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Tables of Contents for Shear Deformable Beams and Plates
Chapter/Section Title
Page #
Page Count
Preface
xiii
Introduction
1
10
Preliminary Comments
1
2
An Overview of Plate Theories
3
2
Present Study
5
6
Problems
6
5
Part 1: Beams
Bending of Beams
11
28
Beam Theories
11
13
Introduction
11
3
Euler-Bernoulli Beam Theory (EBT)
14
3
Timoshenko Beam Theory (TBT)
17
3
Reddy-Bickford Beam Theory (RBT)
20
4
Relationships Between EBT and TBT
24
4
General Comments
24
1
Simply Supported (SS) Beams
25
1
Clamped-Free (CF) Beams
25
1
Free-Clamped (FC) Beams
25
1
Clamped-Simply Supported (CS) Beams
26
1
Simply Supported-Clamped (SC) Beams
26
1
Clamped (CC) Beams
26
1
Summary of Relationships
27
1
Relationships Between EBT and RBT
28
3
Examples
31
5
Simply Supported Beam
32
2
Cantilever Beam
34
2
Summary
36
3
Problems
37
2
Shear-Flexural Stiffness Matrix
39
16
Introduction
39
2
Summary of Relationships
41
3
Relationships Between TBT and EBT
41
1
Relationships Between RBT and EBT
41
1
Relationships Between Simplified RBT and EBT
42
2
Stiffness Matrix
44
4
Frame Structure-An Example
48
2
Concluding Remarks
50
5
Problems
52
3
Buckling of Columns
55
22
Introduction
55
1
Relationship Between Euler-Bernoulli and Timoshenko Columns
56
8
General Relationship
56
2
Pinned-Pinned Columns
58
2
Fixed-Fixed Columns
60
1
Fixed-Free Columns
61
3
Relationship Between Euler-Bernoulli and Reddy-Bickford Columns
64
10
General Relationship
64
5
Pinned-Pinned Columns
69
1
Fixed-Fixed Columns
70
1
Fixed-Free Columns
71
1
Pinned-Pinned Columns with End Rotational Springs of Equal Stiffness
72
2
Concluding Remarks
74
3
Problems
75
2
Tapered Beams
77
12
Introduction
77
1
Stress Resultant-Displacement Relations
78
1
Equilibrium Equations
78
1
Deflection and Force Relationships
79
6
General Relationships
79
1
Simply Supported (SS) Beams
80
1
Clamped-Free (CF) Beams
81
1
Free-Clamped (FC) Beams
81
1
Clamped (CC) Beams
82
1
Clamped-Simply Supported (CS) Beams
82
1
Simply Supported-Clamped (SC) Beams
83
1
An Example
84
1
Symmetrically Laminated Beams
85
1
Concluding Remarks
86
3
Problems
86
3
Part 2: Plates
Theories of Plate Bending
89
22
Overview of Plate Theories
89
3
Classical (Kirchhoff) Plate Theory (CPT)
92
8
Equations of Equilibrium
92
2
Boundary Conditions
94
4
Governing Equations in Terms of the Deflection
98
2
First-Order Shear Deformation Plate Theory (FSDT)
100
5
Equations of Equilibrium
100
2
Plate Constitutive Equations
102
1
Governing Equations in Terms of Displacements
103
2
Third-Order Shear Deformation Plate Theory (TSDT)
105
6
Equations of Equilibrium
105
2
Plate Constitutive Equations
107
1
Problems
108
3
Bending Relationships for Simply Supported Plates
111
22
Introduction
111
1
Relationships Between CPT and FSDT
112
4
Examples
116
2
Simply Supported, Uniformly Loaded, Equilateral Triangular Plate
116
1
Simply Supported, Uniformly Loaded, Rectangular Plate
117
1
Relationships Between CPT and TSDT
118
10
Introduction
118
1
Governing Equations
119
4
The Kirchhoff Plate Theory (CPT)
123
1
Relationships Between the Theories
124
1
An Accurate Simplified Relationship
125
2
An Example
127
1
Closure
128
5
Problems
129
4
Bending Relationships for Levy Solutions
133
20
Introduction
133
1
Governing Equations
134
3
Introduction
134
1
Stress Resultant-Displacement Relations
135
2
Equilibrium Equations
137
1
Bending Relationships
137
11
General Relationships
137
6
SSSS Plates
143
1
SCSC Plates
144
1
SFSF Plates
145
2
SCSS Plates
147
1
SFSS Plates
148
1
Numerical Results
148
5
SCSC Plates
149
2
SFSF Plates
151
1
Problems
152
1
Bending Relationships for Circular and Annular Plates
153
24
Governing Equations
153
3
Relationships Between CPT and FSDT
156
9
General Relationships
156
6
Examples
162
3
Relationships Between CPT and TSDT
165
6
General Relationships
165
4
An Example
169
2
Closure
171
6
Problems
171
6
Bending Relationships for Sectorial Plates
177
18
Introduction
177
1
Formulation
178
4
The Kirchhoff Plate Theory (CPT)
178
2
The Mindlin Plate Theory (FSDT)
180
1
Governing Equations
181
1
Exact Bending Relationships
182
5
General Relationships
182
3
SSS Sectorial Plates
185
1
SSC Sectorial Plates
186
1
SSF Sectorial Plates
186
1
Examples
187
5
SSS Plates
187
1
SSC Plates
188
1
SSF Plates
188
1
Numerical Results
189
3
Conclusions
192
3
Problems
192
3
Buckling Relationships
195
28
Polygonal Plates
195
10
Governing Equations
195
4
Relationships Between CPT and FSDT
199
1
Relationships Between CPT and TSDT
200
5
Circular Plates
205
6
Governing Equations
205
2
Relationship Between CPT and FSDT
207
1
Relationship Between CPT and TSDT
208
2
Numerical Results
210
1
Sectorial Mindlin Plates
211
12
Governing Equations
211
4
Buckling Load Relationship
215
3
Problems
218
5
Free Vibration Relationships
223
20
Introduction
223
3
Relationships Between CPT and FSDT
226
9
General Relationship
226
3
Numerical Results
229
6
Relationships Between CPT and TSDT
235
6
Concluding Remarks
241
2
Problems
241
2
Relationships for Inhomogeneous Plates
243
36
Deflection Relationships for Sandwich Plates
243
10
Introduction
243
1
Governing Equations for Kirchhoff Plates
244
1
Governing Equations for Sandwich Mindlin Plates
245
3
Relationship Between Sandwich and Kirchhoff Plates
248
2
Examples
250
2
Relationship Between Sandwich and Solid Mindlin Plates
252
1
Deflection Relationships for Functionally Graded Circular Plates
253
16
Introduction
253
1
Formulation
254
2
Relationships Between CPT and FSDT
256
4
Relationships for Various Boundary Conditions
260
4
Illustrative Examples
264
5
Buckling Load Relationships for Sandwich Mindlin Plates
269
3
Governing Equations
269
2
Buckling Load Relationship
271
1
Free Vibration Relationships for Sandwich Plates
272
4
Governing Equations
272
3
Free Vibration Relationship
275
1
Summary
276
3
References
279
14
Subject Index
293