Mechanics, Boundary Layers and Function Spaces

ISBN-13: 9781461289098 / Angielski / Miękka / 2011 / 216 str.

Diarmuid O'Mathuna

Opis

Concern with the class of problems investigated in this monograph began for me as a graduate student at MIT (1958-62) when serving as research assistant to Professor Eric Reissner who initiated me into the subject and whose influence - whether directly or dialectically - is probably discernable in the contours of the work. My fIrst attempt at a systematic derivation of the equations of shell theory was made while on a summer assistantship with Professor Norman Levinson in 1960. Beyond gaining a sobering reali zation of the complexities involved, I made little progress at that time. In 1962-64 while a Temporary Member at the Courant Institute of Mathematical Sciences (NYU) I made a fresh start, while benefIting from my association and discus sions with Professor Fritz John. With the conviction that the full integration of the equations with respect to the thickness coordinate, by means of the Legendre repre sentations, must lead to a clarifIcation of the position of the two-dimensional theory in its three-dimensional context, the necessary computations were completed during that period. Several years passed while I became reconciled with the thought that the material needed to be organized as a monograph. This was done during 1969-70 while at the NASA Electronics Research Center in Cambridge, MA.

Spis treści

General Introduction.- One Beam Theory and the Residual Effects in the Elastic Strip.- 1. The Boundary Value Problem.- 2. Normalization of the Transverse Coordinate.- 3. Representations for the Stress Components.- 4. The Face Boundary Conditions.- 5. The Edge Boundary Conditions.- 6. Representation for the Displacement Components.- 7. The Equations for the Unknown Function.- 8. The Uncoupling of Effects: Principal and Residual Parts.- 9. The Problem of Stretching: Restricted Case.- 10. The Problem of Bending: Restricted Case.- Background Survey.- Two Plate Theory and the Edge Effects.- 1. The Coordinate System.- 2. The Boundary Value Problem.- 3. The Normalized Formulation.- 4. Stress Representations: The Face Conditions.- 5. The Edge Boundary Conditions.- 6. Representations for the Displacement Components.- 7. The Equations for the Unknown Functions.- 8. The Uncoupling of Effects: Principal and Residual Parts.- 9. The Problem of Stretching.- 9P. The Principal Stretching Problem: (Generalized Plane Stress).- 9R. The Residual Stretching Problem.- 10. The Problem of Bending.- 10P. The Principal Bending Problem.- 10R. The Residual Bending Problem.- Background Survey.- Three Shell Theory—A First Approximation.- 1. The Coordinate System.- 1A. The Approximation Scheme and Associated Relations.- 2. The Boundary Value Problem.- 2A. The Approximate Constitutive Relations.- 3. The Normalized Formulation.- 4. Stress Representations: The Face Conditions.- 4A. Approximate Form of the Transverse Stress Coefficients.- 5. The Edge Boundary Conditions.- 6. Representations for the Displacement Components.- 7. The Equations for the Unknown Functions.- 8. Detachment of the Residual Problem.- 9. The Principal Problem.- 10. The Contracted Interior Problem.- Background Survey.