MBPTDSF

Format

Example

Definitions

Comments

1. The deformable curve is generated using the CUBIC spline interpolation which requires assumptions on the second derivative of the interpolating function at either end of the curve. The keywords NATURAL, PARABOLIC, PERIODIC and CANTILEVER represent the four standard assumptions defined as:
   $$\begin{array}{l}\text{NATURAL}\hspace{0.17em}(\text{or}\hspace{0.17em}\text{free}):\hspace{0.17em}{f}^{″}(x_0)=f^{″}(x_N)=0\\ \text{PARABOLIC}:\hspace{0.17em}\hspace{0.17em}{f}^{″}(x_0)=f^{″}(x_1),f^{″}(x_N)=f^{″}(x_{N-1})\\ \text{PERIODIC}:\hspace{0.17em}{f}^{″}(x_0)=f^{″}(x_{N-1}),f^{″}(x_N)=f^{″}(x_1)\\ \text{CANTILEVER}:\hspace{0.17em}{f}^{″}(x_0)=\lambda f^{″}(x_1),f^{″}(x_N)=\lambda f^{″}(x_{N-1}),0\le \hspace{0.17em}\lambda \hspace{0.17em}\le \hspace{0.17em}1\end{array}$$

   $\lambda$ =0.0 implies NATURAL (or free) end conditions and $\lambda$ =1.0 implies PARABOLIC end conditions.

2. The MBPTDCV element is not supported by the Force Imbalance method of static equilibrium.
3. In most cases, the interpolation produces a smooth curve but in some cases, it produces a curve that wiggles too much. In those cases, the UTENSION and VTENSION parameters may be specified to smooth out the wiggles in the curve. A value of unity is a good first guess. After that, higher values may be tried, if necessary.
4. The deformable surface itself does not possess any inherent inertia, stiffness or damping properties. You must include other modeling elements to capture those effects. For example, use a deformable surface in conjunction with a flexible body to simulate contact with a rigid body.