《船舶与海洋工程结构风险评估》课程教学课件（讲稿）Lecture 6 Reliability of Steel Plates -I

Elastic Buckling of Plate: Kinematics - Displacement and Strain· Equilibrium Equation - External Forcesand Internal Stress Constitutive - Stresses and Strain6

Elastic Buckling of Plate • Kinematics – Displacement and Strain • Equilibrium Equation – External Forces and Internal Stress • Constitutive – Stresses and Strain 6

Plate BendingConstitutive Relationships

Plate Bending Constitutive Relationships 7

Bending Moments产L-Strain in layer dz,ZM27ar?L公Similarly,PlarctPitelz8

Bending Moments • Strain in layer dz, • Similarly, 2 2 x w z r z x x       2 2 y w z y      8

Hooke'sLawisHAndHWhere v is Poisson's ratioRearrangingE+VeEzaw(a2wax?y1-y29

• Hooke’s Law is • And Where v is Poisson’s ratio. • Rearranging   x x y v E      1   y y x v E      1   x x y v v E       2 1                2 2 2 2 2 1 y w v x w v Ez 9

Total moment on face x=0 or a isM.7aH7Wdzax+t/2EzOt/23(1 v2Ox-Et32M12(1-v210

• Total moment on face x=0 or a is M dy z dy dz x t x t 2 2     dz y w v x w v t Ez t                 2 2 2 2 / 2 / 2 2 2 1                   2 2 2 2 2 3 31 y w v x w v Ez                   2 2 2 2 2 3 12 1 y w v x w v Et  t / 2  t / 2 10