PGC3D¶

This class represents a slender soft body under the Piecewise Gaussian Curvature (PGC) hypothesis with elongation. The strain is modeled as

$\boldsymbol{\xi}(\boldsymbol{q}, s) = \boldsymbol{\Phi}(s)\boldsymbol{q} + \boldsymbol{\xi}_{0} = \frac{1}{L_0} \left(\begin{array}{ccccc} 0 & 0 & -1 & -e^{-(s_{i}-L_{0_{i}}/2)^2} & 0 \\ 1 & e^{-(s_{i}-L_{0_{i}}/2)^2} & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 \end{array}\right)\boldsymbol{q} + \left(\begin{array}{c} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \end{array}\right),$

where $\boldsymbol{q} \in \mathbb{R}^{5 \times 1}$ is the vector of configuration variables and $s \in [0, L_{0}]$ the curvilinear abscissa, with $L_{0}$ the body rest length.

The class is used in Simulation 2 of [1].

class PGC3D¶

Bases: GVSBody

Class modeling a 3D piecewise Gaussian curvature (PGC) body with elongation.

Constructor Summary

PGC3D(Parameters)¶

Construct a 3D PGC body with elongation.

Parameters:: Parameters ([double], [sym]) – Parameters of the body, specified as for GVSBody