Micropolar Theory of Elasticity

ISBN-13: 9783540418351 / Angielski / Twarda / 2004 / 345 str.

Janusz Dyszlewicz

Opis

The monograph Micropolar Theory of Elasticity is devoted to the asymmetric theory of elasticity and thermoelasticity, aiming at researchers and postgraduate students in solid mechanics and applied mathematics, as well as mechanical engineers. It offers various new results including the basic field equations, general methods of integration of basic equations, formulations of problems, as well as solutions to particular problems. The presented general solutions cover those of Galerkin, Green-Lame and Papkovitch-Neuber type, whereas the formulations include the displacement-rotation problems as well as pure stress problems of asymmetric elastodynamics. Solutions to stationary 3D and 2D problems for a half-space, and singular solutions to 3D and 2D asymmetric elastodynamics and the thermoelasto-dynamics problems for an infinite space are given. "

Spis treści

1. Three-dimensional problems.- 1.1 Displacement-rotation equations of elastodynamics and coupled thermoelasticity.- 1.1.1 Vector equations. Superposition method.- 1.1.2 Fields of body loadings. Fundamental solutions and limiting cases.- 1.1.3 Distortion fields. Fundamental solutions.- 1.1.4 Coupled micropolar thermoelasticity. Fundamental solutions.- 1.1.5 Stress-temperature equations of motion of Ignaczak type. Fundamental solutions.- 1.1.6 Radiation conditions of Sommerfeld type.- 1.1.7 Generalized Galerkin vector. Representation of Iacovache type. Micropolar theory and couple-stress theory.- 1.1.8 Generalized representation of Green-Lamé. The method of Nowacki#x2019;s potentials.- 1.2 Displacement-rotation and stress equations of elastostatics and thermoelastostatics.- 1.2.1 Vector equations and superposition method.- 1.2.2 Fields of body loadings. Fundamental solutions.- 1.2.3 Distortion fields. Fundamental solutions and limiting cases.- 1.2.4 Problem of elastic half-space.- 1.2.5 Galerkin vector. Micropolar theory and couple-stress theory.- 1.2.6 Method of potentials. Micropolar theory and limiting theories. Superposition method.- 1.2.7 Method of potentials. Fundamental solutions. Halfspace problem.- 1.2.8 Micropolar half-space. Problem of singularities of physical fields. Three-dimensional problem.- 1.2.9 Stress equations. Fundamental solutions.- 1.2.10 Generalized representation of Papkovich-Neuber. Micropolar theory and couple-stress theory.- 1.2.11 Applications of the generalized Papkovich-Neuber representation.- 1.2.12 Generalized representation of Papkovich-Neuber. The case of nonhomogenous equations of micropolar elastostatics (E-N model).- 2. Axially-symmetric problems.- 2.1 The first axially-symmetric problem. Elastodynamics.- 2.1.1 Equations in displacements and rotations. Body loadings.- 2.1.2 Equations in displacements and rotations. Superposition method.- 2.1.3 Equations in displacements and rotations with a distortion field.- 2.1.4 Stress functions.- 2.1.5 Method of potentials.- 2.1.6 Stress equations of motion of Ignaczak type.- 2.2 The first axially-symmetric problem. Elastostatics and thermoelastostatics.- 2.2.1 Fields of body loadings. Equations for displacements and rotations. Direct method and superposition method.- 2.2.2 Half-space. The problem of Boussinesq-Mindlin type. Limiting cases.- 2.2.3 Elastic half-space. Problem of singularities of physical fields in elastostatics and thermoelastostatics.- 2.2.4 Displacement-rotation equations with a distortion field.- 2.2.5 The generalized Love function.- 2.2.6 Half-space. Application of the generalized Love functions.- 2.2.7 Method of potentials.- 2.2.8 Half-space. Application of the method of potentials.- 2.2.9 Half-space (E-N) with an inside heat source. Thermoelastostatics.- 2.3 The second axially-symmetric problem. Elastodynamics.- 2.3.1 Equations in displacements and rotations. Body loadings.- 2.3.2 The generalized Lamb problem.- 2.3.3 Stress equations of motion problem (SEMP).- 2.3.4 Fundamental solutions for stresses.- 2.3.5 Equations in displacements and rotations. Superposition method.- 2.3.6 Distortion field. Equations in displacements and rotations. Fundamental solutions and limiting results.- 2.3.7 Functions of displacements-rotations and the method of potentials.- 2.3.8 Potentials of Galerkin type.- 2.4 The second axially-symmetric problem. Elastostatics.- 2.4.1 Body loadings. Equations in displacements and rotations. Direct method and superposition method.- 2.4.2 Equations in displacements and rotations with a distortion field.