Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells

Inbunden, Engelska, 2013

Av Hui-Shen Shen, China) Shen, Hui-Shen (Shanghai Jiao Tong University

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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.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 postbucklingPresents not only the theoretical aspect of the techniques, but also engineering applications of the methodA 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.

Produktinformation

Utgivningsdatum2013-10-01
Mått178 x 254 x 23 mm
Vikt717 g
FormatInbunden
SpråkEngelska
Antal sidor368
FörlagJohn Wiley & Sons Inc
ISBN9781118649886

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About the Author ix Preface xiList of Symbols xiii1 Traditional Perturbation Method 11.1 Introduction 11.2 Load-type Perturbation Method 21.3 Deflection-type Perturbation Method 31.4 Multi-parameter Perturbation Method 41.5 Limitations of the Traditional Perturbation Method 5References 62 Nonlinear Analysis of Beams 92.1 Introduction 92.2 Nonlinear Motion Equations of Euler–Bernoulli Beams 102.3 Postbuckling Analysis of Euler–Bernoulli Beams 132.4 Nonlinear Bending Analysis of Euler–Bernoulli Beams 172.5 Large Amplitude Vibration Analysis of Euler–Bernoulli Beams 21References 253 Nonlinear Vibration Analysis of Plates 273.1 Introduction 273.2 Reddy’s Higher Order Shear Deformation Plate Theory 293.3 Generalized Karman-type Motion Equations 353.4 Nonlinear Vibration of Functionally Graded Fiber Reinforced Composite Plates 423.5 Hygrothermal Effects on the Nonlinear Vibration of Shear Deformable Laminated Plate 633.6 Nonlinear Vibration of Shear Deformable Laminated Plates with PFRC Actuators 69References 744 Nonlinear Bending Analysis of Plates 794.1 Introduction 794.2 Nonlinear Bending of Rectangular Plates with Free Edges under Transverse and In-plane Loads and Resting on Two-parameter Elastic Foundations 804.3 Nonlinear Bending of Rectangular Plates with Free Edges under Transverse and Thermal Loading and Resting on Two-parameter Elastic Foundations 914.4 Nonlinear Bending of Rectangular Plates with Free Edges Resting on Tensionless Elastic Foundations 944.5 Nonlinear Bending of Shear Deformable Laminated Plates under Transverse and In-plane Loads 974.6 Nonlinear Bending of Shear Deformable Laminated Plates under Transverse and Thermal Loading 1094.7 Nonlinear Bending of Functionally Graded Fiber Reinforced Composite Plates 116Appendix 4.A 126Appendix 4.B 131Appendix 4.C 132Appendix 4.D 133Appendix 4.E 136Appendix 4.F 137References 1415 Postbuckling Analysis of Plates 1455.1 Introduction 1455.2 Postbuckling of Thin Plates Resting on Tensionless Elastic Foundation 1475.3 Postbuckling of Shear Deformable Laminated Plates under Compression and Resting on Tensionless Elastic Foundations 1635.4 Thermal Postbuckling of Shear Deformable Laminated Plates Resting on Tensionless Elastic Foundations 1715.5 Thermomechanical Postbuckling of Shear Deformable Laminated Plates Resting on Tensionless Elastic Foundations 1785.6 Postbuckling of Functionally Graded Fiber Reinforced Composite Plates under Compression 1855.7 Thermal Postbuckling of Functionally Graded Fiber Reinforced Composite Plates 1945.8 Postbuckling of Shear Deformable Hybrid Laminated Plates with PFRC Actuators 200References 2116 Nonlinear Vibration Analysis of Cylindrical Shells 2156.1 Introduction 2156.2 Reddy’s Higher Order Shear Deformation Shell Theory and Generalized Karman-type Motion Equations 2166.3 Nonlinear Vibration of Shear Deformable Cross-ply Laminated Cylindrical Shells 2196.4 Nonlinear Vibration of Shear Deformable Anisotropic Cylindrical Shells 2336.5 Hygrothermal Effects on the Nonlinear Vibration of Functionally Graded Fiber Reinforced Composite Cylindrical Shells 2526.6 Nonlinear Vibration of Shear Deformable Laminated Cylindrical Shells with PFRC Actuators 257Appendix 6.G 263References 2697 Postbuckling Analysis of Cylindrical Shells 2737.1 Introduction 2737.2 Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells under Axial Compression 2747.3 Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells under External Pressure 2957.4 Thermal Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells 3127.5 Postbuckling of Axially Loaded Anisotropic Cylindrical Shells Surrounded by an Elastic Medium 3207.6 Postbuckling of Internal Pressure Loaded Anisotropic Cylindrical Shells Surrounded by an Elastic Medium 325Appendix 7.H 331Appendix 7.I 339Appendix 7.J 341References 344Index 349