Memorial University of Newfoundland

Faculty of Engineering and Applied Science

Eng. 9545

Topics in Plates and Shells




Plates and shells form a major part of all applications in the area of Structural Mechanics and Materials. Almost all civil and mechanical engineering structures are basically made of components which can be viewed as beams/bars, plates and shells. Behaviour of beams, bars, etc., is usually covered at undergraduate level. Traditionally, graduate students across the world who work in structural mechanics tended to take several courses covering the topics of Advanced Solid Mechanics, Plates, Shells, Stability, Finite Elements, etc. At Memorial University, however, courses in plates, shells and stability have been absent for various reasons. It is long felt that our graduate students are generally lacking in the knowledge of these very important areas. A special topics course covering the twin area of plates and shells would be very helpful in this regard.

The course is intended to familiarize the students with the fundamental concepts, basic development of governing equations, their solution to standard cases, and some special application areas. In addition, an introduction will be given to special solution techniques such as finite differences, etc. This should give the students a firm grounding leading to better understanding of their individual research topics, which usually consist of components such as plates and shells.


Course Outline:



Short introduction -may include brief review of tensors and curvilinear coordinates, Fundamental equations of deformable bodies, Stress-Strain and Compatibility equations


Plates loaded in their plane. Governing equations, basic concepts in the solution

Introduction to the theory of Plates


Fundamental equations of Plate bending


Solutions to rectangular plates and circular plates with regular loading


Engineering Applications

Special Topics in Plates


Introduction to large deflections of plates


Introduction to the stability of plates


Finite difference solution for plates

Introduction to the theory of Shells


Membrane theory of shells


Applications of the membrane theory


Bending theory of shells


Applications for shallow shells

Special Topics in Shells


Axisymmetric shells


Stability and large deformation of shells


Dynamics and vibrations of shells


Engineering applications of shells

Assessment Procedure:



Midterm Examination


Project work


Final Examination



Timishenko, S.P. and S. Woinowsky-Krieger, 1970. "Theory Plates and Shells," McGraw-Hill

R. Szilard. 1974. "Theory and Analysis of Plates -Classical and Numerical Methods," Prentice Hall.

Mansfield, E.H. 1989. "The Bending and Stretching of Plates," Cambridge University Press

Jaeger, L.G. "Elementary Theory of Elastic Plates," Pergamon Press

Salvadori, M.G. and M.L. Baron, 1967. "Numerical Methods in Engineering, " Prentice-Hall

Donnell, L.H., 1976. "Beams, Plates and Shells," McGraw-Hill

Flugge, W., 1990. "Stresses in Shells," Springer

Class Notes on the Theory of Plates S.M.R. Adluri, MUN

Timishenko, S.P. and J. N. Goodier, 1970. "Theory Elasticity," McGraw-Hill

Additional references will be given during the course.





Legal stuff:

The MUN Faculty Association asked us to include the following in Legalese. J So there! J


The lectures and displays (and all material) delivered or provided in this course, including any visual or audio recording thereof, are subject to copyright owned by the instructor for the course (Dr. Seshu Adluri). Other copyrights may also be applicable. It is prohibited to record or copy by any means, in any format, openly or surreptitiously, in whole or in part, in the absence of express written permission from the instructor, Dr. Seshu Adluri any of the lectures, materials provided or published in any form during or from the above course.