This book concerns the elastic stability of thin-walled structures ― one of the most challenging problems facing structural engineers because of its high degree of nonlinearity ― and introduces the innovative approach of using spectral analysis of the shapes and the stiffness to gain insights into the nonlinear deformations. The methodology greatly facilitates correlating the shape changes with the stiffness changes. Professor Doyle also develops specific computer procedures that complement finite element methods so that the ideas and methods are applicable to general structural problems. Basic validity of the procedures is established using key archetypal problems from buckling/post-buckling of columns, arches, curved plates, and cylindrical shells, all worked out in significant detail. The book is ideal for a wide variety of structural engineers, particularly those in aerospace and civil fields. Researchers in computational mechanics also find a rich source of new ideas for post-processing data from nonlinear analyses.
Author(s): James F. Doyle
Publisher: Springer
Year: 2020
Language: English
Pages: 409
City: Cham
Contents
Notation
Introduction
Outline of the Book
References
1 Overview of Shapes and Stiffness
1.1 Deformed Shapes of Simple Slender Members
1.1.1 Comparison of Types of Loads
1.1.2 Deformation Distributions and Degrees of Freedom
1.1.3 Thin-Walled Cross Sections
1.1.4 3D Continuous Solids
1.2 Modeling Continuous Structures
1.2.1 Virtual Work Formulation of Equilibrium
1.2.2 Euler Method
1.2.3 Ritz Method
1.3 Structural Stiffness and Its Spectral Properties
1.3.1 Discrete Stiffness of Structures
1.3.2 Spectral Properties of the Stiffness Matrix
1.4 Spectral Shapes of Slender Members
1.4.1 Generating Spectral Shapes
1.4.2 Spectral Analysis of Stretching, Bending, and Twisting Actions
Case I: Axial Stretching
Case II: Flexure of Beams
Case III: Twisting of Strips
1.4.3 Spectral Form of the Ritz Method
Explorations
References
2 Shapes with Coupled Deformations
2.1 Curved Beams and Arches
2.1.1 Strain and Strain Energy
2.1.2 Fourier Analysis of Shapes
Analysis I: Antisymmetric Shapes
Analysis II: Symmetric Inextensible Shapes
Analysis III: Symmetric Extensible Shapes
2.2 Deflections of Thin Curved Plates and Shells
2.2.1 Governing Equations for Cylinders
2.2.2 Flat Plate Equations
Analysis I: Membrane Behavior
Analysis II: Flexural Behavior
2.2.3 Shallow Curved Plates
2.3 Long Structures with Open Cross Sections
2.3.1 Shear Stress in Open Cross Sections
Analysis I: Shear Stress from Equilibrium
Analysis II: Shear Stress from Shear Deformation
Analysis III: Torsion of Open Sections
2.3.2 General Open Sections
Aspect I: Warping Displacement
Aspect II: Strain Energies
Aspect III: Governing Equations
2.4 Spectral Analysis of Coupled Deformations
2.4.1 Spectral Decomposition of Coupled Deformation Shapes
2.4.2 Spectral Shapes of Flat Plates
2.4.3 Circular Cylinders and Curved Plates
2.4.4 Spectral Shapes of Open Sections
Explorations
References
3 Nonlinear Elastic Shapes
3.1 Stiffness of Nonlinearly Deformed Structures
3.1.1 Equilibrium and Equilibrium Paths
3.1.2 Concept of Structural Stiffness Revisited
3.2 Large Deflections of Thin-Walled Structures
3.2.1 Modeling Large Deformations of Solids
3.2.2 Straight Beams and Flat Plates
Action I: Membrane
Action II: Flexure of Beams
Action III: Approximate Nonlinear Behavior of Plates
3.3 Structures with Initially Coupled Deformations
3.3.1 Modeling Nonlinear Behavior of Curved Beams and Plates
3.4 Monitoring Changes of Shape and Stiffness
3.4.1 Spectral Decomposition and Reconstruction
3.4.2 Monitoring Nonlinear Deformations
Case I: Second-Order Stiffness Effects
Case II: Effect of Initial Orientation
Case III: Initial Stiffness Due to Prestress
Case IV: Approximations When Changes of Shape Are Small
Explorations
References
4 Buckling Shapes
4.1 Buckling Shapes of Straight Beams
4.1.1 Second-Order Approximation for the Energy Contributions
4.1.2 Straight Beam Under Axial Loads
4.1.3 Effect of Distributed Elastic Supports
4.2 Buckling of Arches
4.2.1 Basic Buckling Method
4.2.2 Assessment of the Basic Buckling Method
4.3 Plate and Shell Buckling
4.3.1 Buckling of a Flat Plate
4.3.2 Buckling of a Cylindrical Shell Under Axial Load
4.3.3 Buckling of Curved Plates
Loading I: Transverse
Loading II: Axial Compression
4.4 Load Coupling of Deformation Modes
4.4.1 Lateral Buckling of Beams
4.4.2 Buckling of Thin-Walled Open Sections Under Axial Loads
Explorations
References
5 Studies of Postbuckled Shapes
5.1 Postbuckling of Beams and Arches
5.1.1 Beam Under Axial Loading
5.1.2 Arches and Effects of Boundary Constraints
5.2 Plates and Cylinders
5.2.1 Flat Plates
5.2.2 Shallow Curved Plates
5.2.3 Circular Cylinders
5.3 Mode Interactions with Softening
5.3.1 FE Results for Flange Buckling
5.3.2 Mechanical Models for Mode Interactions
Aspect I: Softening Mechanisms
Aspect II: Secondary Buckling and Mode Jumping
5.3.3 Comments Related to Flange Buckling
Explorations
References
Index
