Equation sheet-exam2 - 1 Important relations and concepts...

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Unformatted text preview: 1 Important relations and concepts in AE 322 1) Theory of elasticity 1.1) 3D theory Equilibrium equations : , ij j i f + = ; ij = ji Cauchys relation : T i = ji n j Kinematic : ij = 1 2 u i, j + u j,i ( ) Compatibility : ij, kl + kl,ij = ik, jl + jl, ik Constitutive (isotropic) : ij = mm ij + 2 ij = E 1 + ( ) 1 2 ( ) , = G = E 2 1 + ( ) 1.2) 2D theory (plane stress) Equilibrium : ( ) , 0; , 1,2 ij j i ij ji f i j + = = Kinematic : ( ) , , 1 2 ij i j j i u u = Compatibility : 2 12,12 = 11, 22 + 22,11 Constitutive (isotropic) : 11 = E 1 2 11 + 22 [ ] , 22 = E 1 2 22 + 11 [ ] , 12 = E 1 + 12 33 = 1 11 + 22 ( ) , 33 = For plane strain : replace E by E/ 1 2 ( ) ; by / 1 ( ) ; 33 = 0; 33 = 11 + 22 ( ) 2 2) Bending and extension of beams 2.1) Conventions for positive force and moment resultants x N N M...
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Equation sheet-exam2 - 1 Important relations and concepts...

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