GVSBody¶

This abstract class represents a slender soft body modeled under the Geometric Variable Strain (GVS) approach of [2]. The class implements all the methods required by a Body. Concrete subclasses must define a strain basis $\boldsymbol{\Phi}(\boldsymbol{q}, s) \in \mathbb{R}^{6 \times n}$ such that

$\boldsymbol{\xi}(\boldsymbol{q}, s) = \boldsymbol{\Phi}(\boldsymbol{q}, s)\boldsymbol{q} + \boldsymbol{\xi}_{0}$

where $\boldsymbol{\xi} \in \mathbb{R}^{6 \times 1}$ is the strain, being $\boldsymbol{\xi}_{0}$ its stress-free value, $\boldsymbol{q} \in \mathbb{R}^{n}$ the vector of configuration variables and $s \in [0, L_{0}]$ the curvilinear abscissa, with $L_{0}$ the body rest length.

See PCC2D or PCC3D for how the strain basis can be implemented.

class GVSBody¶

Bases: Body

Abstract class modeling a 1D continuum under the Geometric Variable Strain (GVS) approach. The internal interaction forces are modeled using a linear visco-elastic law.

Constructor Summary

GVSBody(n, Parameters)¶

Construct a GVS body.

Parameters:

n (double) – Number of DoF of the body
Parameters ([double], [sym]) – Parameters of the body, specified as $L_{0}, R_{\mathrm{base}}, R_{\mathrm{tip}}, \rho, E, \nu, \eta$ and $N_{\mathrm{Gauss}}$

Property Summary

Parameters¶: Vector collecting the parameters of the GVS Body as $\mathrm{Parameters} = \left( L_{0} \,\, R_{\mathrm{base}} \,\, R_{\mathrm{tip}} \,\, \rho \,\, E \,\, \nu \,\, \eta \,\, N_{\mathrm{Gauss}} \right)^{T} \in \mathbb{R}^{8 \times 1}$ , where $L_{0}, R_{\mathrm{base}}$ and $R_{\mathrm{tip}}$ denote the body rest length, the base and tip radius, $\rho$ is the mass density, $E$ the Young modulus, $\nu$ the Poisson ratio, $\eta$ the material damping coefficient, and $N_{\mathrm{Gauss}}$ represents the number of Gaussian points used for the computation of the kinematics and the integrals.

Method Summary

Update(q, dq, ddq, options)¶: Arguments definition

xi(q, s)¶: Output preallocation