FEAElasticity - Procedures of Finite Element Analysis...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Procedures of Finite Element Analysis Two-Dimensional Elasticity Problems Professor M. H. Sadd
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Two Dimensional Elasticity Element Equation Orthotropic Plane Strain/Stress Derivation Using Weak Form – Ritz/Galerin Scheme Displacement Formulation Orthotropic Case 0 0 22 12 66 66 12 11 = + + + + = + + + + y x F y v C x u C y x v y u C x F x v y u C y y v C x u C x strain plane and stress plane ) 1 ( 2 , strain plane ) 2 - )(1 (1 E stress plane 1 strain plane ) 2 - )(1 (1 ) - E(1 stress plane 1 66 2 12 2 22 11 ν + = μ = ν ν + ν ν - ν = ν ν + ν ν - = = E C E C E C C Material Isotropic xy xy y x y y x x e C e C e C e C e C 66 22 12 12 11 = τ + = σ + = σ Law s Hooke'
Image of page 2
Two Dimensional Elasticity Weak Form 0 0 22 12 66 2 66 12 11 1 = + + + + = + + + + dxdy F y v C x u C y x v y u C x w h dxdy F x v y u C y y v C x u C x w h e e y e x e Mulitply Each Field Equation by Test Function & Integrate Over Element Use Divergence Theorem to Trade Differentiation On To Test Function y x y y x x y e y e e x e x e e n y v C x u C n x v y u C T n x v y u C n y v C x u C T ds T w h dxdy F w h dxdy y v C x u C y w x v y u C x w h ds T w h dxdy F w h dxdy x v y u C y w y v C x u C x w h e e e e e e + + + = + + + = + = + + + + = + + + Γ Γ 22 11 66 66 12 11 2 2 22 12 2 66 2 1 1 66 1 12 11 1 , (constant) ickness element th = e h
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Two Dimensional Elasticity Ritz-Galerkin Method Γ Γ ψ + ψ = ψ + ψ = ψ ψ + ψ ψ = ψ ψ + ψ ψ = = ψ ψ + ψ ψ = = = e e e e e e e ds T h dxdy F h F ds T h dxdy F h F dxdy y y C x x C h K dxdy
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern