UID:
almahu_9947367909502882
Format:
1 online resource (561 p.)
Edition:
2nd ed.
ISBN:
1-281-05846-7
,
9786611058463
,
0-08-053591-7
Series Statement:
Studies in mathematics and its applications ; v. 27
Content:
The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established. In the no
Note:
Description based upon print version of record.
,
Front Cover; Mathematical Elasticity: Theory of Plates; Copyright Page; TABLE OF CONTENTS; Mathematical Elasticity: General plan; Mathematical Elasticity: General Preface; Preface to Volume I; Preface to Volume II; Main notations and definitions; Plate equations at a glance; Shallow shell equations at a glance; PART A: LINEAR PLATE THEORY; Chapter 1. Linearly elastic plates; Introduction; 1.1. A lemma of J.L. Lions and the classical Korn inequal- ities; 1.2. The three-dimensional equations of a linearly elastic clamped plate
,
1.3. Transformation into a problem posed over a domain independent of e the fundamental scalings of the unknowns and assumptions on the data; the displacement approach; 1.4. Convergence of the scaled displacements as e? 0; 1.5. The limit scaled two-dimensional flexural and mem- brane equations: Existence, uniqueness, and regularity of solutions; formulation as boundary value problems; 1.6. Convergence of the scaled stresses as e? 0; explicit forms of the limit scaled stresses; 1.7. The two-dimensional equations of a linearly elastic clamped plate; linear Kirchhoff-Love theory
,
1.8. Justification of the linear Kirchhoff-Love theory1.9. Linear plate theories: Historical notes and commen- tary; 1.10. Justifications of the scalings and assumptions in the linear case; 1.11. Asymptotic analysis and F-convergence; 1.12. Error estimates; 1.13. Eigenvalue problems; 1.14. Time-dependent problems; Exercises; Chapter 2. Junctions in linearly elastic multi-structures; Introduction; 2.1. The three-dimensional equations of a linearly elastic multi-structure; 2.2. Transformation into a problem posed over two domains independent of e
,
the fundamental scalings of the unknowns and assumptions on the data2.3. Convergence of the scaled displacements as e? 0; 2.4. The limit scaled problem: Existence and uniqueness of a solution; formulation as a boundary value problem; 2.5. Mathematical modeling of an elastic multi-structure by a coupled, multi-dimensional boundary value problem; junction conditions; 2.6. Commentary; refinements and generalizations; 2.7. Justification of the boundary conditions of a clamped plate; 2.8. Eigenvalue problems; 2.9. Time-dependent problems; Exercises
,
Chapter 3. Linearly elastic shallow shells in Cartesian coordinatesIntroduction; 3.1. The three-dimensional equations of a linearly elastic clamped shell in Cartesian coordinates; 3.2. Transformation into a problem posed over a domain independent of e ; the fundamental scalings of the unknowns and assumptions on the data; 3.3. Technical preliminaries; 3.4. A generalized Korn inequality; 3.5. Convergence of the scaled displacements as e? 0; 3.6. The limit scaled two-dimensional problem: Existence and uniqueness of a solution; formulation as a boundary value problem
,
3.7. Justification of the two-dimensional equations of a linearly elastic shallow shell in Cartesian coordinates
,
English
Additional Edition:
ISBN 0-444-82570-3
Language:
English
