Elasticity in Aerospace Engineering
Learning 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.
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. F2017 Syllabus
Topics Covered: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 classes).
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).