13.182. PLANE182 - 2-D 4-Node Structural Solid

Matrix or VectorGeometryShape Functions Integration Points
Stiffness and Stress Stiffness Matrices; and Thermal Load VectorQuad Equation 11–120 and Equation 11–121

2 x 2 if KEYOPT(1) = 0, 2, or 3
1 if KEYOPT(1) = 1

Triangle Equation 11–100 and Equation 11–101 1
Mass MatrixQuadSame as stiffness matrix2 x 2
Pressure Load VectorSame as stiffness matrix, specialized to face2
Load TypeDistribution
Element TemperatureBilinear across element, constant thru thickness or around circumference
Nodal TemperatureSame as element temperature distribution
PressureLinear along each face

13.182.1. Other Applicable Sections

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.

13.182.2. Theory

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.

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