1. EMA 405 Quadrilateral Elements

2. Introduction Quadrilateral elements are 4-sided, planar elements They can address plane stress, plane strain, or axisymmetric analyses ◦ Plane stress -  z =0 (for thin structures) ◦ Plane strain -  z =0 (for thick structures) ◦ Axisymmetric will be addressed in the next chapter 2-D triangular elements are related and can be thought of as quad elements where two nodes are coincident

3. Element Types in ANSYS Constant Strain Triangle Option for Plane42 in ANSYS 3 2 1

4. What if triangles have midside nodes (linear strain triangle)? 3 4 5 2 6 1 Plane2 element in ANSYS

5. Bilinear quadrilateral element? 3 4 2 1 Option in Plane42 element in ANSYS

6. Bilinear Quadrilateral (cont.) This element does not permit curvature in bending this not this

7. Quadratic quadrilateral element? 3 4 2 1 Plane82 element in ANSYS 7 6 5 8

8. Improved bilinear quadrilateral element This is the default behavior of Plane42 in ANSYS It adds curvature terms to the assumed displacements to permit curvature in bending

9. Von Mises Stress Also known as equivalent stress A common model for the onset of yielding in multiaxial stress states