# AAE 55300: Elasticity in Aerospace Engineering

Description:

A basic course in the theory of elasticity, with emphasis on understanding the fundamental principles and solution techniques used in the stress analysis of elastic solids and structures. Cartesian tensors are introduced for formulations of general deformations and states of stress. Constitutive relations and field equations are derived for large deformation and then reduced to small deformation. Two dimensional problems are solved by using the Airy's stress function method and complex functions approaches. Energy methods and approximate solutions using variational principles are included.

Format: 3 lecture hrs per week

Credit hours: 3

Status: Elective, Structures

Offered: Fall

Pre-requisite: Knowledge of linear algebra and differential equations

Co-requisite: None

Course Instructor: Professors Doyle, Farris, and Sun

Text: Typed class notes

Assessment Method: 3 tests (25% each) and homework (25%)

## Course Objective:

To give the student an in-depth background in mechanics of solids including large deformation, and the ability to perform stress analyses in elastic bodies, especially two-dimensional bodies.

Necessary Background:

1. Introductory mechanics of solids

2. Linear algebra

3. Differential equations

Topics (number of Lectures):

1. Cartesian tensors: indicial notation, coordinate transformation, scalar, vector, tensor, calculus of tensor field, properties of second order tensors (6 classes)

2. Deformation: description of motion, deformation gradients, deformation of lines, areas, and volumes, strain, rotation, deformation in terms of displacement, special deformations (8 classes)

3. Stress: Cauchy stress principle, equations of motion in terms of stress, properties of the Cauchy stress tensor, equations of motion: undeformed state, stress in special deformations (6 classes)

4. Constitutive relations: elastic relations under small deformations, elastic symmetry, engineering elastic constants, isotropic finite elasticity (4 clases).

5. Elasticity problems: linear theory of elasticity, uniqueness of solutions, Levy's problem (2 classes)

6. Plane problems in Cartesian coordinates: reduction to 2D equations, Airy stress function formulation, complex function formulation, Flamant's problem, prismatic beam, harmonic function, displacement formulation (4 classes)

7. Plane problems in cylindrical coordinates: cylindrical coordinates, Golovin's curved beam problem, Lame's pressurized cylinder problem. Kirsch's hole in an infinite sheet, rotating disk (6 classes)

8. Variational methods: principle of virtual work, calculus of variations, Ritz method. (6 classes)

9. Exams (3 classes)

Relationship of course to program objectives:

This course builds on the two previous aero-structure course, AAE204 and AAE 352, and continues to raise the student's level in mechanics of solids and structures (1). It is essential for the student to attain such background in order to take other graduate and dual level courses in structures and materials (2a).

Prepared by: C. T. Sun

Date: March 3, 2001