Meet the editor

Ezgi Günay has been an associate professor at the Mechanical Engineering Department at Gazi University in Turkey since 2010. She graduated from the Engineering Sciences Department (Applied Mechanics Department) of the Engineering Faculty at the Middle East Technical University (METU, Ankara, Turkey) in 1985. She received her Master of Science degree in 1989 from the same department. The title of the thesis was "Development

of a Preprocessor and Modification of a Finite Element Procedure for the Analysis of Metal Forming Processes" (December 1989, METU). She graduated with her PhD degree at Gazi University from the Mechanical Engineering Department in 1996. The title of the thesis was "A Nonlocking Finite Element Model for Nonlinear Analysis of Thin and Thick Composite Plates." She worked as a research assistant between 1993 and 1999 and studied academically by giving basic courses as an assistant professor between 1999 and 2010 at the same department. During these years she has given courses in the following subjects: Technical Drawing, FOR-TRAN-Computer Programming Languages, Applied Mathematics for Mechanical Engineers, Differential Equations, Statics, Dynamics, Strength of Materials, Introduction to Numerical Analysis, Introduction to Composite Materials, Introduction to Finite Element Analysis (FEA), Finite Element Method (FEM), Plate and Shell Theories, and Elasticity. She has authored about 40 papers published in both national and international proceedings and journals. She has three chapters published in international books. She has written two programming e-books in FORTRAN language (co-author) for engineering students.

Ezgi Günay is presently working on the following subjects: finite element linear and geometrically nonlinear analyses of fiber composite-stiffened shell and plate structures, linear and nonlinear FEA buckling analysis of fiber composite-stiffened plates, numerical and experimental studies on micromechanical investigation of layered fiber composites and natural fiber composite wood, FEA and analytical studies on single-walled carbon nano-tubes (SWCN), FEA of stress transfer mechanisms from matrix to fiber in SWCN-reinforced nanocomposites, and experimental and FEA studies on natural fiber composite wood (transversely isotropic) materials.

**Preface III**

General Theorems in Elasticity **1**

**Chapter 1 3**

**Chapter 2 11**

Engineering Applications in Theory of Elasticity **31**

**Chapter 3 33**

**Chapter 4 53**

**Chapter 5 73**

Repair Inspection Technique Based on Elastic-Wave Tomography Applied

*by Katsufumi Hashimoto, Tomoki Shiotani, Takahiro Nishida and Nobuhiro Okude*

FEA and Experimentally Determination of Applied Elasticity Problem

Introductory Chapter: Analytical and Numerical Approaches in

An Overview of Stress-Strain Analysis for Elasticity Equations *by Pulkit Kumar, Moumita Mahanty and Amares Chattopadhyay*

Concept of Phase Transition Based on Elastic Systematics

**Section 1**

Contents

Engineering Elasticity

for Fabricating Aspheric Surfaces

*by Paul S. Nnamchi and Camillus S. Obayi*

for Deteriorated Concrete Structures

*by Duc-Nam Nguyen*

*by Ezgi Günay*

**Section 2**

## Contents


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

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

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.

The title of the second section is "Engineering Applications in Theory of Elasticity"

Determination of Applied Elasticity Problems for Fabricating Aspheric Surfaces"

and consists of three chapters on engineering applications on elasticity.

The first chapter of the second section is entitled "FEA and Experimental

been extensively used to approximate the exact results.

Elastic Systematics."

Chattopadhyay.
