EMA 405Quadrilateral Elements

IntroductionQuadrilateral elements are 4-sided,

planar elementsThey 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

Element Types in ANSYSConstant Strain TriangleOption for Plane42 in ANSYS

3

2

1

53

6

2

654

321

),(

),(

cc

c

c

ycxccyxv

ycxccyxu

xy

y

x

What if triangles have midside nodes (linear strain triangle)?

3

45

26

1

ycxccycxcc

ycxcc

ycxcc

ycxycxcycxccyxv

ycxycxcycxccyxu

xy

y

x

11108653

12119

542

12112

10987

265

24321

22

2

2

),(

),(2

Plane2 element in ANSYS

Bilinear quadrilateral element?

3

4

21yccxcc

xcc

ycc

xycycxccyxv

xycycxccyxu

xy

y

x

8643

87

42

8765

4321

),(

),(

Option in Plane42 element in ANSYS

Bilinear Quadrilateral (cont.)

This element does not permit curvature in bending

this

not this

Quadratic quadrilateral element?

3

4

21

287542

216

215

21413

21211109

28

27

265

24321

22

),(

),(

ycxycycxcxc

xycyxcycxycxcycxccyxv

xycyxcycxycxcycxccyxu

x

Plane82 element in ANSYS

7

6

5

8

Improved bilinear quadrilateral elementThis is the default behavior of

Plane42 in ANSYSIt adds curvature terms to the

assumed displacements to permit curvature in bending

Von Mises Stress

Also known as equivalent stressA common model for the onset of

yielding in multiaxial stress states

222222 62

1yzxzxyzyzxyxe