Preface

During the nineteenth century, mechanics was mainly considered to be a part of applied mathematics. At the beginning of the twentieth century, all topics under the subject of mechanics, "solid mechanics" and "fluid mechanics," were defined with an index notation, and by re-explanation of these issues according to their coordinate systems, continuum mechanics has been created. With the gathering of all subjects in a single title, a new area has been opened in macroscopic (largescale) mechanics. The exact solutions to linear/nonlinear elasticity problems have been discovered by applying analytical, numerical, and experimental methods and techniques to the new generation of computers and experimental equipment. Numerical solutions such as finite differences and finite elements methods have been extensively used to approximate the exact results.

The purpose of writing this book has been summarized in three main concepts. The first objective was to provide the basic information and principles about the history and theory of elasticity. The second was to explain the fundamental equations. The third was to present the recent engineering application studies that have been collected under the following basic headings: "FEA and Experimental Determination of Applied Elasticity Problems for Fabricating Aspheric Surfaces," "Repair Inspection Technique based on Elastic-Wave Tomography Applied for Deteriorated Concrete Structures," and "Concept of Phase Transition Based on Elastic Systematics."

The main subject of this book is engineering elasticity and consists of five chapters in two sections. The title of the first section is "General Theorems in Elasticity" and the first chapter of this section belongs to the editor and is entitled "Analytical and Numerical Approaches in Engineering Elasticity." In this chapter, the historical development of "elasticity theory" is presented briefly, and recent studies performed regarding the elasticity concept are categorized and listed according to their basic engineering problem groups. A literature survey has been performed and categorized between the years 2014 and 2018 and represented in a statistical plot.

The second chapter in the first section is entitled "A General Overview of Stress-Strain Analysis for the Elasticity Equations" and explains the results of elasticity equations and the analysis of stress, strain, and stress–strain relationships through particular sections. In this section the concept of normal and shear stresses, principal stresses, plane stress, Mohr's circle, stress invariants, stress equilibrium equations, linear elasticity, generalized Hooke's law, and stress–strain relationships for triclinic, monoclinic, orthotropic, transversely isotropic, fibre-reinforced, and isotropic materials are discussed by researchers P. Kumar, M. Mahanty, and A. Chattopadhyay.

The title of the second section is "Engineering Applications in Theory of Elasticity" and consists of three chapters on engineering applications on elasticity.

The first chapter of the second section is entitled "FEA and Experimental Determination of Applied Elasticity Problems for Fabricating Aspheric Surfaces" and is written by Dr. D.N. Nguyen. In this chapter, the elastic deformation machining method is explained in two cases "Elastic deformation machining method with mold" and "Elastic deformation machining method without mold." When the vacuum pressure was used in the construction of complex aspherical surfaces, the differential equations of an appropriate plate theory were solved and the amount of deviation of the circular plate was determined and the test results were presented comparatively. Finite element analysis results for "Elastic deformation machining process with mold" were presented by curves. The finite element model was designed for establishing the spherical surface through a simulation of contact processing between workpiece and mold surface. In conclusion it was clarified that the experimental results agreed greatly with FEA results.

The second chapter is entitled "Concept of Phase Transition Based on Elastic Systematics" and is presented by Dr. P.S. Nnamchi and Dr. C.S. Obayi. In this chapter, the authors present the actual scaling of phase transition-driven considerations, such as martensitic transformation and transformable shape memory formation via elastic constant systematics in terms of continuum mechanics. According to this chapter, the results of the scaling procedure and acoustic anisotropy with respect to the mechanical stability criteria of the polycrystals based on the elastic modulus are compatible with the new experimental data obtained from the literature.

The third chapter is entitled "Repair Inspection Technique Based on Elastic-Wave Tomography Applied for Deteriorated Concrete Structures" and was written by Dr. K. Hashimoto, Dr. T. Shiotani, Dr. T. Nishida, and Dr. N. Okude. In this research, the testing results based on the internal damage assessment for the repair condition by applying elastic wave tomography and acoustic emission tomography are presented from a concrete pier, concrete wall, and slab obtained form. Determining the 3D velocity distribution, the repair effects of the epoxy injection method and the patch repair method are quantitatively evaluated and results are explained.

The first section of this book includes the recently published literature on elasticity concepts and basic theoretical knowledge. In the second section, researchers have focused on the engineering applications and on the use of elasticity theory by experimental, numerical, and analytical studies.

#### **Acknowledgments**

The editor would like to express her great appreciation to Ms. Romina Skomersic and Opr. Dr. Ayşe Günay for their valuable supporting studies regarding the formation of this scientific book. My special thanks are extended to the staff of IntechOpen for publishing this book.

### **Assoc. Prof. Dr. Ezgi Günay**

**1**

Section 1

General Theorems in

Elasticity

Gazi University, Engineering Faculty, Mechanical Engineering Department, Ankara, Turkey

## Section 1
