Stability of structures by finite element methods

목차 (Table of Contents)

• CONTENTS
• PREFACE = ⅶ
• 1. INTRODUCTION
• 1.1 Theory of Stability and Finite Element Method = 1
• 1.2 Aims, Assumptions and Contents of the Book = 4
• References = 7
• 2. FOUNDATIONS OF THE THEORY OF STRUCTURAL STABILITY
• 2.1 Continuous Structures and Discrete Systems = 9
• 2.2 Constrainsts and Forces in Discrete Systems = 16
• 2.3 Stability of Motion of Discrete Systems = 21
• 2.4 Linear Autonomous Systems = 26
• 2.5 Conservative and Dissipative Discrete Systems = 31
• 2.6 Critical and Close Postcritical States of Conservative Systems = 34
• 2.6.1 General Information about Behavior of Simple Conservative Systems = 34
• 2.6.2 Postbifurcation Analysis of Systems of 1 DOF = 41
• 2.6.3 Stability Analysis of Systems of N DOF = 44
• 2.6.4 Coupling of Buckling Modes = 49
• 2.7 Stability of Elastic-Plastic Systems = 55
• 2.8 Stability Boundary for Multiple Parameter Loads = 64
• 2.9 Instability of Structures and Theory of Catastrophes = 71
• References = 73
• 3. FINITE ELEMENT METHOD EQUATIONS FOR STRUCTURAL STABILITY
• 3.1 General Remarks = 77
• 3.2 Basic Equations for the Analysis of Large Displacements = 79
• 3.2.1 Matrix Equations for Contimuous Structures = 79
• 3.2.2 Matrix Equations for Discrete Systems = 83
• 3.2.3 Generalized Variables at Cross-Section Level J and Approximation at Element Level E = 89
• 3.2.4 Finite Element Matrices = 95
• 3.2.5 Finite Elements with Imperfections = 99
• 3.2.6 Example of Formulation of FE Matrices = 101
• 3.3 Assembling of Finite Elements into Set of FE = 110
• 3.4 Eigenvalue Problems in the Structural Stability Analysis = 112
• 3.5 Constraint Equation and Extended Set of Nonlinear Equations = 116
• References = 120
• 4. FOUNDATIONS OF THE LINEAR THEORY OF BUCKLING OF DISCRETE SYSTEMS
• 4.1. Main Relations = 123
• 4.1.1 Two Stages of Linear Buckling Analysis = 123
• 4.1.2 Linear Buckling Analysis of Structures with Imperfections = 124
• 4.1.3 Evaluation of the Type of Bifurcation Points = 130
• 4.2. Algorithms for the Analysis of Linear Buckling Problems = 132
• 4.2.1 Full Algorithm = 132
• 4.2.2 Shortened Algorithm = 133
• 4.2.3 Illustration of Algorithms on Example of a Compressed Bar = 133
• 4.3. Evaluation of Nonlinearity of the Prebuckling State on Example of a Triangular Frame = 138
• References = 140
• 5.LINEAR BUCKLING ANALYSIS OF BAR STRUCTURES
• 5.1 Models of Bars = 143
• 5.2 Buckling of Plane Beams and Frames = 146
• 5.2.1 Plane Nonstandard Frame Elements BSB2 and BSB 3 = 146
• 5.2.2 Buckling of a Portal Frame and a Multistory Frame = 151
• 5.2.3 Plane Frame BST1, BST 2, BST3 Elements with Shear Deformation Taken into Account = 157
• 5.2.4 Buckling of a Battened Column and a Lattice Portal Frame = 163
• 5.3 In-Plane Buckling of Circular Arches and Rings = 167
• 5.3.1 Matrix of Load Stiffness = 167
• 5.3.2 Plane Circular BCB1-4 Elements = 171
• 5.3.3 Buckling of Circular Arches and Rings = 175
• 5.4 Buckling of Space Framed Structures of Solid Cross-Sections = 180
• 5.4.1 Space Standard Frame BSB4 Element = 180
• 5.4.2 Numerical Examples = 187
• 5.5 Buckling of Thin-Walled Bar Structures = 194
• 5.5.1 Standard Thin-Walled Bar Element BSV1 = 194
• 5.5.2 Numerical Examples = 202
• References = 210
• 6. LINEAR BUCKLING ANALYSIS OF SURFACE STRUCTURES
• 6.1 Models of Surface Structures = 215
• 6.2 Simple Plate Elements = 217
• 6.2.1 Basic Euations and Matrices of Homogeneous Plate Element = 217
• 6.2.2 Nonconforming Triangular PTK1 Element = 221
• 6.2.3 Nonconforming Rectangular PQK1 Element = 224
• 6.2.4 Conforming Rectangular PQK3 Element = 225
• 6.3 Isoparametric Shell Elements = 227
• 6.3.1 Isoparametric Approximation of Geometry and Field Equations = 227
• 6.3.2 Shell SQR1 and SQR2 Elements = 232
• 6.3.3 Numerical Integration = 234
• 6.4 Numerical Analysis of Homogeneous Plates Buckling = 239
• 6.4.1 Buckling of Rectangular Plates = 239
• 6.4.2 Numerical Analysis of Square Plates with Circular Holes = 252
• 6.4.3 Bucking of Imperfect Square Plates = 256
• 6.5 Buckling of Sandwich Plates = 259
