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## Über dieses Buch

This book presents a method which is capable of evaluating the deformation characteristics of thin shell structures A free vibration analysis is chosen as a convenient means of studying the displacement behaviour of the shell, enabling it to deform naturally without imposing any particular loading conditions. The strain-displacement equations for thin shells of arbitrary geometry are developed. These relationships are expressed in general curvilinear coordinates and are formulated entirely in the framework of tensor calculus. The resulting theory is not restricted to shell structures characterized by any particular geometric form, loading or boundary conditions. The complete displacement and strain equations developed by Flugge are approximated by the curvilinear finite difference method and are applied to computing the natural frequencies and mode shapes of general thin shells. This approach enables both the displacement components and geometric properties of the shell to be approximated numerically and accurately. The selection of an appropriate displacement field to approximate the deformation of the shell within each finite difference mesh is discussed in detail. In addition, comparisons are made between the use of second and third-order finite difference interpolation meshes.

## Inhaltsverzeichnis

### 1. Introduction

Abstract
Shell structures are widely used in a variety of engineering applications ranging from domes for major buildings and components of flight structures to liquid storage containers. These structures often have arbitrary shape and support conditions to meet functional and manufacturing requirements.
Steve Naomis, Paul C. M. Lau

### 2. General Theory

Abstract
This chapter deals with the mathematical formulation of the theory of general thin shells.
Steve Naomis, Paul C. M. Lau

### 3. Numerical Fundamentals

Abstract
In the proposed method, the curvilinear finite difference (CFD) method [74] is combined with the strain-displacement equations developed by Flugge [1] and the Principle of Virtual Displacements to formulate a technique capable of computing the dynamic characteristics of thin shells. This chapter presents and discusses the numerical techniques utilized in the formulation.
Steve Naomis, Paul C. M. Lau

### 4. Numerical Implementation

Abstract
In the previous chapter, the curvilinear finite difference method was derived in general form for two dimensional field problems and combined with the Principle of Virtual Displacements to formulate a technique capable of determining the free vibration characteristics of shell structures. Included within the following sections are details relating to the implementation of a second order nine node and a third order sixteen node finite difference approximation.
Steve Naomis, Paul C. M. Lau

### 5. Numerical Applications

Abstract
Details relating to a numerical method capable of determining the dynamic characteristics of shell structures have been presented in the preceding chapters. The methodology is based on the strain-displacement equations of Flugge [1] and uses the curvilinear finite difference method in order to approximate the geometric properties and displacement behaviour of the shell. Such an approach enables shells of arbitrary geometry to be analysed.
Steve Naomis, Paul C. M. Lau

### 6. Summary

Abstract
A technique capable of computing the natural frequencies and mode shapes of thin shells has been developed and applied successfully to a number of shallow and non-shallow shell structures.
Steve Naomis, Paul C. M. Lau

### Backmatter

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