Micropolar theory of elasticity
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Bibliographic Information
Micropolar theory of elasticity
（Lecture notes in applied and computational mechanics, v. 15）
Springer, c2004
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Includes bibliographical references (p. [335]-345) and indexes
Description and Table of Contents
Description
This monograph contains the results of my research in the area of asymmet- ric theory of elasticity, conducted from 1969 to 1986 under the direction of PROFESSOR WITOLD NOWACKI. I am indebted to PROFESSOR NOWACKI, thanks to whose invaluable and very kind research assistance I obtained the results which were the foundation of this monograph. Therefore, I would like to express my deepest gratitude to him and honour his memory. He will remain in my thoughts with due respect. During my research assistantship at the Institute of Mechanics at the Uni- versity of Warsaw in 1970-1973 I had the opportunity to participate in sem- inars and conferences, study critical reviews and carryon numerous discus- sions and conversations. All this resulted in many valuable remarks included in this monograph. In this connection, I would like to thank Professor J6zef Ignaczak and Professor Marek Sokolowski from the Institute of Fundamental Problems of Technology at the Polish Academy of Sciences, as well as Pro- fessor Zbigniew Olesiak and Professor Adam Piskorek from the Institute of Mechanics at the University of Warsaw.
Table of Contents
- 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-Lame. 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.
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