Theories and applications of plate analysis : classical, numerical and engineering methods

Başlık:

Yazar:

Szilard, Rudolph, 1921-

ISBN:

9780471429890

Ek Yazar:

Szilard, Rudolph, 1921-

Yayım Bilgisi:

Hoboken, N.J. ; [Chichester] : Wiley, c2004.

Fiziksel Tanım:

xxiii, 1024 p. ; 24 cm. + 1 CD-ROM (4.75 in.)

General Note:

A completely reworked and extended version of Theory and analysis of plates : classical and numerical methods. Upper Saddle River, N.J. : Prentice -Hall, 1974.

The accompanying CD-ROM contains WinPlatePrimer finite element analysis program and 170 plate formulas in pdf format.

Konu Terimleri:

Plates (Engineering)

Plaklar (Mühendislik)

Added Author:

Szilard, Rudolph, 1921- Theory and analysis of plates.

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Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0055457	TA660.P6S94 2003	Searching... Unknown

This book by a renowned structural engineer offers comprehensive coverage of both static and dynamic analysis of plate behavior, including classical, numerical, and engineering solutions. It contains more than 100 worked examples showing step by step how the various types of analysis are performed.

Author Notes

Rudolph Szilard, Dr.-Ing., P.E., is Emeritus Professor of Structural Mechanics at the University of Hawaii

