UID:
almahu_9947367859902882
Format:
1 online resource (662 p.)
ISBN:
1-281-03640-4
,
9786611036409
,
0-08-051123-6
Series Statement:
Studies in mathematics and its applications ; v. 29
Content:
The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the ""small"" parameter.
Note:
Description based upon print version of record.
,
Front Cover; Mathematical Elasticity: General plan; Mathematical Elasticity: Theory of Shells; Copyright Page; Mathematical Elasticity: General preface; Preface to Volume I; Preface to Volume II; Preface to Volume III; Table of Contents; Differential geometry at a glance; Three-dimensional elasticity in curvilinear coordinates at a glance; Two-dimensional linear shell equations at a glance; Two-dimensional nonlinear shell equations at a glance; PART A: LINEAR SHELL THEORY; Chapter 1. Three-dimensional linearized elasticity and Korn's inequalities in curvilinear coordinates; Introduction
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1.1 Three-dimensional linearized elasticity in Cartesian coordinates1.2 Curvilinear coordinates and metric tensor in a three- dimensional domain; 1.3 The variational equations of three-dimensional linearized elasticity in curvilinear coordinates; 1.4 Covariant derivatives and Christoffel symbols in a three- dimensional domain; 1.5 Linearized change of metric tensor in curvilinear coordinates; 1.6 The boundary value problem of three-dimensional linearized elasticity in curvilinear coordinates; 1.7 A lemma of J. L. Lions
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three-dimensional Korn's inequalities and infinitesimal rigid displacement lemma in curvilinear coordinates1.8 Existence and uniqueness theorem in curvilinear coordinates; 1.9 Complement: Recovery of a three-dimensional manifold from its metric tensor field; Exercises; Chapter 2. Inequalities of Korn's type on surfaces; Introduction; 2.1. Curvilinear coordinates and metric tensor on a surface; 2.2. Curvature tensor on a surface; 2.3. Covariant derivatives and Christoffel symbols on a surface; 2.4. Linearized change of metric tensor on a surface
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2.5. Linearized change of curvature tensor on a surface2.6. Inequalities of Korn's type and infinitesimal rigid displacement lemma on a general surface; 2.7. Inequality of Korn's type and infinitesimal rigid displacement lemma on an elliptic surface; 2.8 Complement: Recovery of a surface from its metric and curvature tensor fields; Exercises; Chapter 3. Asymptotic analysis of linearly elastic shells: Preliminaries and outline; Introduction; 3.1. The three-dimensional equations of a linearly elastic shell; 3.2. The three-dimensional equations over a domain independent of ε
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3.3. Geometrical and mechanical preliminaries3.4. The two-dimensional equations of linearly elastic ""membrane"" and ""flexural"" shells derived by means of a formal asymptotic analysis; 3.5. Summary of the convergence theorems; Exercises; Chapter 4. Linearly elastic elliptic membrane shells; Introduction; 4.1. Linearly elastic elliptic membrane shells: Definition, example, and assumptions on the data; the three- dimensional equations over a domain independent of ε; 4.2. Averages with respect to the transverse variable
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4.3. A three-dimensional inequality of Korn's type for a family of linearly elastic elliptic membrane shells
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English
Additional Edition:
ISBN 0-444-82891-5
Language:
English
