Problems and Solutions in Thermoelasticity and Magneto-thermoelasticity

by B. Das

Overview

This book presents problems and solutions of the mathematical theories of thermoelasticity and magnetothermoelasticity. The classical, coupled and generalized theories are solved using the eigenvalue methodology. Different methods of numerical inversion of the Laplace transform are presented and their direct applications are illustrated. The book is very useful to those interested in continuum mechanics.

Product Details

ISBN-13:	9783319488073
Publisher:	Springer International Publishing
Publication date:	11/27/2016
Edition description:	1st ed. 2017
Pages:	104
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Dr. Bas works as an Assistant Professor in Mathematics at the Ramakrishna Mission Vidyamandira, an autonomous college with post-graduation and Ph.D. degree under University of Calcutta, India.

Table of Contents

Chapter – 1 1-16

(A) Solution of Vector-matrix Differential Equation 3

(B) Numerical Inversion of Laplace Transform 11

i)Bellman Method 11

ii) Zakian Method 13

Chapter – 2 17-59

1. Eigenvalue Approach To Coupled Thermoelasticity With Temperature Dependent Modulus of Elasticity In A Isotropic Elastic Medium With A Cylindrical Hole 19-35

Introduction 19

Nomenclature 21

Basic Equations and Formulation of the Problem 22

Solution Procedure 26

Boundary Conditions 30

Numerical Solution 32

Figures 33

Concluding Remarks 35

2. Eigenvalue Approach To Thermoelastic Interactions In An Unbounded Body With A

Spherical Cavity 36-59

Introduction 36

Nomenclature 39

Basic Equations and Formulation of the Problem 39

Solution Procedure 41

Boundary Conditions 45

Numerical Solution 49

Figures 50

Concluding Remarks 57

Chapter - 3 60-123

3. Eigenvalue Approach To Generalized Thermoelastic Interactions In An Unbounded Body With Circular Cylindrical Hole Without Energy Dissipation 62-80

Introduction 62

Nomenclature 64

Basic Equations and Formulation of the Problem 64

Solution Procedure 66

Boundary Conditions 70

Numerical Solution 71

Figures 72

Concluding Remarks 79

4. Eigenvalue Approach To Study The Effect Of Rotation In Three Dimensional Problem Of

Generalized Thermoelasticity 81-102

Introduction 81

Nomenclature 83

Basic Equations and Formulation of the Problem 85

Solution Procedure 87

Numerical Solution 93

Figures 95

Concluding Remarks 101

5. Eigenvalue Approach To Two Dimensional Problem Of Generalized Thermoelasticity For A

Half-Space With Body Force 103-123

Introduction 103

Nomenclature 106

Basic Equations and Formulation of the Problem 107

Solution Procedure 109

Boundary Conditions 114

Numerical solution 116

Figures 117

Concluding Remarks 122

Chapter – 4 124-213

6. One Dimensional Generalized Magnetothermoelastic Problem : For A Half-Space 126-158

Introduction 126

Nomenclature 128

Basic Equations and Formulation of the Problem <129 Solution Procedure 133

Boundary Conditions 137

Numerical Solution 140

Figures 142

Concluding Remarks 153

7. A Two Dimensional Problem Of Generalized Magnetothermoelastic Interactions

For Half-Space In Rotating Medium 159-188

Introduction 159

Nomenclature 161

Basic Equations and Formulation of the Problem 162

Solution Procedure 167

Boundary Conditions 172

Numerical Solution 174

Figures 175

Concluding Remarks 185

8. A Two Dimensional Problem Of Generalized Magnetothermoelasticity

With Heat-Source 189-213

Introduction 189

Nomenclature 192

Basic Equations and Formulation of the Problem 193

Solution Procedure 197

Boundary Conditions 202

Numerical Solution 204

Figures 205

Concluding Remarks 211