Functions
def	analytical_contact_pressures (sigma, alpha, n, A, R, t, p_int, p_ext)

def	critical_curvature (slenderobject, contact_pressure, frictionfactors=np.array([5, 5, 5]))

def	local_bending (thickness, width, alpha, theta, phi, e, r, type, bend_model="Savik")

def	tension_stress_history (t_eff, p_int, p_ext, alpha, R, thick, A, E, n)

def	bending_stress_history (slenderobject, curvhist, ntheta=16, nphi=16, bend_model="Savik")

def	stick_stress (model, curv, critcurv, theta=None)

def	fric_stress (curv, eps_mat, sig_mat, midpoint)

def	max_stickstress (model, critcurv)

Detailed Description

Copyright (C) 2016 Joakim A. Taby

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.

Function Documentation

def coefficients.analytical_contact_pressures	(	sigma,
		alpha,
		n,
		A,
		R,
		t,
		p_int,
		p_ext
	)

Finding contact pressure from pressure differencial between layers. Using B1.23 from handbook, assuming
sliding occurs along midpoint between layers.

Definition at line 17 of file coefficients.py.

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def coefficients.bending_stress_history	(	slenderobject,
		curvhist,
		ntheta = `16`,
		nphi = `16`,
		bend_model = `"Savik"`
	)

Calculates the stress history from time histories of curvatures and axial stress coefficient
:param bend_model: Which bend model to apply. Savik or Tan implemented
:param nphi: Number of points around tendon to perform calculation. 4 is used of rectangular
             tendon given.
:param ntheta: number of points around the cross section to perform calculation
:param slenderobject, instande of the Slender class
:param curvhist: numpy array containg each curvature time series as a column vector
:return: stress history for each point on defined in bendcoeff

Definition at line 209 of file coefficients.py.

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def coefficients.critical_curvature	(	slenderobject,
		contact_pressure,
		frictionfactors = `np.array([5, 5, 5])`
	)

Finding the critical curvature. Need to find where this is taken from.
:param frictionfactors: friction factors between layer and the layer inside
:param contact_pressure: contact line load. A matrix [2,nlayers] for outside and inside of layer
                      respectively
:param slenderobject: Object of slender type from the sledner class of slenders

Definition at line 72 of file coefficients.py.

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def coefficients.fric_stress	(	curv,
		eps_mat,
		sig_mat,
		midpoint
	)

2D elastoplastic materialmodel with kinematic hardening
:param midpoint: the midpoint of the yield surface at simulation start
:param sig_mat: the stress at yield
:param eps_mat: the strain at yield
:param curv: curvature history 2xN
:return: Frictional stress

Definition at line 289 of file coefficients.py.

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def coefficients.local_bending	(	thickness,
		width,
		alpha,
		theta,
		phi,
		e,
		r,
		type,
		bend_model = `"Savik"`
	)

Calculating the local bending coefficients
Equations from 'On stresses and fatigue in flexible pipes' by Savik 1992 and
'Validity and limitation of analytical models for the bending stress of a helical
wire in unbonded flexible pipes' Tang et.al. 2015

:param bend_model: Which bend model to apply. Savik or Tan implemented
:param e: Youngs modulus. One for each layer
:param geometry of the tendon. one item means circular, two means rectangular
:param alpha: lay_angle of slender structure, list
:param theta: position around the crossection for calculation, numpy vector
:param phi: local position for calculation of coefficient, numpy vector
:return:list of numpy arrays defining the coefficients for each layer

Definition at line 129 of file coefficients.py.

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def coefficients.max_stickstress	(	model,
		critcurv
	)

Definition at line 332 of file coefficients.py.

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def coefficients.stick_stress	(	model,
		curv,
		critcurv,
		theta = `None`
	)

Calculating the stick stress at position theta on the crossection, limited by the critical curvature.
Equations from 'Bending Behavior of Helically Wrapped Cables' Hong et.al. 2005
:param theta: Position around cross section range [0 2*pi]
:param critcurv: Critical curvature. Curvature at which slip initiates for each layer
:param curv: Curvature history Dim: 2xN
:param model: Slender object as defined in slenders.Slender

Definition at line 245 of file coefficients.py.

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def coefficients.tension_stress_history	(	t_eff,
		p_int,
		p_ext,
		alpha,
		R,
		thick,
		A,
		E,
		n
	)

Solving for axial stress accorind got Handbook B1.10, B1.23 and B1.13

:param t_eff: history of effective tension
:param p_int: history of internal pressure
:param p_ext: history of external pressure
:param alpha: lay angles of the layers
:param R: radiuses of the layers
:param thick: thickness of the layers
:param A: Area of the tendons
:param E: young's modulus of the tendons
:param n: number of tendons in each layer
:return: numpy array with tension stress histories

Definition at line 171 of file coefficients.py.

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Functions

Detailed Description

Function Documentation