梁、板、壳结构非线性分析的二次摄动法

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-parametar 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-Bemoulli 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 Kfirmin-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

Reterences

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 RectanguIar 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 Posthuckling 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 Cmnpression

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

Kfirmn-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

《材料与力学进展：梁、板、壳结构非线性分析的二次摄动法（英文版）》讨论了二次摄动法及其在梁、板、壳结构非线性分析中的应用；系统地总结了20世纪90年代以来在梁、板、壳结构非线性分析中所取得的最新成果；提供了一个完整的理论体系来处理新型复合材料板壳结构的非线性行为，特别是在复杂环境或复杂荷载作用下的非线性行为。涉及梁、板、壳结构的非线性弯曲、后屈曲和非线性振动等领域。《材料与力学进展：梁、板、壳结构非线性分析的二次摄动法（英文版）》所介绍的二次摄动法可推广应用于微纳米尺度梁、板、壳结构的非线性分析。
　　《材料与力学进展：梁、板、壳结构非线性分析的二次摄动法（英文版）》可供结构设计人员和梁、板、壳结构非线性行为研究的学者及高等院校的研究生参考。