13.226. SOLID226 - 3-D 20-Node Coupled-Field Solid

Matrix or VectorGeometryShape FunctionsIntegration Points
Stiffness and Stress Stiffness Matrices; and Thermal Expansion, Diffusion Expansion, and Electrostatic Force Load VectorBrickEquation 11–232, Equation 11–233, and Equation 11–234

14 if KEYOPT(6) = 0

2 x 2 x 2 if KEYOPT(6) = 1

WedgeEquation 11–208, Equation 11–209, and Equation 11–2103 x 3
PyramidEquation 11–192, Equation 11–193, and Equation 11–1942 x 2 x 2
TetEquation 11–184, Equation 11–185, and Equation 11–1864
Mass MatrixSame as stiffness matrix.3 x 3 x 3 if brick. If other shapes, same as stiffness matrix
Pressure Load VectorQuadEquation 11–84 and Equation 11–853 x 3
TriangleEquation 11–57 and Equation 11–586
Thermal Conductivity Matrix and Heat Generation Load VectorBrickEquation 11–23514 [1]
WedgeEquation 11–2113 x 3
PyramidEquation 11–1952 x 2 x 2
TetEquation 11–1874
Specific Heat MatrixSame as thermal conductivity matrix
Convection Surface Matrix and Load VectorQuadEquation 11–91 3 x 3
TriangleEquation 11–63 6
Dielectric Permittivity and Electrical Conductivity Matrices; Charge Density, Joule Heating, and Peltier Heat Flux Load VectorsBrickEquation 11–23614 [1]
WedgeEquation 11–2123 x 3
PyramidEquation 11–1962 x 2 x 2
TetEquation 11–1884
Diffusivity Matrix and Diffusing Substance Generation Load VectorBrickEquation 11–23814 [1]
WedgeEquation 11–2133 x 3
PyramidEquation 11–1972 x 2 x 2
TetEquation 11–1904
Diffusion Damping MatrixSame as diffusivity matrix. If KEYOPT(10)=1, matrix is diagonalized as described in Lumped Matrices
Diffusion Flux Load VectorQuadEquation 11–933 x 3
TriangleEquation 11–656
Thermoelastic stiffness and Damping MatricesSame as combination of stiffness and thermal conductivity matrices
Piezoelectric Coupling MatrixSame as combination of stiffness matrix and dielectric matrix
Seebeck Coefficient Coupling MatrixSame as combination of electrical conductivity and thermal conductivity matrices
Diffusion-elastic stiffness and damping matricesSame as combination of stiffness and diffusivity matrices
Surface Charge Density Load VectorQuadEquation 11–1963 x 3
TriangleEquation 11–646
  1. When KEYOPT(6) = 1 in a coupled-field analysis with structural DOFs, the unified reduced integration scheme with 2 x 2 x 2 integration points is used to form the thermal, electric, electrostatic matrices and load vectors.

13.226.1. 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. Electromagnetics describes the derivation of dielectric and electric conduction matrices. Piezoelectrics discusses the piezoelectric capability used by the element. Piezoresistivity discusses the piezoresistive effect. Thermoelectrics discusses the thermoelectric effects. Thermoelasticity discusses the thermoelastic effects. Electroelasticity discusses the Maxwell stress electroelastic coupling. Thermoplasticity discusses the thermoplastic effect. Structural-Diffusion Coupling discusses diffusion strain coupling.

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