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

SOLID186 is available in two forms:

### 13.186.1. SOLID186 - 3-D 20-Node homogeneous Structural Solid Matrix or VectorGeometryShape FunctionsIntegration Points
Stiffness and Stress Stiffness Matrices; and Thermal Load VectorBrickEquation 11–232, Equation 11–233, and Equation 11–234

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

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
TriangleEquation 11–57 and Equation 11–586
Element TemperatureSame as shape functions thru element
Nodal TemperatureSame as shape functions thru element
PressureBilinear across each face

### 13.186.2. SOLID186 - 3-D 20-Node Layered Structural Solid Matrix or VectorGeometryShape FunctionsIntegration Points
Stiffness and Stress Stiffness Matrices; and Thermal Load VectorBrickEquation 11–232, Equation 11–233, and Equation 11–234

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 11–208, Equation 11–209, and Equation 11–210

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

TriangleEquation 11–57 and Equation 11–586
Element TemperatureBilinear in plane of element, linear thru each layer
Nodal TemperatureSame as shape functions thru element
PressureBilinear across each face

Reference: Zienkiewicz()

### 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.