Prismatic beam
Nodes
The element has 2 nodes with global numbers N1 and N2. In the figure, N1 < N2 is assumed.
Each node has six degrees of freedom $[u,v,w,\varphi_x,\varphi_y,\varphi_z]$ and three temperatures $[T,T_\eta,T_\zeta].$ The rotations are related to the global coordinate system. The temperature gradients are expressed in the local coordinate system: $$T_\eta=\partial T/\partial\eta,\quad T_\zeta=\partial T/\partial\zeta.$$
Local coordinate system
The axis $\xi$ coincides with the element’s edge in the direction from N1 to N2, therefore, its orientation depends on the particular mesh numbering.
The axes $\eta$ and $\zeta$ are the principal central axes of the cross-section. The direction and sense of the axis $\eta$ is given by the projection $\mathbf{p}'$ of the directional vector $\mathbf{p}$ on the plane perpendicular to the axis $\xi.$ The vector $\mathbf{p}$ must be entered.
Geometrical characteristics
| $A$ | Cross-sectional area $[\text{m}^2].$ |
|---|---|
| $I_k$ | Moment of stiffness in torsion $[\text{m}^4].$ |
| $W_k$ | Sectional modulus of torsion $[\text{m}^3].$ |
| $I_\eta$ | Quadratic moment about the local axis $\eta$ $[\text{m}^4].$ |
| $W_\eta$ | Cross-sectional modulus of bending about the local axis $\eta$ $[\text{m}^3].$ |
| $I_\zeta$ | Quadratic moment about the local axis $\zeta$ $[\text{m}^4].$ |
| $W_\zeta$ | Cross-sectional modulus of bending about the local axis $\zeta$ $[\text{m}^3].$ |
| $p_x,p_y,p_z$ | Components of the directional vector $\mathbf{p}.$ |