Generating and saving fiber positions (class DiscretizedFiber)

class DiscretizedFiber.DiscretizedFiber(Discretization, Xs=None, XMP=None)

Object that stores the points and forces for each fiber. That is \(X\), \(\tau\), and \(X_{mp}\) are the only things stored here, as well as the discretization of the fiber.

__init__(Discretization, Xs=None, XMP=None)

Constructor.

Parameters:

  • Discretization (FibCollocationDiscretization object) – Stores all the Chebyshev information,

  • Xs (array, optional) – \(N \times 3\) array of tangent vectors. Only set if you want to instantiate a specific fiber

  • XMP (array) – \(3 \times 1\) array with the fiber midpoint. Only set if you want to instantiate a specific fiber.

initFib(Lengths, Xs=None, XMP=None)

Initialize a straight fiber with constant tangent vector. This method uses the method of Archimedes to sample uniformly on the unit sphere. The steps are

  1. Set \(u=1-2r_1\), where \(r_1 \sim U(0,1)\)

  2. Set \(v=\sqrt{1-u^2}\)

  3. Set \(w=2 \pi r_2\), where \(r_2 \sim U(0,1)\)

  4. Set \(\tau=\left(v\cos{w}, v \sin{w}, u\right)\), which is the tangent vector we use for the straight fiber.

In addition, we also compute a random midpoint for the fiber, setting \(X_{mp}=\left(r_x L_x, r_y L_y, r_z L_z\right)\), where \(r_x\), \(r_y\), and \(r_z\) are all random draws from \(U(0,1)\).

Parameters:

  • Lengths (3-array) – The length of the periodic domain in each direction, \(\left(L_x, L_y, L_z\right)\)

  • Xs (array, optional) – \(N \times 3\) array of tangent vectors. Only set if you want to instantiate a specific fiber

  • XMP (array) – \(3 \times 1\) array with the fiber midpoint. Only set if you want to instantiate a specific fiber.

passXsandX(Xs, XMP)

Update X and Xs just by passing in the configurations

Parameters:

  • Xs (array, optional) – \(N \times 3\) array of tangent vectors. Only set if you want to instantiate a specific fiber

  • XMP (array) – \(3 \times 1\) array with the fiber midpoint. Only set if you want to instantiate a specific fiber.

getPositions()

Get the position and tangent vector as reshaped N x 3 arrays.

Returns:

Three arrays: the first is the \(N_x \times 3\) array of the fiber positions. The second is the \(N \times 3\) array of the fiber tangent vectors. The last is the \(3 \times 1\) array of the fiber midpoint.

Return type:

(array, array,array)