Sandwich Structures Theory and Responses 2021

This book provides a solid foundation from which most practical, theoretical problems related to sandwich structures can be derived and solved. The text brings together many problems found in the literature, such as those concerning buckling, post-buckling, free vibration, and dynamic response under various types of loadings. Sandwich construction with functionally graded facings is also briefly discussed, wherein topics obtain theoretical solutions from one comprehensive, consistent theory. The basic governing equations are presented in orthogonal curvilinear coordinates considering the shallow shell theory, which includes the strain-displacement equations, the constitutive equations, equations of motion, and the compatibility equations. Providing a clear theoretical foundation for engineers and research scientists in need of detail on sandwich structures in professional practice, the book is an ideal reference for understanding these structures through a comprehensive treatment ofthe theory, mathematical procedures, and applications. Preface Acknowledgements Contents Chapter 1: Introduction 1.1 Preliminary Overview 1.2 Composition of the Sandwich Structure 1.3 Failure Modes of Sandwich Structures 1.4 Contents of the Text References Chapter 2: Theory of Sandwich Plates and Shells with an Transversely Incompressible Core 2.1 Introduction 2.2 Preliminaries and Basic Assumption 2.3 Basic Equations 2.3.1 Displacement Field 2.3.2 Strain-Displacement Relationships 2.3.3 Constitutive Equations 2.3.4 Stress and Moment Resultants 2.4 Hamilton ́s Principle 2.4.1 Hamilton ́s Equation 2.4.2 Strain Energy 2.4.3 Kinetic Energy 2.4.4 Work Done by External Loads 2.5 Equations of Motion - Nonlinear Formulation 2.5.1 The Mixed Formulation for Sandwich Plate and Shells 2.5.2 Displacement Formulation for Sandwich Plates and Shells 2.5.3 Displacement Formulation for Sandwich Plates 2.6 Equations of Motion - Linear Formulation 2.6.1 Displacement Formulation for Sandwich Shells 2.6.2 Displacement Formulation for Sandwich Plates 2.7 Boundary Conditions 2.8 Summary References Chapter 3: Buckling of Sandwich Plates and Shells 3.1 Introduction 3.2 Preliminaries and Basic Assumptions 3.3 Buckling of Flat Sandwich Panels 3.3.1 Governing System 3.3.2 Solution Methodology 3.3.3 Validation of the Theoretical Results 3.3.4 Results and Discussion 3.4 Buckling of Doubly Curved Sandwich Panels 3.4.1 Governing System 3.4.2 Solution Methodology 3.4.3 Validation of the Theoretical Results 3.4.4 Results and Discussion 3.5 Stress/Strain Theory 3.6 Summary References Chapter 4: Post-Buckling 4.1 Introduction 4.2 Preliminaries and Basic Assumptions 4.3 Cross-Ply Laminated Sandwich Shells 4.3.1 Governing System 4.3.2 Solution Methodology 4.3.3 Numerical Results and Discussion 4.4 Angle-Ply Laminated Sandwich Plates 4.4.1 Governing System 4.4.2 Solution Methodology 4.4.3 Numerical Results and Discussion 4.5 Angle-Ply Laminated Sandwich Shells 4.5.1 Governing System 4.5.2 Solution Methodology 4.5.3 Numerical Results and Discussion 4.6 Immovability of the Edges 4.7 End-Shortening 4.8 Summary References Chapter 5: Free Vibration 5.1 Introduction 5.2 Preliminaries and Basic Assumptions 5.3 Flat Sandwich Panels 5.3.1 Governing System 5.3.2 Solution Methodology 5.3.3 Validation of the Theoretical Structural Model 5.3.4 Results and Discussion 5.4 Doubly Curved Sandwich Panels 5.4.1 Governing System 5.4.2 Solution Methodology 5.4.3 Validation of the Theoretical Model 5.4.4 Present Results and Discussion 5.5 Summary References Chapter 6: Dynamic Response to Time-Dependent External Excitations 6.1 Introduction 6.2 Preliminaries and Basic Assumptions 6.3 Flat Sandwich Panels 6.3.1 Governing System 6.3.2 Solution Methodology 6.4 Doubly Curved Sandwich Panels 6.4.1 Governing System 6.4.2 Solution Methodology 6.5 Explosive Pressure Pulses and Numerical Results 6.5.1 Sonic Boom 6.5.2 Rectangular Pulse 6.5.3 Heaviside Pulse 6.5.4 Sine Pulse 6.5.5 Tangential Blast Pulse 6.5.6 Friedlander Explosive Blast Pulse 6.5.7 Underwater Shock Pulse 6.6 Summary References Chapter 7: Theory of Sandwich Plates and Shells with an Transversely Compressible Core - Theory One 7.1 Introduction 7.2 Preliminaries and Basic Assumptions 7.3 Basic Equations 7.3.1 Displacement Field 7.3.2 Nonlinear Strain-Displacement Equations 7.3.3 Constitutive Equations 7.4 Hamilton ́s Principle 7.4.1 Strain Energy 7.4.2 Work Done by External Loads 7.4.3 Kinetic Energy 7.5 Governing Equations 7.5.1 Equations of Motion 7.5.2 Boundary Conditions 7.6 The Stress Resultants, Stress Couples, and Stiffnesses 7.7 Comments 7.8 Application - Dynamic Response of Flat Sandwich Panels 7.8.1 Preliminaries 7.8.2 Governing Equations 7.8.3 Solution Methodology 7.9 Comments References Chapter 8: Theory of Sandwich Plates and Shells with an Transversely Compressible Core - Theory Two 8.1 Introduction 8.2 Preliminaries and Basic Assumptions 8.3 Basic Equations 8.3.1 Displacement Field 8.3.2 Nonlinear Strain-Displacement Equations 8.3.3 Constitutive Equations 8.4 Hamilton ́s Principle 8.4.1 Strain Energy 8.4.2 Work Done by External Loads 8.4.3 Kinetic Energy 8.5 Governing System 8.5.1 Equations of Motion 8.5.2 Boundary Conditions 8.6 The Stress Resultants, Stress Couples, and Stiffnesses 8.7 Comments 8.8 Application - Buckling/Post-Buckling 8.8.1 Comments 8.8.2 Governing Equations 8.8.3 Solution Methodology References Chapter 9: Theory of Functionally Graded Sandwich Plates and Shells 9.1 Introduction 9.2 Preliminaries and Basic Assumptions 9.3 Basic Equations 9.3.1 Displacement Field 9.3.2 Nonlinear Strain-Displacement Equations 9.3.3 Constitutive Equations 9.4 Hamilton ́s Principle 9.4.1 Strain Energy 9.4.2 Work Done by External Loads 9.4.3 Kinetic Energy 9.5 Equations of Motion 9.5.1 Equations of Motion - Mixed Formulation 9.5.2 The Equations of Motion - The Displacement Formulation 9.5.3 The Boundary Conditions 9.6 Final Comments References Index