| Matrix or Vector | Shape Functions | Integration Points |
|---|---|---|
| Stiffness Matrix; and Thermal Load Vector | Equation 11–69, Equation 11–70, Equation 11–71, Equation 11–72, Equation 11–73, and Equation 11–74 |
In-plane:
|
| Consistent Mass and Stress Stiffness Matrices | Equation 11–69, Equation 11–70, Equation 11–71, Equation 11–72, Equation 11–73, and Equation 11–74 | Closed form integration |
| Lumped Mass Matrix | Equation 11–69, Equation 11–70, Equation 11–71 | Closed form integration |
| Transverse Pressure Load Vector | Equation 11–71 | 2 x 2 |
| Edge Pressure Load Vector | Equation 11–69 and Equation 11–70 specialized to the edge | 2 |
| Load Type | Distribution |
|---|---|
| Element Temperature | Bilinear in plane of element, linear thru each layer |
| Nodal Temperature | Bilinear in plane of element, constant thru thickness |
| Pressure | Bilinear in plane of element and linear along each edge |
References: Ahmad([1]), Cook([5]), Dvorkin([96]), Dvorkin([97]), Bathe and Dvorkin([98]), Allman([113]), Cook([114]), MacNeal and Harder([115])
Structures describes the derivation of structural element matrices and load vectors as well as stress evaluations.
Normals to the centerplane are assumed to remain straight after deformation, but not necessarily normal to the centerplane.
Each set of integration points thru a layer (in the r direction) is assumed to have the same element (material) orientation.
The assumed displacement and transverse shear strain shape functions are given in Shape Functions. The basic functions for the transverse shear strain have been changed to avoid shear locking (Dvorkin([96]), Dvorkin([97]), Bathe and Dvorkin([98])).
A membrane option is available for SHELL181 if KEYOPT(1) = 1. For this option, there is no bending stiffness or rotational degrees of freedom. There is only one integration point per layer, regardless of other input.
