ElasticityRectangular_01_PlaneProblems

ElasticityRectangular_01_PlaneProblems - Section 3.1 Solid...

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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 stress-strain law (Part I, Eqns. 4.2.11-14), the strain-displacement 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 Strain-displacement 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.

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ElasticityRectangular_01_PlaneProblems - Section 3.1 Solid...

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