AE361 Applied Elasticity

Course Description:
Concepts of stress and strain in 3-D. Transformations of stress and strain in 2-D and 3-D. Stress-strain and strain-displacement relations. Generalized Hooke's law. Energy methods. Castigliano's theorem. Problems in two-dimensional elasticity. Plane stress and plane strain applications. Polar coordinates. Torsion of noncircular bars. Axisymmetrically loaded members. Rotating disks, thin and thick cylinder applications.

Prerequisite(s):
AE264 'Mechanics of Materials' or consent of the department.

Textbook(s) and/or Other Required Material:
Textbook:
A.C. Ugural and S.K. Fenster, "Advanced Strength and Applied Elasticity" Prentice Hall PTR, 3rd Edition, 1995, ISBN: 0-13-137589-X

Reference books:
B.K. Donaldson, "Analysis of Aircraft Structures" Mc Graw-Hill Book Company, 1993, ISBN: 0-07-112591-4
S.Timoshenko and J.N. Goodier, "Theory of Elasticity", Mc Graw-Hill Book Company, 3rd Edition, 1982, ISBN: 0-07-Y85805-5

Course Objectives:
This course lays down the fundamentals of linear elasticity. It introduces the advanced methods for the analysis of deformable bodies and educates students to apply this knowledge in the solution of aerospace engineering problems. It also equips students with the necessary background to design aerosystems and components.

Syllabus:
Analysis of Stress in 2-D and 3-D - 2 Weeks
Variation of stress within a body in 2-D and 3-D
Mohr's circle for 2-D stress
Principal stresses in 2-D and 3-D
Variation of stress at the boundary of a body

Strain and Stress-Strain Relations - 2 Weeks
Equations of compatibility
Generalized Hooke's Law

Energy Methods - 2 Weeks
Strain Energy
Principles of Work and Energy
Castigliano's Theorem

Two-dimensional Problems in Elasticity - 3 Weeks
Plane strain problems
Plane stress problems
Airy's stress function and its applications
Thermal stresses
Basic relations in polar coordinates

Torsion of Non-circular Bars - 2 Weeks
General solution of the torsion problem
Prandtl's Membrane Analogy
Torsion of thin-walled members of open cross-section

Axisymmetrically Loaded Members - 3 Weeks
Thin and thick-walled cylinders
Maximum tangential stress
Rotating disks of constant thickness
Rotating disks of variable thickness

Class/Laboratory Schedule:
The course has three lecture hours and no laboratory sessions. The duration of each lecture hour is 50 minutes.

Homework, Quizzes and Projects:
Regular homework will be given.
Quizzes will be given.
No projects will be assigned.

Computer Usage: Homework will require computer applications.
Laboratory Work: None

Contribution of Course to Meeting the Professional Component:
Mathematics and Basic Sciences: None
Engineering Design: None
Engineering Sciences: 2 credits
Humanities and Social Sciences: None
Departmental Content: 1 credit

Relationship of Course to Program Objectives:
The course intends to satisfy the first, second, fourth, fifth and sixth objectives of the Department of Aerospace Engineering.

Prepared By:
Yavuz YAMAN
01-23-2002