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About this book

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 of the theory, mathematical procedures, and applications.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
Sandwich structures have several prominent roles in the aerospace industry such as their use in aircraft engines, the fuselage, the floor, side-panels, overhead bins, and the ceiling. These structures have many additional applications such as their use in naval ship bulkheads, deck houses, aircraft hangars, locomotive cabs, buses, satellites, automobiles, etc. With this in mind, a very intensive study of their structural performance is necessary under extreme complex loading conditions. As an introduction, a very preliminary overview of the composition of typical sandwich structures are discussed with regard to their structural elements. Secondly various applications of this type of structure are listed. A few historical applications are briefly mentioned with various types of failure modes, such as wrinkling, that sandwich structures can endure. Finally, an overview of the text is presented for the readers benefit.
Terry John Hause

Chapter 2. Theory of Sandwich Plates and Shells with an Transversely Incompressible Core

Abstract
An extremely robust geometrical nonlinear theory of initially imperfect doubly curved sandwich shells with an incompressible core is presented. The aspects of the theory consider dissimilar face sheets with imposed anisotropic laminated composite construction. The core is considered broad in its inherent properties by considering both the weak and strong core types. The influence of the geometric imperfections on the theoretical developments are also included which adds an additional level of complexity. The governing equations are simplified for various specialized cases for two formulations referred to as the mixed formulation and the displacement formulation. These formulations are then broken down individually each for plate and shell-type sandwich construction. Finally, the boundary conditions are briefly discussed.
Terry John Hause

Chapter 3. Buckling of Sandwich Plates and Shells

Abstract
Application of the governing linear equations of equilibrium and the associated boundary conditions as applied to the stability of sandwich plates and shells with anisotropic laminated composite facings and a weak core is addressed while the facings are considered symmetric with respect to both their local and global mid-surfaces. Both sandwich plates and shells are considered with implications of various structural configurations. Such structural configurations consider the structural tailoring of the face sheets, the panel face thickness, the aspect ratio, etc. on the buckling load. Finally, validations are made with results found within the existing literature.
Terry John Hause

Chapter 4. Post-Buckling

Abstract
Sandwich structures are capable of sustaining loading beyond the buckling bifurcation point. With this in mind, a comprehensive geometrically nonlinear theoretical treatment of sandwich plates and shells is considered to provide insight into their structural performance within this loading region. Within this comprehensive theoretical treatment, there are few structural and material conditions considered. The face sheets are considered symmetric with respect to their local and global mid-surfaces while constructed from anisotropic laminated composites. The facings are assumed imperfect and thin thereby neglecting the transverse shear stresses in the facings. The core is assumed to be of the weak-type construction. With these theoretical aspects, two cases of laminated facings are considered, cross-ply and angle-ply. Two formulations, the mixed formulation and the displacement formulation, are presented within the theoretical developments. To arrive at the post-buckling solution, the extended Galerkin method and Newton’s method are adopted. Finally, a number of kinematical and physical parameters are considered in regard to the load-carrying capacity of these sandwich panels. Several results are presented which provides sufficient insight to the behavior of these structures.
Terry John Hause

Chapter 5. Free Vibration

Abstract
An advanced model of sandwich plates and shells considering anisotropic laminated composite face sheets with a weak orthotropic core, in the context of determining the eigenfrequencies, is presented. Within this advanced model, adoption of the shallow shell theory is adhered to. The influence of several geometrical and material characteristics of the sandwich panel are considered with regard to the eigenfrequencies. The influence of these characteristics such as the panel geometry, the ply angle and stacking sequence of the face sheets, the orthotropicity ratio of the core, the panel face thickness, the aspect ratio, etc. are all determined to have an effect on the eigenfrequencies of the sandwich panel. Due to the nature of the governing equations, a closed form solution is obtainable with reasonable results. Several validations are made with several prominent author’s results found within the literature. With this is hand, appropriate conclusions are made.
Terry John Hause

Chapter 6. Dynamic Response to Time-Dependent External Excitations

Abstract
An advanced theoretical model pertaining to sandwich structures characterized by anisotropic laminated facings and a weak orthotropic core is addressed, in regard to the dynamic response problem. In this regard, several time-dependent external pressure pulses are considered which lend themself to a closed form solution, for both the eigenfrequencies and the dynamic response problem, utilizing the Laplace transform and the extended Galerkin method. Finally, a detailed analysis considering the influence of several parameters is conducted, with numerical results covering a broad spectrum of responses to various material or geometrical configurations presented with a thorough discussion of the results.
Terry John Hause

Chapter 7. Theory of Sandwich Plates and Shells with an Transversely Compressible Core – Theory One

Abstract
A comprehensive detailed nonlinear theoretical model of asymmetric anisotropic doubly curved laminated composite sandwich plates and shells considering the case for the transversely compressible core, thereby capturing the wrinkling phenomenon of the sandwich panel, is presented. The theory assumes a transversal displacement of the core in terms of a first-order power series expansion, thus theory one. The governing equations are developed by way of an energy approach known as Hamilton’s principle. Finally, an application of the governing equations is provided to demonstrate the solution approach to these equations through the use of the extended Galerkin method.
Terry John Hause

Chapter 8. Theory of Sandwich Plates and Shells with an Transversely Compressible Core – Theory Two

Abstract
A further comprehensive detailed nonlinear theoretical model of asymmetric anisotropic doubly curved laminated composite sandwich plates and shells considering the case for the transversely compressible core in sufficient detail, thereby capturing the wrinkling phenomenon of the sandwich panel, is presented. The theory assumes a transversal displacement of the core in terms of a second-order power series expansion, thus theory two. The governing equations are developed by way of an energy approach known as Hamilton’s principle. Finally, an application of the governing equations with regard to buckling and postbuckling is provided to demonstrate the solution approach to these equations through the use of the extended Galerkin method.
Terry John Hause

Chapter 9. Theory of Functionally Graded Sandwich Plates and Shells

Abstract
The foundation of functionally graded doubly curved sandwich structures is presented. The theory considers a comprehensive nonlinear theory with two types of variations of the constituent materials. The theory considers the first-order shear deformation construct at the cost of only a slight decrease in accuracy. An energy approach is taken in the formulation of the governing equations. Within the context of this theoretical model, the work due to edge loads, lateral loads, and surface tractions is included.
Terry John Hause

Backmatter

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