13.222. PLANE222 - 2-D 4-Node Coupled-Field Solid

Matrix or Vector

Geometry

Shape Functions

Integration Points

Stiffness and Stress Stiffness Matrices; and Thermal Expansion Load Vector

Quad

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

Mass Matrix

Quad

Same as stiffness matrix

2 x 2

Triangle

Pressure Load Vector

Same as stiffness matrix, specialized to the face

Thermal Conductivity Matrix and Heat Generation Load Vector

Quad

Equation 11–128

2 x 2

Triangle

Equation 11–108

Specific Heat Matrix

Same as conductivity matrix. Matrix is diagonalized as described in Lumped Matrices.

Same as conductivity matrix

Convection Surface Matrix and Load Vector

Same as conductivity matrix evaluated at the face

Thermoelastic Stiffness and Damping Matrices

Same as combination of stiffness and thermal conductivity matrices

13.222.1. Other Applicable Sections

General Element Formulations gives the general element formulations used by this element. Structures describes the derivation of structural element matrices and load vectors as well as stress evaluations. Heat Flow describes the derivation of the thermal element matrices and load vectors as well as heat flux evaluations. Thermoelasticity discusses the thermoelastic effects. Thermoplasticity discusses the thermoplastic effect.

13.222.2. Theory

This element uses the method (selective reduced integration technique for volumetric terms) (Hughes([220]), Nagtegaal et al. ([221]))