Week 1: Introduction to Stability and Bifurcation Analysis
Introduce key stability concepts including stability, instability and buckling. Discuss different buckling analysis methods and introduce bifurcation analysis.
Week 2: Energy Methods and First Order Differential Equations (DE)
Introduce energy methods for buckling analysis including the effects of large deformations and imperfects. Begin discussing first order differential equations governing buckling behavior.
Week 3: First Order Differential Equations and Stress Calculations
Continue discussing first order differential equations with special attention to torsion differential equations. Discuss calculating the stress associated with bending, shear, and torsion.
Week 4: Second Order Differential Equations
Detail second order differential equations governing structural stability including axial, flexural, and torsion.
Week 5: Elastic Buckling of Columns
Simplify differential equations previously discussed to look at elastic buckling of columns. Derive governing equations for elastic buckling of doubly symmetric, singly symmetric, and asymmetric column buckling.