Stability and Analysis of Structures I

This course introduces analytical and numerical techniques for the modeling and analysis of representative aerospace structures under mechanical loading, with particular emphasis on determining their stability. The course covers the connection between the principle of minimum potential energy, the variational formulation and the classical (differential) formulation of quasi-static structural problems. Basic structural components are analyzed using beam and plate theory. The basic theory of structural stability is introduced through asymptotic analysis in order to establish the buckling equation. Buckling equations are formulated and solved for geometrically non-linear elastic beams and plates. The methodology is extended to formulate stability analysis of representative aerospace components. Emphasis is placed on the understanding of the models, their assumptions, and ranges of applicability.

The topics covered include:

- Introduction to structural analysis.

- Review of global and local balance principles.

- Constitutive relations, material symmetries and strain energy.

- Formulations of structural problems: differential, variational and minimum formulations.

- Introduction to calculus of variations and approximate solution methods (Ritz and Galerkin).

- Applications to beams and plates: solution to basic structural problems.

- Introduction to buckling: Eigenvalue buckling problem (bifurcation buckling).

- Imperfection analysis (snap buckling) and stability analysis.

- Buckling of non-linear beams/columns and plates.

- Design methodology for thin-walled aerospace structures.