| Matrix or Vector | Geometry | Shape Functions | Integration Points |
|---|---|---|---|
| Stiffness Matrix and Thermal Load Vector | Quad | Equation 11–84, Equation 11–85, Equation 11–86, Equation 11–87, Equation 11–88, and Equation 11–89 | In-plane: 2 x 2 |
| Triangle | Equation 11–57, Equation 11–58, Equation 11–59, Equation 11–60, Equation 11–61, and Equation 11–62 | In-plane: 3 | |
| Consistent Mass and Stress Stiffness Matrices | Quad | Equation 11–84, Equation 11–85, Equation 11–86, Equation 11–87, Equation 11–88, and Equation 11–89 | Same as stiffness matrix |
| Triangle | Equation 11–57, Equation 11–58, Equation 11–59, Equation 11–60, Equation 11–61, and Equation 11–62 | Same as stiffness matrix | |
| Lumped Mass Matrix | Quad | Equation 11–84, Equation 11–85, and Equation 11–86 | Same as stiffness matrix |
| Triangle | Equation 11–57, Equation 11–58, and Equation 11–59 | Same as stiffness matrix | |
| Transverse Pressure Load Vector | Quad | Equation 11–86 | 2 x 2 |
| Triangle | Equation 11–59 | 3 | |
| Edge Pressure Load Vector | Same as in-plane mass matrix, specialized to the edge | 2 | |
| Load Type | Distribution |
|---|---|
| Element Temperature | Linear thru thickness, bilinear in plane of element |
| Nodal Temperature | Constant thru thickness, bilinear in plane of element |
| Pressure | Bilinear in plane of element, 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.
A membrane option is available for SHELL281 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.