Stability of Structures by Finite Element Methods


  • Z. Waszczyszyn
  • Cz. Cichoń
  • M. Radwańska, Cracow University of Technology, Institute of Computer Methods and Civil Engineering, Cracow, Poland

This book is the consequence of research undertaken by the authors in the field of advanced problems of structural mechanics. Stability analysis of structures comes under this area because of the complex models and computational methods needed for analysis. In the mid seventies, a joint effort began between a group of researchers and teachers of the Department of Civil Engineering and Computer Center of the Cracow University of Technology. One of the important results of the collaboration has been this publication.
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Book information

  • Published: November 1994
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-82123-2

Table of Contents

Preface. 1. Introduction. 1.1. Theory of stability and finite element method. 1.2. Aims, assumptions and contents of the book. 2. Foundations of the Theory of Structural Stability. 2.1 Continuous structures and discrete systems. 2.2. Constraints and forces in discrete systems. 2.3. Stability of motion of discrete systems. 2.4. Linear autonomous systems. 2.5. Conservative and dissipative discrete systems. 2.6. Critical and close postcritical states of conservative systems. 2.7. Stability of elastic-plastic systems. 2.8. Stability boundary for multiple parameter loads. 2.9. Instability of structures and theory of catastrophes. 3. Finite Element Method Equations for Structural Stability. 3.1 General remarks. 3.2. Basic equations for the analysis of large displacements. 3.3. Assembling of finite elements into set of FE. 3.4. Eigenvalue problems in the structural stability analysis. 3.5. Constraint equation and extended set of nonlinear equations. 4. Foundations of the Linear Theory of Buckling of Discrete Systems. 4.1. Main relations. 4.2. Algorithms for the analysis of linear buckling problems. 4.3. Evaluation of nonlinearity of the prebuckling state on example of a triangular frame. 5. Linear Buckling Analysis of Bar Structures. 5.1. Models of bars. 5.2. Buckling of plane beams and frames. 5.3. In-plane buckling of circular arches and rings. 5.4. Buckling of space framed structures of solid cross-sections. 5.5. Buckling of thin-walled bar structures. 6. Linear Buckling Analysis of Surface Structures. 6.1. Models of surface structures. 6.2. Simple plate elements. 6.3. Isoparametric shell elements. 6.4. Numerical analysis of homogeneous plates buckling. 6.5. Buckling of sandwich plates. 6.6. Buckling of plates with discrete stiffening. 6.7. Buckling of shells of revolution. 6.8. Buckling analysis of generals shells. 6.9. Elements with drilling degrees of freedom. 7. Foundations of Nonlinear Analysis of Discrete Systems. 7.1. General remarks about nonlinear analysis of discrete systems. 7.2. Method of initial modal superposition. 7.3. Incremental methods. 8. Nonlinear Analysis of Stability of Selected Structures. 8.1. Nonlinear analysis of fundamental equilibrium path by initial modal superposition. 8.2. Large displacements and instability of bar structures. 8.3. Large displacements and instability of elastic cylindrical panels. 8.4. Stability of structures under multiple parameter loads. 9. Application of Exact Finite Elements to Structural Stability Analysis. 9.1. Introductory remarks. 9.2. Finite-difference analysis of 2-points BVP and eigenvalue problem. 9.3. Exact finite elements and buckling analysis. 9.4. Application of EFEs to buckling analysis of bar structures. 9.5. Buckling of shells of revolution. 9.6. Finite displacements and instability of elastic plane frames. Appendices. A.1. Finite elements used in the book. A.2. ANKA computer code. A.3. MANKA computer code. A.4. Equations of moderately large displacements of thin-walled bars. A.5. Equations of moderately large rotations of elastic shells of revolution. Author Index. Subject Index.