Projecto Avançado de Estruturas Navais Mestrado em Engenharia Naval

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

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

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

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

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

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

Local Buckling

Cylindrical shell

Snap-through

Non linearity Physical non-linearity Geometrical non-linearity

Bifurcation Instability

Snap-through Instability

Initial Imperfections

Initial Imperfections (Example)

Material (Plasticity) Plasticity Residual stresses

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

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

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