1. Projecto Avançado de Estruturas Navais Mestrado em Engenharia Naval

2. Contents (1) Structural Stability – basic principles –Linear approach –Non-linear response Non-linear behavior of beam-columns and plates subjected to compressive and combined loading. –Influence of initial imperfections Buckling of plates and stiffened plates –Initial imperfections –Residual stresses

3. Contents (2) Ultimate strength of plates and stiffened plates –Concept of effective width –Reduction of strength due to imperfections and welding Residual strength and post buckling behavior of components Hull girder strength –Linear and Non-linear behavior –Ultimate bending moment –Residual strength

4. Structural Stability Basic principles Equilibrium stability concept –A) Stable –B) Unstable –C) Neutral Structural limit states –Ultimate limit Global Failure Local Failure –Serviceable limit

5. Structural Stability Stability and Instability –Ex: Euler column EI – Structural modulus

6. Equilibrium state A) Stable B) Unstable C) Stable Transition between different states of equilibrium

7. Types of instability Bifurcation Snap-through Euler column P/P E =1+(  q/l) 2 /8

8. Local Buckling

9. Cylindrical shell

10. Snap-through

11. Non linearity Physical non-linearity Geometrical non-linearity

12. Bifurcation Instability

13. Snap-through Instability

14. Initial Imperfections

15. Initial Imperfections (Example)

16. Material (Plasticity) Plasticity Residual stresses

17. Stability Criteria Static criteria –Adjacent equilibrium criteria (bifurcation) –Energy criteria (Minimum Potential Energy)

18. Linear Analysis Discrete systems Continuous systems Aproximate methods –Finite differences method –Engesser-Newmark method –Galerkin method (diferential equations) –Rayleigh-Ritz method (potential energy) –Finite element method

19. Basic concepts Effective length –Boundary conditions Effective width –Boundary conditions –Loading –Manufacturing Initial geometric imperfections –Residual stresses and welding procedure –Mounting process and restraining Residual stresses –Welding procedure –Restraining –Physical properties Loading of the component –Combined loading –Boundary conditions