Preface	p. xvii
Symbols	p. xxi
I Introduction	p. 1
II Historical Background	p. 10
Part I Plate Theories and Analytical Solutions of Static, Linear-Elastic Plate Problems	p. 21
1 Elastic Plate Theories and Their Governing Differential Equations	p. 23
1.1 Classical Small-Deflection Theory of Thin Plates	p. 23
1.2 Plate Equation in Cartesian Coordinate System	p. 26
1.3 Boundary Conditions of Kirchhoff's Plate Theory	p. 35
1.4 Differential Equation of Circular Plates	p. 42
1.5 Refined Theories for Moderately Thick Plates	p. 45
1.6 Three-Dimensional Elasticity Equations for Thick Plates	p. 53
1.7 Membranes	p. 57
1.8 Summary	p. 60
Problems	p. 61
2 Exact and Series Solutions of Governing Differential Equations	p. 62
2.1 Rigorous Solution of Plate Equation	p. 62
2.2 Solutions by Double Trigonometric Series (Navier's Approach)	p. 69
2.3 Solutions by Single Trigonometric Series (Levy's Method)	p. 75
2.4 Further Examples of Series Solutions	p. 83
2.5 Extensions of Navier's and Levy's Methods	p. 92
2.6 Method of Images	p. 97
2.7 Plate Strips	p. 99
2.8 Rigorous Solution of Circular Plates Subjected to Rotationally Symmetric Loading	p. 110
2.9 Solutions of Membrane Problems	p. 116
2.10 Series Solutions of Moderately Thick Plates	p. 120
2.11 Summary	p. 126
Problems	p. 127
3 Further Plate Problems and Their Classical Solutions	p. 129
3.1 Plates on Elastic Foundation	p. 129
3.2 Plates with Variable Flexural Rigidity	p. 139
3.3 Simultaneous Bending and Stretching	p. 147
3.4 Plates of Various Geometrical Forms	p. 150
3.5 Various Types of Circular Plates	p. 156
3.6 Circular Plate Loaded by an Eccentric Concentrated Force	p. 161
3.7 Plates with Edge Moments	p. 165
3.8 Solutions Obtained by Means of Superposition	p. 168
3.9 Continuous Plates	p. 173
3.10 Summary	p. 179
Problems	p. 180
4 Energy and Variational Methods for Solution of Lateral Deflections	p. 181
4.1 Introduction and Basic Concepts	p. 181
4.2 Ritz's Method	p. 187
4.3 Galerkin's Method and Its Variant by Vlasov	p. 196
4.4 Further Variational and Energy Procedures	p. 212
4.5 Techniques to Improve Energy Solutions	p. 226
4.6 Application of Energy Methods to Moderately Thick Plates	p. 231
4.7 Summary	p. 234
Problems	p. 235
Part II Numerical Methods for Solution of Static, Linear-Elastic Plate Problems	p. 237
5 Finite Difference Methods	p. 247
5.1 Ordinary Finite Difference Methods	p. 247
5.2 Improved Finite Difference Methods	p. 276
5.3 Finite Difference Analysis of Moderately Thick Plates	p. 303
5.4 Advances in Finite Difference Methods	p. 312
5.5 Summary and Conclusions	p. 314
Problems	p. 315
6 Gridwork and Framework Methods	p. 317
6.1 Basic Concepts	p. 317
6.2 Equivalent Cross-Sectional Properties	p. 320
6.3 Gridwork Cells and Their Stiffness Matrices	p. 328
6.4 Computational Procedures for Gridworks	p. 336
6.4.1 Procedures Using Commercially Available Programs	p. 337
6.4.2 Guidance for Gridwork Programming	p. 343
6.5 Summary and Conclusions	p. 361
Problems	p. 362
7 Finite Element Method	p. 364
7.1 Introduction and Brief History of the Method	p. 364
7.2 Engineering Approach to the Method	p. 370
7.3 Mathematical Formulation of Finite Element Method	p. 380
7.3.1 Consideration of Total System	p. 380
7.3.2 Formulation of Element Stiffness Matrices	p. 383
7.4 Requirements for Shape Functions	p. 389
7.5 Various Shape Functions and Corresponding Element Families	p. 392
7.5.1 Polynomials and Their Element Families	p. 393
7.5.2 Hermitian Elements	p. 399
7.5.3 Other Element Families	p. 403
7.6 Simple Plate Elements	p. 406
7.6.1 Rectangular Element with Four Corner Nodes	p. 406
7.6.2 Triangular Element with Three Corner Nodes	p. 411
7.7 Higher-Order Plate Elements	p. 418
7.7.1 Rectangular Element with 16 DOF	p. 418
7.7.2 Discrete Kirchhoff Triangular Element	p. 423
7.8 Computation of Loads and Stress Resultants	p. 434
7.9 Moderately Thick Plate Elements	p. 446
7.10 Thick-Plate Elements	p. 453
7.11 Numerical Integration	p. 458
7.12 Modeling Finite Element Analysis	p. 463
7.13 Programming Finite Element Analysis	p. 465
7.14 Commercial Finite Element Codes	p. 469
7.15 Summary and Conclusions	p. 472
Problems	p. 474
8 Classical Finite Strip Method	p. 475
8.1 Introduction and Basic Concepts	p. 475
8.2 Displacement Functions for Classical FSM	p. 477
8.3 Formulation of the Method	p. 481
8.4 Outline of Computational Procedures	p. 489
