Problems and Solutions in Thermoelasticity and Magneto-Thermoelasticity

ISBN-13: 9783319840192 / Angielski / Miękka / 2018 / 104 str.

B. Das

Spis treści

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

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

O autorze

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. 

Blurb

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.