| Matrix or Vector | Shape Functions | Integration Points |
|---|---|---|
| Stiffness and Stress Stiffness Matrices; and Thermal and Newton-Raphson Load Vectors | Equation 11–19, Equation 11–20, Equation 11–21, Equation 11–22, Equation 11–23, and Equation 11–24 | Along the length: 2 Across the section: see PIPE288 - 3-D 2-Node Pipe |
| Consistent Mass Matrix and Pressure, Hydrostatic, and Hydrodynamic Load Vectors | Same as stiffness matrix | Along the length: 3 [1] Across the section: 1 |
| Lumped Mass Matrix | Equation 11–19, Equation 11–20, and Equation 11–21 | Along the length: 3 Across the section: 1 |
| Load Type | Distribution |
|---|---|
| Element Temperature | KEYOPT(1) = 0 Linear thru wall and linear along length KEYOPT(1) = 1 Bilinear across cross-section and linear along length |
| Nodal Temperature | Constant across cross-section, linear along length |
| Internal and External Pressures | Constant, except as adjusted by the affect of internal and external fluids. |
References: Simo and Vu-Quoc([238]), Ibrahimbegovic([239]).
The theory for this element is identical to that of PIPE288 - 3-D 2-Node Pipe, except that this element is a 3-node pipe.