Mechanics, Boundary Layers and Function Spaces

Diarmuid Ó'Mathúna (Autor)

Buch | Hardcover

216 Seiten

1989
Birkhauser Boston Inc (Verlag)
978-0-8176-3464-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	1.10.1989
Zusatzinfo	VIII, 216 p.
Verlagsort	Secaucus
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Technik ► Maschinenbau
ISBN-10	0-8176-3464-9 / 0817634649
ISBN-13	978-0-8176-3464-3 / 9780817634643
Zustand	Neuware