| Matrix or Vector | Geometry | Shape Functions | Integration Points |
|---|---|---|---|
| Stiffness and Stress Stiffness Matrices; and Thermal Load Vector | Quad | Equation 11–122 and Equation 11–123 |
2 x 2 if KEYOPT(1) = 0, 2, or 3 |
| Triangle | Equation 11–101 and Equation 11–102 | 1 | |
| Mass Matrix | Quad | Same as stiffness matrix | 2 x 2 |
| Triangle | 1 | ||
| Pressure Load Vector | Same as stiffness matrix, specialized to face | 2 | |
| Load Type | Distribution |
|---|---|
| Element Temperature | Bilinear across element, constant thru thickness or around circumference |
| Nodal Temperature | Same as element temperature distribution |
| Pressure | Linear along each face |
Structures describes the derivation of structural element matrices and load vectors as well as stress evaluations. General Element Formulations gives the general element formulations used by this element.
If KEYOPT(1) = 0, this element uses
method (selective reduced integration technique for volumetric terms) (Hughes([221]), Nagtegaal et al.([222])).
If KEYOPT(1) = 1, the uniform reduced integration technique (Flanagan and Belytschko([233])) is used.
If KEYOPT(1) = 2 or 3, the enhanced strain formulations from the work of Simo and Rifai([318]), Simo and Armero([319]), Simo et al.([320]), Andelfinger and Ramm([321]), and Nagtegaal and Fox([322]) are used. It introduces 5 internal degrees of freedom to prevent shear and volumetric locking for KEYOPT(1) = 2, and 4 internal degrees of freedom to prevent shear locking for KEYOPT(1) = 3. If mixed u-P formulation is employed with the enhanced strain formulations, only 4 degrees of freedom for overcoming shear locking are activated.