changing Technology

Trends and Directions in the Applications of Numerical Analysis

1. Introduction

2. Alternative Variational Principles

3. Constraint Equation Procedures

4. Interdisciplinary Applications

5. Concluding Remarks

References

Vehicle Crashworthiness

1. Introduction

2. Crash Environment

3. Injury Causes and Patterns

4. Crash Survival

5. Conclusions

References

Computational Fracture Mechanics

1. Introduction

2. Numerical Determination of Elastic Stress Intensity Factors (Two-Dimensional Problems)

3. Crack Tip Plasticity

4. Singular Finite-Element Formation and Results

5. Three-Dimensional Problems

6. Micromechanics and Development of Fracture Criteria

7. Conclusion

References

Biomechanics

1. Mechanics in Living Systems

2. The Tasks of Biomechanics

3. A Function-Oriented Taxonomy of the Mechanics of Living Systems

4. Characteristics of Biomechanics Problems

5. The Role of Numerical Solutions in Biomechanics

6. State of the Art Examples of Numerical Solutions in Biomechanics

7. Conclusions: Artimechanics, Physimechanics, and Biomechanics

References

The Computer in Ship Structure Design

1. Introduction

2. Current and Future Developments in Computer Hardware

3. Current and Future Developments in Structural Analysis Software

4. Relationship Between the Computer and the Engineer

5. Future Trends in Ship Structure Analysis

6. Problems and Useful Techniques in Interactive Analysis

7. The Local Analysis Procedure

8. The Reduced Substructure Technique (RESS)

9. Automatic Data Generation and Interpretation of Results

10. Data Banks

11. Multistep Solutions

12. Dynamic Modeling Using Compatible Finite Elements of Different Order

13. The Problem of Storage in a Small Computer

14. Method of Additional Constraints (MAC)

15. Variations on the Gauss-Seidel Iterative Technique

16. Conclusion

Appendix A. Nomenclature

References

Author Index

## Product details

- No. of pages: 698
- Language: English
- Copyright: © Academic Press 1973
- Published: January 1, 1973
- Imprint: Academic Press
- eBook ISBN: 9781483272542

## About the Editors

### Steven J. Fenves

### Nicholas Perrone

### Arthur R. Robinson

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