13.186. SOLID186 - 3D 20-Node homogeneous/Layered Structural Solid

SOLID186 is available in two forms:

13.186.1. SOLID186 - 3D 20-Node Homogeneous Structural Solid

Matrix or VectorGeometryShape FunctionsIntegration Points
Stiffness and Stress Stiffness Matrices; and Thermal Load VectorBrickEquation 11–236, Equation 11–237, and Equation 11–238

14 if KEYOPT(2) = 1
2 x 2 x 2 if KEYOPT(2) = 0

WedgeEquation 11–211, Equation 11–212, and Equation 11–2133 x 3
PyramidEquation 11–195, Equation 11–196, and Equation 11–1972 x 2 x 2
TetEquation 11–187, Equation 11–188, and Equation 11–1894
Mass MatrixSame as stiffness matrix.14 if brick. If other shapes, same as stiffness matrix
Pressure Load VectorQuadEquation 11–82 and Equation 11–833 x 3
TriangleEquation 11–58 and Equation 11–596
Load TypeDistribution
Element TemperatureSame as shape functions thru element
Nodal TemperatureSame as shape functions thru element
PressureBilinear across each face

13.186.2. SOLID186 - 3D 20-Node Layered Structural Solid

Matrix or VectorGeometryShape FunctionsIntegration Points
Stiffness and Stress Stiffness Matrices; and Thermal Load VectorBrickEquation 11–236, Equation 11–237, and Equation 11–238

In-plane:
2 x 2
Thru-the-thickness:
2 if no shell section
 defined.
1, 3, 5, 7, or 9 per 
layer if a shell 
section is defined

WedgeEquation 11–211, Equation 11–212, and Equation 11–213

In-plane: 3
Thru-the-thickness:
2 if no shell section 
defined.
1, 3, 5, 7, or 9 per 
layer if a shell 
section is defined

Mass MatrixSame as stiffness matrix.

In-plane:
3 x 3 if brick
3 if wedge
Thru-the-thickness:
Same as stiffness matrix

Pressure Load VectorQuadEquation 11–82 and Equation 11–833 x 3
TriangleEquation 11–58 and Equation 11–596
Load TypeDistribution
Element TemperatureBilinear in plane of element, linear thru each layer
Nodal TemperatureSame as shape functions thru element
PressureBilinear across each face

Reference: Zienkiewicz([40])

13.186.3. 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.

13.186.4. Shear Correction

The element does not perform interlaminar shear correction. Stresses are calculated from strains as is.