The Behavior of Sandwich Structures of Isotropic and Composite Materials

SANDWICH STRUCTURES: ORIGINS, ADVANTAGES, AND USES
Description of Various Sandwich Constructions
Advantages of Sandwich Construction over Construction Monocoque Thin Walled Construction
Origins of Sandwich Construction
Uses of Sandwich Construction
Present Approach to Analysis
Problems
References

ANISTROPIC ELASTICITY AND COMPOSITE LAMINATE THEORY
Introduction
Derivation of the Anisotropic Elastic Stiffness and Compliance Matrices
The Physical Meaning of the Components of the Orthotropic Elasticity Tensor
Methods to Obtain Composite Elastic Properties from Fiber and Matrix Properties
Thermal and Hygrothermal Considerations
Time-Temperature Effects on Composite Materials
High Strain Rate Effects on Material Properties
Laminae of Composite Materials
Laminate Analysis
[A], [B], and [D] Stiffness Matrices for a Mid-Plane Symmetric Sandwich Structure
Piezoelectric Effects
Problems
References

DERIVATION OF THE GOVERNING EQUATIONS FOR SANDWICH PLATES (PANELS)
Introduction
Plate Equilibrium Equations
The Bending of Composite Material Laminated and/or Sandwich Plates: Classical Theory
Classical Plate Theory Boundary Conditions
Analysis of Composite Materials Laminated and/or Sandwich Panels Including Transverse Shear Deformation Effects
Boundary Conditions for a Plate Using the Refined Plate Theory
Laminated or Sandwich Plate on an Elastic Foundation
Laminated or Sandwich Plates Subjected to Dynamic Loads
Problems
References

BEAMS, COLUMNS, AND RODS OF COMPOSITE MATERIALS Development of Classical Beam Theory
Some Simplified Sandwich-Beam Solutions
Eigenvalue Problems of Sandwich Beams: Natural Vibrations and Elastic Stability
Other Considerations
Problems
References

ENERGY METHODS FOR SANDWICH STRUCTURES
Introduction
Theorem of Minimum Potential Energy
Analysis of a Beam in Bending Using the Theorem of Minimum Potential Energy
Reissner's Variational Theorem and Its Applications
Static Deformation of Moderately Thick Beams
Flexural Vibrations of Moderately Thick Beams
Flexural Natural Frequencies of a Simply Supported Beam Including Transverse Shear Deformation and Rotatory Inertia Effects
Minimum Potential Energy for Rectangular Plates
A Rectangular Composite Material Plate Subjected to Lateral and Hygrothermal Loads
In-Plane Shear Strength Determination of Composite Materials in Laminated and Sandwich Panels
Problems
References

SOLUTIONS FOR RECTANGULAR SANDWICH PLATES
Introduction
Navier Solutions for Rectangular Sandwich Plates
Levy Solutions for Plates of Composite Materials
Perturbation Solutions for the Bending of a Composite Material Sandwich Plate, with Mid-Plane Symmetry and No Bending-Twisting Coupling
Isotropic Sandwich Panels Subjected to a Uniform Lateral Load
Minimum Weight Optimization for a Sandwich Panel Subjected to a Distributed Lateral Load
Analysis of an Isotropic Sandwich Plate on an Elastic Foundation Subjected to a Uniform Lateral Load
Static Analysis of Sandwich Plates of Composite Materials Including Transverse Shear Deformation Effects
Exact Solution
Other Considerations
Problems
References

DYNAMIC EFFECTS ON SANDWICH PANELS
Introduction
Natural Flexural Vibrations of Sandwich Plates: Classical Theory
Natural Flexural Vibrations of Sandwich Plates Including Transverse Shear Deformation Effects
Forced-Vibration Response of a Sandwich Plate Subjected to a Dynamic Lateral Load
Dynamic Response of Sandwich Plates to Localized Loads
Large Amplitude Nonlinear Oscillations of Sandwich Plates Simply Supported on All Edges
Linear and Nonlinear Oscillations of Specially Orthotropic Sandwich Panels with Various Boundary Conditions
Vibration Damping
Problems
References

THERMAL AND MOISTURE EFFECTS ON SANDWICH STRUCTURES
General Considerations
Derivation of the Governing Equations for a Thermoplastic Isotropic Plate
Boundary Conditions
General Treatment of Plate Nonhomogeneous Boundary Conditions
Thermoelastic Effects on Beams
Self-Equilibrium of Thermal Stress
Rectangular Composite Material Plate Subjected to Lateral and Hygrothermal Loads
References

ELASTIC INSTABILITY (BUCKLING) OF SANDWICH PANELS General Considerations
The Buckling of an Orthotropic Sandwich Plate Subjected to In-Plane Loads Classical Theory
Elastic Stability of a Composite Sandwich Panel Including Transverse Shear Deformation and Hygrothermal Effects
The Buckling of an Isotropic Plate on an Elastic Foundation Subjected to Biaxial In-Plane Compressive Loads
The Buckling of Honeycomb Core Sandwich Panels Subjected to In-Plane Compressive Loads
The Buckling of Solid- or Foam-Core Sandwich Panels Subjected to In-Plane Compressive Loads
Buckling of a Truss-Core Sandwich Panel Subjected to Uniaxial Compression
Elastic Stability of a Web-Core Sandwich Panel Subjected to a Uniaxial Compressive In-Plane Load
Buckling of Honeycomb-Core Sandwich Panels Subjected to In-Plane Shear Loads
Buckling of Solid-Core or Foam-Sandwich Panel Subjected to In-Plane Shear Loads
Buckling of a Truss-Core Sandwich Panel Subjected to In-Plane Shear Loads
Buckling of a Web-Core Sandwich Panel Subjected to an In-Plane Shear Load
Other Considerations
Problems
References

