ME 544Tentative Course Outline (2012-2)
Weeks / Date / Topics2 / February 18th / Introduction. Basic concepts in mechanics. Equilibrium, geometry of deformation, constitutive relation, principle of virtual work. Description of beam, plate and shell. Exact theory (elasticity) vs structural theories (beam, plate and shell).
3 / February25th / Review of theory of elasticity. Basic definitions in Cartesian coordinates (Stresses, displacements, strains, equilibrium equations, stress-strain relations, compatibility equations, strain energy). St. Venant principle.Elasticity equations in cylindrical and spherical coordinates.
4 / March 4th / Variational principles. Classical (Euler-Bernoulli) beam theory. Love-Kirchoff approximation. Derivation of governing equations. Solutions of classical beam theory. Buckling of beams.
5 / March 11th / Timoshenko beam theory. Basic assumptions. Derivation of governing equations. Solutions of Timoshenko beam theory. Applications of variational methods to beam problems.
6 / March 18th / Midterm Examination I
7 / March 25th / Classical (Kirchhoff) plate theory. Basic assumptions. Derivation of governing equations in Cartesian coordinates. Solutions to problems of rectangular plates.
8 / April 1st / Circular plates under axisymmetric loads.Derivation of governing equations. Solutions to problems of circular plates.
9 / April 8th / Buckling of plates (Using classical plate theory).
Mindlin Plate theory. Derivation of governing equations.
10 / April 15th / Direct use of variational methods in the solution of plate problems. Rayleigh-Ritz Method. Galerkin Method.
11 / April 22nd / Midterm Examination II
12 / April 29th / Mathematical basics for the study of shell theories. General curvilinear coordinates. Space curves. Surfaces.
13 / May 6th / Classical Theory of Shells. Love-Kirchoff approximation. Derivation of governing equations.
14 / May 13th / Simplifications on the general theory. Shallow shells. Membrane theory of shells. Shells of revolution.
15 / May 20th / Solutions to sample problems using simplified shell theories.
15 / May 24th / Last Day of Classes-Two extra class hours possible according to Wednesday schedule
ME 544 Beams, Plates, Shells (Spring 2013)
Instructor:F. Suat Kadıoğlu
Office: B318
Ext.:5294
e-mail:
Schedule:Monday 11.40-12.30G103
Wednesday 9.40-11.30G103
Grading:Midterms27.50 % each
Final30.00 %
Homeworks15.00 %
TextBook:None
References:"Stresses in Plates and Shells, Third Edition", Ansel C. Ugural, CRC press, 2009.
"Solid Mechanics: A Variational Approach", Clive L. Dym and Irving H. Shames, McGraw-Hill, 1973.
"Theory of Plates and Shells", S. P. Timoshenko and S.W. Krieger, McGraw-Hill, 1959.
"The behavior of Thin Walled Structures: Beams, Plates and Shells", Jack R.Vinson, Kluwer Academic Publishers, 1989
"Beams, Plates and Shells", L. Hamilton Donnell, McGraw-Hill, 1976.
"Mechanics of Laminated Composite Plates-Theory and Analysis", J.N. Reddy, CRC 1997.
"Thin Elastic Shells", H. Krauss, Wiley, 1967
Course Objectives:Objective of this course is to give basic knowledge about the theories which are used to determine the displacement, strain and stress fields in beams, plates and shells. For this purpose;
he differences between theory of elasticity and structural theories are pointed out.
Formulation of structural theories by using equilibrium as well as energy (variational) methods is demonstrated.
Some exact and approximate solution methods which are used in certain types of beam, plate and shell problems are introduced.
Prerequisites:Topics: Basic elasticity, variational approach to elasticity problems, curvilinear coordinates, curves and surfaces. Some proficiency in a mathematics software such as MathCAD, Mathematica, etc.
Course: None
Remarks:The dates in the course outline are all tentative.
Examinations will be classical type with open books and notes.