Ebook: Treatise on Classical Elasticity: Theory and Related Problems

Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation.

The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used.

This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too.

Audience: researchers in applied mathematics, mechanical and civil engineering.

Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation.

The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used.

This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too.

Audience: researchers in applied mathematics, mechanical and civil engineering.

Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation.

The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used.

This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too.

Audience: researchers in applied mathematics, mechanical and civil engineering.

Content:
Front Matter....Pages i-xi
Introduction....Pages 1-32
Geometry and Kinematics of Deformation....Pages 33-71
Mechanics of Stresses....Pages 73-113
Mathematical Models in Mechanics of Deformable Solids....Pages 115-189
General Equations of the Theory of Elasticity. Formulation of Problems ....Pages 191-242
Principles and General Theorems of the Theory of Elasticity. Computation Methods....Pages 243-306
Introduction to the Theory of Cosserat Type Bodies ....Pages 307-355
Theory of Concentrated Loads ....Pages 357-391
Elastic Space. Elastic Half-Space....Pages 393-426
Elastic Eighth-Space. Elastic Quarter-Space....Pages 427-479
Elastic Parallelepiped. Elastic Strip. Elastic Layer. Thick Plate ....Pages 481-515
Dynamical Problems of Elastic Bodies....Pages 517-546
Particular Cases of States of Strain and Stress....Pages 547-613
Anisotropic and Non-homogeneous Bodies....Pages 615-669
Introduction to Thermoelasticity....Pages 671-698
Introduction to Linear Viscoelasticity....Pages 699-728
Back Matter....Pages 729-802

Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation.

The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used.

This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too.

Audience: researchers in applied mathematics, mechanical and civil engineering.

Content:
Front Matter....Pages i-xi
Introduction....Pages 1-32
Geometry and Kinematics of Deformation....Pages 33-71
Mechanics of Stresses....Pages 73-113
Mathematical Models in Mechanics of Deformable Solids....Pages 115-189
General Equations of the Theory of Elasticity. Formulation of Problems ....Pages 191-242
Principles and General Theorems of the Theory of Elasticity. Computation Methods....Pages 243-306
Introduction to the Theory of Cosserat Type Bodies ....Pages 307-355
Theory of Concentrated Loads ....Pages 357-391
Elastic Space. Elastic Half-Space....Pages 393-426
Elastic Eighth-Space. Elastic Quarter-Space....Pages 427-479
Elastic Parallelepiped. Elastic Strip. Elastic Layer. Thick Plate ....Pages 481-515
Dynamical Problems of Elastic Bodies....Pages 517-546
Particular Cases of States of Strain and Stress....Pages 547-613
Anisotropic and Non-homogeneous Bodies....Pages 615-669
Introduction to Thermoelasticity....Pages 671-698
Introduction to Linear Viscoelasticity....Pages 699-728
Back Matter....Pages 729-802
....