8.5 Summary and Conclusions	p. 494
Problems	p. 495
9 Boundary Element Method	p. 496
9.1 Introduction	p. 496
9.2 Basic Concepts of Boundary Element Method	p. 497
Part III Advanced Topics	p. 505
10 Linear Considerations	p. 507
10.1 Orthotropic Plates	p. 507
10.2 Laminated and Sandwich Plates	p. 530
10.2.1 Classical Laminated Plate Theory	p. 531
10.2.2 Sandwich Plates	p. 534
10.2.3 Moderately Thick Laminated Plates	p. 539
10.3 Analysis of Skew Plates	p. 546
10.4 Thermal Bending of Plates	p. 561
10.5 Influence Surfaces	p. 571
10.6 Continuous Plates Supported by Rows of Columns	p. 578
10.7 Additional Topics Related to FEM	p. 590
10.7.1 Various Convergence Tests	p. 590
10.7.2 Elements with Curved Sides	p. 594
10.8 Extensions of Classical Finite Strip Method	p. 597
10.8.1 Spline Finite Strip Method	p. 598
10.8.2 Computed Shape Functions	p. 605
10.8.3 Finite Strip Formulation of Moderately Thick Plates	p. 606
10.9 Summary and Conclusions	p. 611
Problems	p. 612
11 Nonlinear Aspects	p. 614
11.1 Large-Deflection Analysis	p. 614
11.2 Numerical Methods for Geometrically Nonlinear Analysis	p. 624
11.2.1 Various Finite Element Procedures	p. 637
11.3 Material Nonlinearity	p. 645
11.3.1 Nonlinear Stress-Strain Relationships	p. 645
11.3.2 Computational Procedures	p. 648
11.4 Combined Geometrical and Material Nonlinearities	p. 656
11.5 Reinforced-Concrete Slabs	p. 662
11.6 Summary and Conclusions	p. 672
Problems	p. 672
Part IV Engineering Solution Procedures	p. 673
12 Practical Design Methods	p. 675
12.1 Need for Engineering Solution Procedures	p. 675
12.2 Elastic Web Analogy for Continuous Plate Systems	p. 676
12.3 Simplified Slope-Deflection Method	p. 689
12.4 Moment Distribution Applied to Continuous Plates	p. 700
12.5 Practical Analysis of RC Floor Slabs	p. 710
12.6 Equivalent Frame Method Applied to Flat Slabs	p. 718
12.7 Other Practical Design Methods	p. 727
12.7.1 Approximate Analysis of Bridge Decks	p. 727
12.7.2 Simplified Treatments of Skew Plates	p. 730
12.7.3 Degree-of-Fixity Procedure	p. 733
12.8 Summary and Conclusions	p. 739
Problems	p. 740
13 Yield-Line Method	p. 742
13.1 Introduction to Yield-Line Method	p. 742
13.2 Work Method	p. 751
13.3 Equilibrium Method	p. 758
13.4 Further Applications of Yield-Line Analysis	p. 763
13.5 Yield Lines due to Concentrated Loads	p. 770
13.6 Summary and Conclusions	p. 781
Problems	p. 782
Part V Dynamic Analysis of Elastic Plates	p. 785
14 Classical and Energy Methods in Dynamic Analysis	p. 787
14.1 Introduction to Structural Dynamics	p. 787
14.2 Differential Equations of Lateral Motion	p. 802
14.3 Free Flexural Vibration of Plates	p. 804
14.4 Free Transverse Vibration of Membranes	p. 810
14.5 Energy Methods for Determination of Natural Frequencies	p. 815
14.6 Natural Frequencies Obtained from Static Deflections	p. 824
14.7 Forced Transverse Vibration of Rectangular Plates	p. 830
14.8 Free Vibration of Moderately Thick Plates	p. 839
14.9 Summary and Conclusions	p. 842
Problems	p. 843
15 Numerical Methods in Plate Dynamics	p. 845
15.1 Solution of Differential Equation of Motion by Finite Differences	p. 845
15.2 Application of Finite Element Method to Plate Dynamics	p. 856
15.2.1 Matrix Equations of Free Vibrations	p. 856
15.2.2 Mass Matrix	p. 860
15.2.3 Forced Vibrations	p. 870
15.3 Damping of Discrete Systems	p. 883
15.4 Slab Bridges under Moving Loads	p. 889
15.5 Large-Amplitude Free-Vibration Analysis	p. 895
15.6 Summary and Conclusions	p. 899
Problems	p. 902
Part VI Buckling of Plates	p. 903
16 Fundamentals of Stability Analysis	p. 905
16.1 Basic Concepts	p. 905
16.2 Equilibrium Method	p. 911
16.3 Energy Methods in Stability Analysis	p. 919
16.4 Finite Differences Solution of Plate Buckling	p. 928
16.5 Finite Element and Gridwork Approach to Stability Analysis	p. 938
16.6 Dynamic Buckling	p. 946
16.7 Buckling of Stiffened Plates	p. 953
16.8 Thermal Buckling	p. 961
16.9 Buckling of Moderately Thick Plates	p. 963
16.10 Postbuckling Behavior	p. 966
16.11 Inelastic Buckling and Failure of Plates	p. 978
16.12 Summary and Conclusions	p. 982
Problems	p. 983
Appendix A.1 Fourier Series	p. 985
Appendix A.2 Conversion from One Poisson Ratio to Another	p. 999
Appendix A.3 Units	p. 1001
Appendix A.4 About the CD	p. 1003
A.4.1 Plate Formulas	p. 1003
A.4.2 WinPlatePrimer Program System	p. 1004
Index	p. 1015

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