Theory of Elasticity for Scientists and EngineersThis book is intended to be an introduction to elasticity theory. It is as sumed that the student, before reading this book, has had courses in me chanics (statics, dynamics) and strength of materials (mechanics of mate rials). It is written at a level for undergraduate and beginning graduate engineering students in mechanical, civil, or aerospace engineering. As a background in mathematics, readers are expected to have had courses in ad vanced calculus, linear algebra, and differential equations. Our experience in teaching elasticity theory to engineering students leads us to believe that the course must be problem-solving oriented. We believe that formulation and solution of the problems is at the heart of elasticity theory. 1 Of course orientation to problem-solving philosophy does not exclude the need to study fundamentals. By fundamentals we mean both mechanical concepts such as stress, deformation and strain, compatibility conditions, constitu tive relations, energy of deformation, and mathematical methods, such as partial differential equations, complex variable and variational methods, and numerical techniques. We are aware of many excellent books on elasticity, some of which are listed in the References. If we are to state what differentiates our book from other similar texts we could, besides the already stated problem-solving ori entation, list the following: study of deformations that are not necessarily small, selection of problems that we treat, and the use of Cartesian tensors only. |
Contents
38 | 41 |
Analysis of Strain | 47 |
Boundary Value Problems of Elasticity Theory | 113 |
Solutions for Some Problems of Elasticity Theory | 143 |
106 | 168 |
Plane State of Strain and Plane State of Stress | 223 |
Hookes | 263 |
Other editions - View all
Theory of Elasticity for Scientists and Engineers Teodor M. Atanackovic,Ardeshir Guran Limited preview - 2012 |
Theory of Elasticity for Scientists and Engineers Teodor M. Atanackovic,Ardeshir Guran No preview available - 2000 |
Theory of Elasticity for Scientists and Engineers Teodor M. Atanackovic,Ardeshir Guran No preview available - 2012 |
Common terms and phrases
arbitrary assume axes becomes body forces boundary conditions boundary value problem C₁ Cartesian Cartesian coordinate system concentrated force conclude Consider const constant coordinate system corresponding cross-section cylindrical coordinate system defined deformation denote determine displacement field displacement vector elastic body elasticity theory equal to zero equilibrium equations expression Əxi Əxj F₁ Figure follows force F fundamental boundary value given Hooke's law integrating Lamé equations linear loaded matrix method nonlinear obtain plane problems plate principal radius rotation Saint-Venant satisfies Section shear stress shown in Fig solution spherical coordinate system strain tensor stress components stress field stress tensor stress vector Suppose surface symmetric theorem thermoelastic torsion transform u₁ unit normal unit vector x₁ θρ μθ ΟΦ σρρ ди дио მე მთვ მი მუ Աշ
Popular passages
Page v - Deduce that on their common boundary t(z,n) = -t(z, -n) Cauchy's lemma The stress vectors acting upon opposite sides of the same surface at a given point are equal in magnitude and opposite in direction. 2.2.2 The stress tensor We ask here how t(z,n) varies as the position z is held fixed and n changes.