Matrix or Vector | Geometry | Shape Functions | Integration Points |
---|---|---|---|

Stiffness and Stress Stiffness Matrices; and Thermal Load Vector | Quad | Equation 11–120 and Equation 11–121 |
2 x 2 if KEYOPT(1) = 0, 2, or 3 |

Triangle | Equation 11–100 and Equation 11–101 | 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([220]), Nagtegaal et al.([221])).

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([319]), Simo and Armero([320]), Simo et al.([321]), Andelfinger and Ramm([322]), and Nagtegaal and Fox([323]) 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.