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The capability to predict the nonlinear response of beams, plates and shells when subjected to thermal and mechanical loads is of prime interest to structural analysis. In fact, many structures are subjected to high load levels that may result in nonlinear load-deflection relationships due to large deformations. One of the important problems deserving special attention is the study of their nonlinear response to large deflection, postbuckling and nonlinear vibration.
The capability to predict the nonlinear response of beams, plates and shells when subjected to thermal and mechanical loads is of prime interest to structural analysis. In fact, many structures are subjected to high load levels that may result in nonlinear load-deflection relationships due to large deformations. One of the important problems deserving special attention is the study of their nonlinear response to large deflection, postbuckling and nonlinear vibration.
A two-step perturbation method is firstly proposed by Shen and Zhang (1988) for postbuckling analysis of isotropic plates. This approach gives parametrical analytical expressions of the variables in the postbuckling range and has been generalized to other plate postbuckling situations. This approach is then successfully used in solving many nonlinear bending, postbuckling, and nonlinear vibration problems of composite laminated plates and shells, in particular for some difficult tasks, for example, shear deformable plates with four free edges resting on elastic foundations, contact postbuckling of laminated plates and shells, nonlinear vibration of anisotropic cylindrical shells. This approach may be found its more extensive applications in nonlinear analysis of nano-scale structures.
Concentrates on three types of nonlinear analyses: vibration, bending and postbuckling
Presents not only the theoretical aspect of the techniques, but also engineering applications of the method
A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells is an original and unique technique devoted entirely to solve geometrically nonlinear problems of beams, plates and shells. It is ideal for academics, researchers and postgraduates in mechanical engineering, civil engineering and aeronautical engineering.
Table of Contents
About the Author
Preface
List of Symbols
1 Traditional Perturbation Method
1.1 Introduction
1.2 Load-type Perturbation Method
1.3 Deflection-type Perturbation Method
1.4 Multi-parameter Perturbation Method
1.5 Limitations of the Traditional Perturbation Method
References
2 Nonlinear Analysis of Beams
2.1 Introduction
2.2 Nonlinear Motion Equations of Euler–Bernoulli Beams
2.3 Postbuckling Analysis of Euler–Bernoulli Beams
2.4 Nonlinear Bending Analysis of Euler–Bernoulli Beams
2.5 Large Amplitude Vibration Analysis of Euler–Bernoulli Beams
References
3 Nonlinear Vibration Analysis of Plates
3.1 Introduction
3.2 Reddy’s Higher Order Shear Deformation Plate Theory
3.3 Generalized Karman-type Motion Equations
3.4 Nonlinear Vibration of Functionally Graded Fiber Reinforced Composite Plates
3.5 Hygrothermal Effects on the Nonlinear Vibration of Shear Deformable Laminated Plate
3.6 Nonlinear Vibration of Shear Deformable Laminated Plates with PFRC Actuators
References
4 Nonlinear Bending Analysis of Plates
4.1 Introduction
4.2 Nonlinear Bending of Rectangular Plates with Free Edges under Transverse and In-plane Loads and Resting on Two-parameter Elastic Foundations
4.3 Nonlinear Bending of Rectangular Plates with Free Edges under Transverse and Thermal Loading and Resting on Two-parameter Elastic Foundations
4.4 Nonlinear Bending of Rectangular Plates with Free Edges Resting on Tensionless Elastic Foundations
4.5 Nonlinear Bending of Shear Deformable Laminated Plates under Transverse and In-plane Loads
4.6 Nonlinear Bending of Shear Deformable Laminated Plates under Transverse and Thermal Loading
4.7 Nonlinear Bending of Functionally Graded Fiber Reinforced Composite Plates
Appendix 4.A
Appendix 4.B
Appendix 4.C
Appendix 4.D
Appendix 4.E
Appendix 4.F
References
5 Postbuckling Analysis of Plates
5.1 Introduction
5.2 Postbuckling of Thin Plates Resting on Tensionless Elastic Foundation
5.3 Postbuckling of Shear Deformable Laminated Plates under Compression and Resting on Tensionless Elastic Foundations
5.4 Thermal Postbuckling of Shear Deformable Laminated Plates Resting on Tensionless Elastic Foundations
5.5 Thermomechanical Postbuckling of Shear Deformable Laminated Plates Resting on Tensionless Elastic Foundations
5.6 Postbuckling of Functionally Graded Fiber Reinforced Composite Plates under Compression
5.7 Thermal Postbuckling of Functionally Graded Fiber Reinforced Composite Plates
5.8 Postbuckling of Shear Deformable Hybrid Laminated Plates with PFRC Actuators
References
6 Nonlinear Vibration Analysis of Cylindrical Shells
6.1 Introduction
6.2 Reddy’s Higher Order Shear Deformation Shell Theory and Generalized Karman-type Motion Equations
6.3 Nonlinear Vibration of Shear Deformable Cross-ply Laminated Cylindrical Shells
6.4 Nonlinear Vibration of Shear Deformable Anisotropic Cylindrical Shells
6.5 Hygrothermal Effects on the Nonlinear Vibration of Functionally Graded Fiber Reinforced Composite Cylindrical Shells
6.6 Nonlinear Vibration of Shear Deformable Laminated Cylindrical Shells with PFRC Actuators
Appendix 6.G
References
7 Postbuckling Analysis of Cylindrical Shells
7.1 Introduction
7.2 Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells under Axial Compression
7.3 Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells under External Pressure
7.4 Thermal Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells
7.5 Postbuckling of Axially Loaded Anisotropic Cylindrical Shells Surrounded by an Elastic Medium
7.6 Postbuckling of Internal Pressure Loaded Anisotropic Cylindrical Shells Surrounded by an Elastic Medium
Appendix 7.H
Appendix 7.I
Appendix 7.J
References
Index
