1. Review for Final Exam
Basic knowledge of vector & index notation, matrix-tensor theory, coordinate transformation, principal value problems, vector calculus
Use of strain-displacement & rotation-displacement relations; determine strains/rotations given the displacements, integrate strains to find displacements
Use of strain compatibility equations
Traction vector & stress tensor definitions and relations
Use of equilibrium equations
Use of general and isotropic forms of Hooke’s law; both stress in terms of strain, and strain in terms of stress
General elasticity boundary-value problem formulation
Boundary & interface condition specification (pointwise and integrated forms)
Displacement formulation – Navier’s equations
Stress formulation – Beltrami-Michell compatibility + equilibrium equations
Strain energy – basic forms
Plane strain, plane stress and antiplane strain formulation
Two-dimensional problem solution in Cartesian and polar coordinates using Airy stress function and displacement formulation
Torsion formulation and problem solution using stress function and displacement formulation