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Unformatted text preview: Section 3.1 Solid Mechanics Part II Kelly 43 3.1 Plane Problems What follows is to be applicable to any two dimensional problem, so it is taken that = = xz yz σ σ , which is true of both plane stress and plane strain. 3.1.1 Governing Equations for Plane Problems To recall, the equations governing the elastostatic problem are the elastic stressstrain law (Part I, Eqns. 4.2.1114), the straindisplacement relations (Eqns. 1.2.5) and the equations of equilibrium (1.1.10) [ ] [ ] ( ) yy xx zz xy xy xx yy yy yy xx xx E E E E σ σ ν ε σ ν ε νσ σ ε νσ σ ε + − = + = − = − = 1 , 1 , 1 Plane Stress (3.1.1a) [ ] [ ] ( ) yy xx zz xy xy yy xx yy yy xx xx E E E σ σ ν σ σ ν ε σ ν νσ ν ε νσ σ ν ν ε + = + = − + − + = − − + = 1 , ) 1 ( 1 , ) 1 ( 1 Plane Strain (3.1.1b) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ = ∂ ∂ = ∂ ∂ = x u y u y u x u y x xy y yy x xx 2 1 ε ε ε Straindisplacement relations (3.1.2) = + ∂ ∂ = + ∂ ∂ + ∂ ∂...
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This note was uploaded on 01/20/2012 for the course ENGINEERIN 2 taught by Professor Staff during the Fall '11 term at Auckland.
 Fall '11
 Staff
 Strain, Stress

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