Reflecting new developments in the study of Saint-Venant's problem, Classical and Generalized Models of Elastic Rods focuses on the deformation of elastic cylinders for three models of continuum: classical elastic continuum, Cosserat elastic body, and porous elastic material. The author presents a method to construct Saint-Venant's solutions, minimum energy characterizations of these solutions, and a proof of Saint-Venant's principle. He then discusses the deformation of nonhomogenous and isotropic cylinders as well as the problem of loaded anisotropic elastic cylinders. The book also deals with the deformation of cylinders within the linearized theory of homogeneous Cosserat elastic solids, the deformation of nonhomogeneous Cosserat cylinders, and the extension, bending, and torsion of porous elastic cylinders. With numerous results not found in related texts, this book provides a unique, unified point of view in the theory of the deformation of elastic cylinders.
AI. I. Cuza University of Iasi, Romania Virginia Tech, Blacksburg, Virginia, USA University of Illinois, Urbana, USA
Preface Saint-Venant's Problem Preliminaries Formulation of Saint-Venant's Problem Saint-Venant's Solutions Unified Treatment Plane Deformation Properties of the Solutions to Saint-Venant's Problem New Method of Solving Saint-Venant's Problem Minimum Energy Characterizations of Solutions Truesdell's Problem Saint-Venant's Principle Theory of Loaded Cylinders Problems of Almansi and Michell Almansi-Michell Problem Almansi Problem Characterization of Solutions Direct Method Applications Deformation of Nonhomogeneous Cylinders Preliminaries Plane Strain Problem: Auxiliary Plane Strain Problems Extension and Bending of Nonhomogeneous Cylinders Torsion Flexure Elastic Cylinders Composed of Different Nonhomogeneous and Isotropic Materials Piecewise Homogeneous Cylinders Applications Anisotropic Bodies Preliminaries Generalized Plane Strain Problem Extension, Bending, and Torsion Flexure of Anisotropic Cylinders Minimum Energy Characterizations of Solutions Global Strain Measures Problem of Loaded Cylinders Orthotropic Bodies Plane Strain Problem of Orthotropic Bodies Deformation of Elastic Cylinders Composed of Nonhomogeneous and Anisotropic Materials Cylinders Composed of Different Orthotropic Materials Cosserat Elastic Continua Basic Equations Plane Strain Saint-Venant's Problem for Cosserat Cylinders Minimum Principles Global Strain Measures Theory of Loaded Cosserat Cylinders Nonhomogeneous Cosserat Cylinders Plain Strain Problems Saint-Venant's Problem Problems of Almansi and Michell Anisotropic Cosserat Cylinders Cylinders Composed of Different Elastic Materials Porous Elastic Bodies Basic Equations Plane Strain Extension, Bending, and Torsion of Porous Elastic Cylinders Cylinders Composed of Different Porous Materials Applications Answers to Selected Problems Bibliography Index Exercises appear at the end of each chapter.
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