Product: ABAQUS/Standard
Linear elastic, Young's modulus = 30 × 106, Poisson's ratio = 0.3.
Boundary conditions:
.
An out-of-plane displacement of 0.01 units (motion of one bounding plane relative to the other) is applied to degree of freedom 3 of the reference node, which is the change in fiber length degree of freedom.
Analytical solution:
Stresses
At every node 
3.0 × 105.
Strains
At every node 
–3.0 × 10–3, 
1.0 × 10–2.
A relative rotation of 0.01 radians about the y-axis is applied to degree of freedom 5 of the reference node (the rotation degree of freedom of one bounding plane relative to the other).
Analytical solution:
Stresses
Maximum tensile stress 
1.5 × 105.
Strains
Maximum tensile strain 
5 × 10–3.
For Step 1, all element types yield the exact solution. The results for Step 2 are given in the following table:
| Element type |  |  |
|---|---|---|
| CPEG3 | 1.264 × 105 | 4.167 × 10–3 |
| CPEG3H | 1.264 × 105 | 4.167 × 10–3 |
| CPEG3HT | 1.264 × 105 | 4.167 × 10–3 |
| CPEG3T | 1.264 × 105 | 4.167 × 10–3 |
| CPEG4 | 1.131 × 105 | 3.750 × 10–3 |
| CPEG4H | 1.131 × 105 | 3.750 × 10–3 |
| CPEG4HT | 1.131 × 105 | 3.750 × 10–3 |
| CPEG4I | 1.500 × 105 | 5.000× 10–3 |
| CPEG4IH | 1.500 × 105 | 5.000 × 10–3 |
| CPEG4R | 1.125 × 105 | 3.750 × 10–3 |
| CPEG4RH | 1.125 × 105 | 3.750 × 10–2 |
| CPEG4RHT | 1.125 × 105 | 3.750 × 10–2 |
| CPEG4RT | 1.125 × 105 | 3.750 × 10–3 |
| CPEG4T | 1.131 × 105 | 3.750 × 10–3 |
| CPEG6 | 1.500× 105 | 5.000× 10–3 |
| CPEG6H | 1.500× 105 | 5.000 × 10–3 |
| CPEG6M | 1.504× 105 | 5.000 × 10–3 |
| CPEG6MH | 1.504 × 105 | 5.000× 10–3 |
| CPEG6MHT | 1.504 × 105 | 5.000× 10–3 |
| CPEG6MT | 1.504 × 105 | 5.000× 10–3 |
| CPEG8 | 1.500 × 105 | 5.000 × 10–3 |
| CPEG8H | 1.500 × 105 | 5.000 × 10–3 |
| CPEG8HT | 1.500 × 105 | 5.000 × 10–3 |
| CPEG8R | 1.500 × 105 | 5.000 × 10–3 |
| CPEG8RH | 1.500 × 105 | 5.000 × 10–3 |
| CPEG8RHT | 1.500 × 105 | 5.000 × 10–3 |
| CPEG8T | 1.500 × 105 | 5.000 × 10–3 |
Second-order quadrilateral elements, first-order incompatible mode elements, and quadratic triangles yield the exact solutions. Modified triangles yield nearly exact solutions. Other element types exhibit stiff response.
CPEG3 and CPEG3H elements.
CPEG4, CPEG4I, CPEG4R, CPEG4IH, CPEG4H, and CPEG4RH elements.
CPEG6, CPEG6H, CPEG6M, and CPEG6MH elements.
CPEG8, CPEG8R, CPEG8H, and CPEG8RH elements.
CPEG3HT and CPEG3T elements.
CPEG4HT, CPEG4RHT, CPEG4RT, and CPEG4T elements.
CPEG6, CPEG6H, CPEG6MT, and CPEG6MHT elements.
CPEG8HT, CPEG8RHT, and CPEG8T elements.