Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition

Front Cover
CRC Press, Nov 24, 2003 - Science - 858 pages
The use of composite materials in engineering structures continues to increase dramatically, and there have been equally significant advances in modeling for general and composite materials and structures in particular. To reflect these developments, renowned author, educator, and researcher J.N. Reddy created an enhanced second edit
 

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Contents

Equations of Anisotropic Elasticity Virtual Work Principles and Variational Methods
1
12 Mathematical Preliminaries
3
13 Equations of Anisotropic Elasticity
12
132 StrainDisplacement Equations
13
133 Strain Compatibility Equations
18
135 Equations of Motion
19
136 Generalized Hookes Law
22
137 Thermo dynamic Principles
34
743 Numerical Examples
415
75 Antisymmetric AnglePly Laminates with Two Opposite Edges Simply Supported
421
753 The LÚvy Solution
423
754 Numerical Examples
425
76 Transient Solutions
430
77 Vibration Control of Laminated Plates
437
772 Theoretical Formulation
438
774 Analytical Solution
439

14 Virtual Work Principles
38
143 Variational Operator and Euler Equations
40
144 Principle of Virtual Displacements
44
15 Variational Methods
58
153 WeightedResidual Methods
64
16 Summary
71
Problems
72
References for Additional Reading
78
Introduction to Composite Materials
81
212 Laminae and Laminates
83
22 Constitutive Equations of a Lamina
85
222 Characterization of a Unidirectional Lamina
86
23 Transformation of Stresses and Strains
89
232 Transformation of Stress Components
90
233 Transformation of Strain Components
93
234 Transformation of Material Coefficients
96
24 Plane Stress Constitutive Relations
99
Problems
103
References for Additional Reading
106
Classical and FirstOrder Theories of Laminated Composite Plates
109
32 An Overview of Laminated Plate Theories
110
33 The Classical Laminated Plate Theory
112
332 Displacements and Strains
113
333 Lamina Constitutive Relations
117
334 Equations of Motion
119
335 Laminate Constitutive Equations
127
336 Equations of Motion in Terms of Displacements
129
34 The FirstOrder Laminated Plate Theory
132
342 Equations of Motion
134
343 Laminate Constitutive Equations
137
344 Equations of Motion in Terms of Displacements
139
35 Laminate Stiffnesses for Selected Laminates
142
352 SingleLayer Plates
144
353 Symmetric Laminates
148
354 Antisymmetric Laminates
152
355 Balanced and QuasiIsotropic Laminates
156
Problems
157
References for Additional Reading
161
OneDimensional Analysis of Laminated Composite Plates
165
42 Analysis of Laminated Beams Using CLPT
167
422 Bending
169
423 Buckling
176
424 Vibration
182
43 Analysis of Laminated Beams Using FSDT
187
432 Bending
188
433 Buckling
192
434 Vibration
197
44 Cylindrical Bending Using CLPT
200
442 Bending
203
443 Buckling
208
444 Vibration
209
45 Cylindrical Bending Using FSDT
214
452 Bending
215
453 Buckling
216
454 Vibration
219
46 Vibration Suppression in Beams
222
463 Analytical Solution
227
464 Numerical Results
230
47 Closing Remarks
232
References for Additional Reading
242
Analysis of Specially Orthotropic Laminates Using CLPT
245
52 Bending of Simply Supported Rectangular Plates
246
522 The Navier Solution
247
53 Bending of Plates with Two Opposite Edges Simply Supported
255
532 Analytical Solutions
257
533 Ritz Solution
262
54 Bending of Rectangular Plates with Various Boundary Conditions
265
542 Clamped Plates
266
543 Approximation Functions for Other Boundary Conditions
269
55 Buckling of Simply Supported Plates Under Compressive Loads
271
552 The Navier Solution
272
553 Biaxial Compression of a Square Laminate k l
273
554 Biaxial Loading of a Square Laminate
274
56 Buckling of Rectangular Plates Under InPlane Shear Load
278
563 Clamped Plates
280
57 Vibration of Simply Supported Plates
282
58 Buckling and Vibration of Plates with Two Parallel Edges Simply Supported
285
582 Buckling by Direct Integration
287
583 Vibration by Direct Integration
288
59 Transient Analysis
290
593 Time Integration
292
510 Closure
293
References for Additional Reading
296
Analytical Solutions of Rectangular Laminated Plates Using CLPT
297
62 Admissible Boundary Conditions for the Navier Solutions
299
63 Navier Solutions of Antisymmetric CrossPly Laminates
301
632 Solution
304
633 Bending
308
634 Determination of Stresses
309
635 Buckling
317
636 Vibration
323
64 Navier Solutions of Antisymmetric AnglePly Laminates
326
642 Solution
328
643 Bending
329
644 Determination of Stresses
330
645 Buckling
335
646 Vibration
337
65 The LÚvy Solutions
339
652 Solution Procedure
342
653 Antisymmetric CrossPly Laminates
348
654 Antisymmetric AnglePly Laminates
353
66 Analysis of Midplane Symmetric Laminates
356
663 Weak Forms
357
664 The Ritz Solution
358
666 Other Boundary Conditions
360
67 Transient Analysis
361
673 Numerical Time Integration
362
674 Numerical Results
364
68 Summary
371
References for Additional Reading
