29.5.2. Shell Belt
Shell Belt is constructed with shell4 elements. The shell4 elements are the same FFlex/Shell4 element (3D and Plane stress shell type element). All nodes of shell4 have 6 DOFs.
Coordinate System
Figure 29.86 Coordinate system of the belt body
The node is described as a sphere.
The center marker is located at the central point of sphere and its orientation is dependent on the direction used when the belt is created as shown in Figure 29.86.
If you apply the plus values in the initial velocity of belt, the belt moves into the plus direction of the x-axis of the center marker of each belt body.
The shell force markers of each belt body are located at the center marker and their orientations are the same orientation of each center marker.
Mass and Moment of Inertia
Figure 29.87 Nodal Masses and Moments of Inertia
Total mass ( \({M}\) ):
\({M} = {density} (\rho) * {volumne} {V}\)
Mass coefficient ( \({m}\) ):
\({m} = \frac{M}{1+{n}_1 {n}_2 - {n}_1 - {n}_2}\)\({n}_2 :\) The number of nodes in the lateral directionMoments of Inertia ( \({I}\) ):
\({L}_1 :\) The length of the sheet in the longitudinal direction\({L}_2 :\) The length of the sheet in the lateral direction\({I} = \begin{bmatrix} \frac{m}{12} \left[ \left( \frac{L_2}{n_2 -1} \right)^2 + h^2 \right] & 0 & 0 \\ 0 & \frac{m}{12} \left[ \left(\frac{L_2}{n_2 -1}\right)^2 + \left(\frac{L_1}{n_1 -1}\right)^2 \right] & 0 \\ 0 & 0 & \frac{m}{12} \left[ \left(\frac{L_1}{n_1 -1}\right)^2 + h^2 \right] \end{bmatrix}\)Nodal masses:
\({Type I} = \mathbf{\frac{m}{4}}\) For nodes at four corners\({Type II} = \mathbf{\frac{m}{2}}\) For nodes on four edges\({Type III} = \mathbf{m}\) For internal nodesNodal moments of inertia:
\({Type I} = \mathbf{\frac{I}{4}}\) For nodes at four corners\({Type II} = \mathbf{\frac{I}{2}}\) For nodes on four edges\({Type III} = \mathbf{I}\) For internal nodes
Contact Geometry of Shell Belt
Figure 29.88 Contact geometry of belt