STRUCTURAL OPTIMIZATION TO OBTAIN MINIMUM-WEIGHT SANDWICH PANELS
Introduction
Minimum Weight Optimization of Honeycomb-Core Sandwich Panels Subjected to a Unidirectional Compressive Load
Minimum Weight Optimization of Foam-Core Sandwich Panels Subjected to a Unidirectional Compressive Load
Minimum Weight Optimization of Truss-Core Sandwich Panels Subjected to a Unidirectional Compressive Load
Minimum Weight Optimization of Web-Core Sandwich Panels Subjected to a Unidirectional Compressive Load
Minimum Weight Optimization of Honeycomb-Core Sandwich Panels Subjected to In-Plane Shear Loads
Minimum Weight Optimization of Solid- and Foam-Core Sandwich Panels Subjected to In-Plane Shear Loads
Minimum Weight Optimization of Truss-Core Sandwich Panels Subjected to In-Plane Shear Loads
Minimum Weight Optimization of Web-Core Sandwich Panels Subjected to In-Plane Shear Loads
Optimal Stacking Sequences for Composite Material Laminate Faces for Various Sandwich Panels Subjected to Various Loads
Problems
References

SANDWICH SHELLS
Introduction
Analysis of Sandwich Cylindrical Shells under Axially Symmetric Loads
A General Solution for Orthotropic-Sandwich Cylindrical Shells under Axially Symmetric Loads
Shells with Mid-Plane Asymmetry
Other Considerations
Problems
References

BUCKLING OF SANDWICH CYLINDRICAL SHELLS
Buckling of a Solid- or Foam-Core Sandwich Cylindrical Shell with Isotropic Faces Subjected to an Axially Symmetric Compressive End Load
Buckling of a Solid- or Foam-Core Sandwich Cylindrical Shell with Orthotropic Composite Faces Subjected to an Axially Symmetric Compressive Load
Buckling of a Honeycomb-Core Sandwich Cylindrical Shell with Composite Faces Subjected to an Axially Symmetric Compressive End Load
Overall Buckling of Sandwich Cylindrical Shells Subjected to an Overall Bending Moment
Buckling of a Sandwich Cylindrical Shell Due to External Pressure
Buckling of a Sandwich Cylindrical Shell Due to Torsion
Dynamic Buckling
Problems
References

MINIMUM WEIGHT OPTIMIZATION OF SANDWICH CYLINDRICAL SHELLS
General Discussion
Minimum Weight Optimization of a Solid Foam-Core Sandwich Cylindrical Shell with Isotropic Faces Subjected to an Axially Compressive Load
Minimum Weight Optimization of a Solid- or Foam-Core Sandwich Cylindrical Shell with Orthotropic Composite Material Faces Subjected to an Axially Compressive Load
Minimum Weight Optimization of a Honeycomb-Core Sandwich Cylindrical Shell with Composite Material Faces Subjected to an Axially Symmetric Compressive Load
Problems
References

APPENDIX 1: Core Materials
APPENDIX 2: Face Materials
APPENDIX 3: American Society for Testing Materials (ASTM) Standards for Sandwich Structures and Materials

INDEX

Biography

Vinson, JackR.

"Most composite textbooks focus on basic laminate theory. This is an important subject, but it will only get you so far. At some point, you will need to move beyond simple point stress analysis and start looking at complex structures.
One of Jack Vinson's earlier books, The Behavior of Structures Composed of Composite Materials, has long been on my list of essential references. It starts with a brief review of lamination theory, then gets right into the analysis of beams, plates, and shells. It is a graduate level textbook, but could be targeted to advanced seniors.
The Behavior of Sandwich Structures picks up where The Behavior of Structures leaves off. It essentially covers the same types of structures, but at a more advanced level. It also covers some new subject areas like structural optimization.
Any sandwich structure, whether it has isotropic or anisitropic facesheets, can be treated as a composite. Traditional composite theories can be used, with the important addition of transverse shear effects.
Governing differential equations are given for beams, plates, and shells. Several solution methods are outlined, including both direct solutions and energy methods. Solutions for some specific geometries and boundary conditions are worked out in full, but most are left as an excercise (this is a textbook, after all). Governing equations and solutions cover static and dynamic loads, thermal and moisture effects, and eigenvalues (natural frequencies and stability).
As one would expect from a book on sandwich structures, special failure modes such as face wrinkling and core shear instability are discussed. Core materials aren't limited to honeycomb, but also include foam-cores, web-cores, and truss-cores.
One of the more important topics in composite structure design is optimization, and Dr. Vinson provides two chapters on the subject: one for sandwich plates; and one for sandwich shells. The optimization techniques are all closed form, so you won't see much on layup optimization, but the methods are applicable to material selection and geometric design. After working through some optimization solutions, some general design guidelines become apparent.
Aside from the primary technical content, Sandwich Structures contains a list of homework problems (again, it's meant to be a textbook) and references at the end of each chapter. Many of the references are to other works by Dr. Vinson, but that just shows he is the right person to author this book.
If you've read any of my earlier reviews, you know that I'm quite picky when it comes to typography and grammar. In that sense, this book was a pleasant change: I found only a few typos in equations, and even fewer obvious grammatical errors. … the binding is of good quality.
Even if you aren't designing sandwich structures, you will still find this book useful. Because sandwiches are treated like composites, the theories and solutions can be applied to monocoque structures. And if you are designing sandwich structures, then this book will make your job a lot easier."
-About.com book review