- 2.4.3 Stress equations of Beltrami-Michell type and stress functions. Half-space problem.- 2.4.4 Functions of displacements-rotations.- 2.4.5 Method of potentials.- 2.4.6 Functions of Love type.- 2.4.7 Problem of singularities of physical fields in the halfspace twisted on the boundary.- 3. Two-dimensional problems.- 3.1 The first problem of plane strain state. Elastodynamics 217 3.1.1 Equations in displacements and rotations with a field of body loadings.- 3.1.2 Equations in displacements and rotations with a distortion field. Fundamental solutions and limiting cases.- 3.1.3 The method of potentials.- 3.1.4 Wave equations in polar coordinates.- 3.1.5 SEMP.- 3.2 The first problem of plane strain state. Elastostatics.- 3.2.1 Equations in displacements-rotations with a field of body loadings.- 3.2.2 Distortion field. Fundamental solutions for displacements and rotations.- 3.2.3 Stress equations of thermoelastostatics and displacement potentials in polar coordinates.- 3.2.4 Concentration of stresses. The problem of cylindrical inclusion. The case of a circular hole.- 3.2.5 Stress concentration problem. Perfectly rigid cylindrical inclusion.- 3.2.6 Method of potentials.- 3.2.7 Half-space problem. Application of the method of potentials.- 3.3 The second problem of plane strain state. Elastodynamics.- 3.3.1 Body loadings. Equations in displacements and rotations.- 3.3.2 Equations in displacements and rotations with a distortion field. Fundamental solutions and limiting cases.- 3.3.3 Functions of displacements and rotations.- 3.3.4 Method of potentials.- 3.3.5 Rotation potentials in polar coordinates.- 3.3.6 SEMP.- 3.4 The second problem of plane strain state. Elastostatics.- 3.4.1 Equations in displacements and rotations with body loadings. Fundamental solutions.- 3.4.2 Equations in displacements and rotations with a distortion field. Fundamental solutions.- 3.4.3 Method of potentials.- 3.4.4 Potentials in polar coordinates.- 3.4.5 Half-space problem.- 3.4.6 The problem of singularities of physical fields in the half-space loaded on the boundary.- 4. Hemitropic medium.- 4.1 Vector equations. Elastodynamics.- 4.1.1 Equations in displacements and rotations with body vectors. The method of direct integration.- 4.1.2 The vector of Galerkin-Cauchy type.- 4.2 Three-dimensional problems. Elastostatics.- 4.2.1 Vector equations in displacements and rotations. Separated equations.- 4.2.2 Generalized vectors of Galerkin type.- 4.2.3 The problem of isotropic hemitropic half-space.- 4.2.4 Potentials of Nowacki in elastostatics and thermoelastostatics.- 4.2.5 Method of potentials. Certain solutions in ?3.- 4.2.6 Hypothetical hemitropic medium.- 4.2.7 Boussinesq#x2019;s problem. Method of potentials. Singularities of physical fields in the half-space.- 4.3 One-dimensional problems of elastostatics and thermoelastostatics.- 4.3.1 The half-space problem.- 4.3.2 The problem of a layer with temperature field.- 4.4 Remarks and conclusions concerning vector equations.- 4.4.1 On the derivation of vector equations.- 4.4.2 Hemitropic medium. Elastodynamics. Analysis of vector equations.- 4.4.3 Displacement-rotation equations describing plane and axially-symmetric problems of micropolar theory.- 4.4.4 Superposition method. Analysis of equations with the vector ?.- References.- Author Index.

O autorze

Janusz Dyszlewicz is Professor of Mathematics at the Wroclaw University of Technology. He received a diploma in Civil Engineering at the Wroclaw University of Technology and research experience at the Warsaw University and the Institute of Fundamental Technological Research of the Polish Academy of Sciences. He is the author of about 40 research papers. The main areas of his research are Micropolar Theory of Elasticity and Asymmetric Thermoelasticity.

Blurb

The monograph "Micropolar Theory of Elasticity" is devoted to the asymmetric
theory of elasticity and thermoelasticity, aiming at researchers and
postgraduate students in solid mechanics and applied mathematics, as
well as mechanical engineers. It offers various new results including the basic field equations, general methods of integration of basic equations, formulations of problems, as well as solutions to particular problems. The presented general solutions cover those of
Galerkin, Green-Lamé and Papkovitch-Neuber type, whereas the
formulations include the displacement-rotation problems as well as pure
stress problems of asymmetric elastodynamics. Solutions to stationary 3D
and 2D problems for a half-space, and singular solutions to 3D and 2D
asymmetric elastodynamics and the thermoelasto-dynamics problems for an
infinite space are given.