• 6.5.1 Basic Equations and Matrices of Sandwich Plate Elements = 259
• 6.5.2 Sandwich Plate PTS1, PQS1, PQS3 Elements = 265
• 6.5.3 Buckling of Unidirectionally Compressed Plates Simply-Connected and with Holes = 265
• 6.6 Buckling of Plates with Descrete Stiffening = 270
• 6.6.1 Buckling of Stiffend Surface Structures = 270
• 6.6.2 Stiffener BSB6 Element = 272
• 6.6.3 Buckling of Square Plates = 274
• 6.7 Buckling of Shells of Revolution = 280
• 6.7.1 Conical Shell SRK1 Element = 280
• 6.7.2 Ring Stiffener BCB5 = 284
• 6.7.3 Numerical Examples = 288
• 6.8 Buckling Analysis of Generals Shells = 297
• 6.9 Elements with Drilling Degrees of Freedom = 305
• 6.9.1 Triangular FTK1 Element = 306
• 6.9.2 Quadrilateral 8-Node FQR1 Element = 309
• 6.9.3 Numerical Examples = 311
• References = 316
• 7. FOUNDATIONS OF NONLINEAR ANALYSIS OF DISCRETE SYSTEMS
• 7.1 General Remarks about Nonlinear Analysis of Discrete Systems = 323
• 7.2 Method of Initial Modal Superposition = 325
• 7.3 Incremental Methods = 327
• References = 332
• 8. NONLINEAR ANALYSIS OF STABILITY OF SELECTED STRUCTURES
• 8.1 Nonlinear Analysis of Fundamental Equilibrium Path by Initial Modal Superposition = 335
• 8.2 Large Displacements and Instability of Bar Structures = 339
• 8.2.1 Space Truss BTB1 Element and Its Applications = 339
• 8.2.2 Plane Frame BSB5 Element = 347
• 8.2.3 Application of the BSB5 Element to the Analysis of Elastic Plane Frames = 351
• 8.2.4 Analysis of Elastic Plane Frames by Means of BSB5 Element = 356
• 8.2.5 Analysis of Reinforced-Concrete Bar Structures by Means of BSB5 Element = 361
• 8.3 Large Displacements and Instability of Elastic Cylindrical Panels = 367
• 8.4 Stability of Structures under Multiple Parameter Loads = 377
• References = 383
• 9. APPLICATION OF EXACT FINITE ELEMENTS TO STRUCTURAL STABILITY ANALYSIS
• 9.1 Introductory Remarks = 387
• 9.2 Finite-Difference Analysis of 2-Points BVP and Eignvalue Problem = 389
• 9.3 Exact Finite Elements and Buckling Analysis = 391
• 9.3.1 Matrices of EFE = 391
• 9.3.2 Algorithm of the Eigenanalysis = 392
• 9.4 Application of EFEs to Buckling Analysis of Bar Structures = 393
• 9.4.1 Canonic Set of Equations for Plane Elements of Solid Cross-Sections = 393
• 9.4.2 Numerical Examples of In-Plane Buckling = 397
• 9.4.3 Lateral Buckling of Structures with Solid Cross-Sections = 402
• 9.4.4 Buckling of Thin-Walled Straight Bar Structures = 404
• 9.4.5 Lateral Buckling of Thin-Walled Arches = 408
• 9.5 Buckling of Shells of Revolution = 411
• 9.5.1 EFE Matrices and Eigenanalysis = 411
• 9.5.2 Numerical Examples = 412
• 9.6 Finite Diplacements and Instability of Elastic Plane Frames = 416
• 9.6.1 Canonic Set of Equations = 416
• 9.6.2 Computation of EFE Matrices = 418
• 9.6.3 Numerical Analysis = 418
• References = 421
• APPENDICES
• A.1 Finite Elements Used in the Book = 45
• A.2 ANKA Computer Code = 430
• A.2.1 Introductory Remarks = 430
• A.2.2 Computer Requirements = 432
• A.2.3 User Interfaces = 432
• A.2.4 Authors of ANKA and Distribution of the Code = 433
• A.3 MANKA Computer Code = 434
• A.3.1 Introductory Remarks = 434
• A.3.2 General Structure of MANKA = 435
• A.3.3 Formulation of a New MANKA Program = 435
• A.3.4 Exectuion of the MANKA Program = 436
• A.3.5 Program Installation = 437
• A.3.6 Authors of MANKA and Distribution of the Code = 437
• A.4 Equations of Modertely Large Displacements of Thin-Walled Bars = 438
• A.4.1 Assumptions = 438
• A.4.2 Strain-Displacement Relations = 438
• A.4.3 Generalized Stresses, Strins and Physical Relations = 440
• A.4.4 Equilibrium Equations and Boundary Conditions = 442
• A.4.5 Canonic Sets of Differential Equations = 444
• A.4.6 Approximate Stability Equations = 447
• A.4.7 Components of the Inital Stress Stiffness Matrix of BSV1 Elment = 449
• A.5 Equations of Moderately Large Rotations of Elastic Shells of Revolution = 451
• A.5.1 Assumptions and Notations = 451
• A.5.2 Strain-Displacement Relations = 452
• A.5.3 Generalized Stresses and Physical Equations = 453
• A.5.4 Equilibrium Equations and Boundary Conditions = 453
• References = 456
• AUTHOR INDEX = 459
• SUBJECT INDEX = 463