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

SOLID186 is available in two forms:

homogeneous (nonlayered) structural solid (KEYOPT(3) = 0, the default) - see SOLID186 - 3-D 20-Node homogeneous Structural Solid.
Layered structural solid (KEYOPT(3) = 1) - see SOLID186 - 3-D 20-Node Layered Structural Solid.

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

Matrix or Vector	Geometry	Shape Functions	Integration Points
Stiffness and Stress Stiffness Matrices; and Thermal Load Vector	Brick	Equation 11–232, Equation 11–233, and Equation 11–234	14 if KEYOPT(2) = 1 2 x 2 x 2 if KEYOPT(2) = 0
	Wedge	Equation 11–208, Equation 11–209, and Equation 11–210	3 x 3
	Pyramid	Equation 11–192, Equation 11–193, and Equation 11–194	2 x 2 x 2
	Tet	Equation 11–184, Equation 11–185, and Equation 11–186	4
Mass Matrix	Same as stiffness matrix.		3 x 3 x 3 if brick. If other shapes, same as stiffness matrix
Pressure Load Vector	Quad	Equation 11–84 and Equation 11–85	3 x 3
Pressure Load Vector	Triangle	Equation 11–57 and Equation 11–58	6

Load Type	Distribution
Element Temperature	Same as shape functions thru element
Nodal Temperature	Same as shape functions thru element
Pressure	Bilinear across each face

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

Matrix or Vector	Geometry	Shape Functions	Integration Points
Stiffness and Stress Stiffness Matrices; and Thermal Load Vector	Brick	Equation 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
	Wedge	Equation 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 Matrix	Same as stiffness matrix.		In-plane: 3 x 3 if brick 3 if wedge Thru-the-thickness: Same as stiffness matrix
Pressure Load Vector	Quad	Equation 11–84 and Equation 11–85	3 x 3
Pressure Load Vector	Triangle	Equation 11–57 and Equation 11–58	6

Load Type	Distribution
Element Temperature	Bilinear in plane of element, linear thru each layer
Nodal Temperature	Same as shape functions thru element
Pressure	Bilinear across each face

Reference: Zienkiewicz([39])

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.