375
Analytical Solutions of Rectangular Laminated Plates Using FSDT
377
72 Simply Supported Antisymmetric CrossPly Laminated Plates
379
722 Bending
381
723 Buckling
388
724 Vibration
394
73 Simply Supported Antisymmetric AnglePly Laminated Plates
400
732 The Navier Solution
402
733 Bending
404
734 Buckling
405
735 Vibration
406
74 Antisymmetric CrossPly Laminates with Two Opposite Edges Simply Supported
412
742 The LÚvy Type Solution
413
775 Numerical Results and Discussion
441
78 Summary
442
Problems
444
References for Additional Reading
445
Theory and Analysis of Laminated Shells
449
82 Governing Equations
450
822 Kinetics of the Shell
454
823 Kinematics of the Shell
455
824 Equations of Motion
457
825 Laminate Constitutive Relations
461
83 Theory of DoublyCurved Shells
462
832 Analytical Solution
463
84 Vibration and Buckling of CrossPly Laminated Circular Cylindrical Shells
473
842 Analytical Solution Procedure
475
843 Boundary Conditions
479
844 Numerical Results
480
Problems
483
Linear Finite Element Analysis of Composite Plates and Shells
487
92 Finite Element Models of the Classical Plate Theory CLPT
488
922 Spatial Approximations
490
923 Semidiscrete Finite Element Model
499
924 Fully Discretized Finite Element Models
500
925 Quadrilateral Elements and Numerical Integration
503
926 PostComputation of Stresses
510
93 Finite Element Models of Shear Deformation Plate Theory FSDT
515
932 Finite Element Model
516
933 Penalty Function Formulation and Shear Locking
520
934 PostComputation of Stresses
524
935 Bending Analysis
525
936 Vibration Analysis
540
937 Transient Analysis
542
94 Finite Element Analysis of Shells
543
942 Finite Element Model
546
943 Numerical Results
549
95 Summary
558
Problems
560
References for Additional Reading
561
Nonlinear Analysis of Composite Plates and Shells
567
102 Classical Plate Theory
568
1022 Virtual Work Statement
569
1023 Finite Element Model
572
103 FirstOrder Shear Deformation Plate Theory
575
1032 Virtual Work Statements
576
1033 Finite Element Model
578
104 Time Approximation and the NewtonRaphson Method
583
1042 The NewtonRaphson Method
584
1043 Tangent Stiffness Coefficients for CLPT
586
1044 Tangent Stiffness Coefficients for FSDT
590
1045 Membrane Locking
594
105 Numerical Examples of Plates
596
1053 Laminated Composite Plates
601
1054 Effect of Symmetry Boundary Conditions on Nonlinear Response
604
1055 Nonlinear Response Under InPlane Compressive Loads
608
1057 Transient Analysis of Composite Plates
612
106 Functionally Graded Plates
613
1062 Theoretical Formulation
615
1063 Thermomechanical Coupling
616
1064 Numerical Results
617
107 Finite Element Models of Laminated Shell Theory
621
1072 Finite Element Model
622
1073 Numerical Examples
625
108 Continuum Shell Finite Element
627
1082 Incremental Equations of Motion
628
1083 Continuum Finite Element Model
631
1084 Shell Finite Element
633
1085 Numerical Examples
638
1086 Closure
644
109 Postbuckling Response and Progressive Failure of Composite Panels in Compression
645
1093 Finite Element Models
647
1094 Failure Analysis
648
1095 Results for Panel C4
650
1096 Results for Panel H4
655
1010 Closure
658
References for Additional Reading
664
ThirdOrder Theory of Laminated Composite Plates and Shells
671
1122 Strains and Stresses
674
113 HigherOrder Laminate Stiffness Characteristics
677
1131 SingleLayer Plates
678
1132 Symmetric Laminates
680
1133 Antisymmetric Laminates
681
114 The Navier Solutions
682
1142 Antisymmetric CrossPly Laminates
684
1143 Antisymmetric AnglePly Laminates
687
1144 Numerical Results Bending Analysis
689
115 LÚvy Solutions of CrossPly Laminates
699
1152 Solution Procedure
701
1153 Numerical Results
704
116 Finite Element Model of Plates
706
1162 Finite Element Model
707
1163 Numerical Results
712
1164 Closure
714
117 Equations of Motion of the ThirdOrder Theory of DoublyCurved Shells
718
Problems
720
References for Additional Reading
721
Layerwise Theory and Variable Kinematic Models
725
1212 An Overview of Layerwise Theories
726
122 Development of the Theory
730
1222 Strains and Stresses
733
1223 Equations of Motion
734
1224 Laminate Constitutive Equations
736
123 Finite Element Model
738
1232 Full Layerwise Model Versus 3D Finite Element Model
739
1233 Considerations for Modeling Relatively Thin Laminates
742
1234 Bending of a Simply Supported 0900 Laminate
746
1235 Free Edge Stresses in a 4545s Laminate
753
124 Variable Kinematic Formulations
759
1242 Multiple Assumed Displacement Fields
762
1243 Incorporation of Delamination Kinematics
764
1244 Finite Element Model
766
1245 Illustrative Examples
769
125 Application to Adaptive Structures
780
1252 Governing Equations
783
1253 Finite Element Model
785
1254 An Example
787
126 Layerwise Theory of Cylindrical Shells
794
1263 Stiffened Shells
798
1264 Postbuckling of Laminated Cylinders
806
127 Closure
812
References for Additional Reading
816
Subject Index
821
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