Numerical and Computer Methods in Structural Mechanics

Numerical and Computer Methods in Structural Mechanics

1st Edition - January 1, 1973

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  • Editors: Steven J. Fenves, Nicholas Perrone, Arthur R. Robinson
  • eBook ISBN: 9781483272542

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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


    Part I. Finite Elements—Fundamentals

    Variational Procedures and Convergence of Finite-Element Methods


    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


    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


    Hybrid Models

    1. Introduction

    2. Formulation of Hybrid Stress Model

    3. Features of Hybrid Stress Model

    4. Hybrid Displacement Models

    5. Conclusion


    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


    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


    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


    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


    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


    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


    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


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


    1. Introduction

    2. Analysis

    3. Numerical Results

    4. Comments on Application to Two-Dimensional Problems

    5. Conclusions



    Comparison of Finite-Element and Finite-Difference Methods

    1. Introduction

    2. A Problem in Wave Mechanics

    3. Early Literature


    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


    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


    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


    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


    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


    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


    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


    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


    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


    Vehicle Crashworthiness

    1. Introduction

    2. Crash Environment

    3. Injury Causes and Patterns

    4. Crash Survival

    5. Conclusions


    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



    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


    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


    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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