{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

plane_cst-lst

# plane_cst-lst - Plane Problems Constitutive Equations...

This preview shows pages 1–6. Sign up to view the full content.

1 Plane Problems: Constitutive Equations Constitutive equations for a linearly elastic and isotropic material in plane stress (i.e., σ z = τ xz = τ yz =0): where the last column has the initial (thermal) strains which are 0 , xy0 0 0 = = = γ α ε ε T y x • Rewriting in a compact form and solving for the stress vector, where

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

View Full Document
2 Plane Problems: Approximate Strain-Displacement Relations • From the above, by definition , , x v y u y v x u xy y x + γ ε ε
3 Plane Problems: Strain-Displacement Relations As the size of the rectangle goes to zero, in the limit,

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

View Full Document
4 Plane Problems: Displacement Field Interpolated Interpolating the displacement field, u(x,y) and v(x,y), in the plane finite element from nodal displacements, where entries of matrix N are the shape (interpolation) functions N i . From the previous two equations, where B is the strain-displacement matrix .
5 Stiffness Matrix and strain energy Strain energy density of an elastic material (energy/volume) ε ε

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}