tmdsimpy.jax.nlforces.ElasticDryFriction3D¶

class tmdsimpy.jax.nlforces.ElasticDryFriction3D(Q, T, kt, kn, mu, u0=0, meso_gap=0)¶

Bases: NonlinearForce

3D Elastic Dry Friction (Spring + Coulomb Friction) Model

Parameters:

Q(Nnl, N) numpy.ndarray: Matrix tranform from the N degrees of freedom (DOFs) of the system to the Nnl local nonlinear DOFs. Nnl should be even. Rows 0::3 correspond to local tangential DOFs in X direction. Rows 1::3 correspond to local tangential DOFs in X direction. Rows 2::3 correspond to local normal DOFs.
T(N, Nnl) numpy.ndarray: Matrix tranform from the local Nnl forces to the N global DOFs. Columns 0::3 correspond to local tangential forces in X direction. Columns 1::3 correspond to local tangential forces in Y direction. Columns 2::3 correspond to local normal forces.
ktfloat: Tangential stiffness in X and Y direction
knfloat: Tangential stiffness
mufloat: Friction coefficient
u0float, (Nnl,) numpy.ndarray, or None, optional: If a float, all sliders in AFT are initialized at that displacement and zero force. If a numpy.ndarray, entries 0::3 and 1::3 correspond to the initial slider displacements and zero force for AFT. If None, then the zeroth harmonic displacements are used to initialize the slider position in AFT. Highly recommended not to use u0=None because may result in non-unique solutions. Not fully verified for None option. The default is 0.
meso_gapfloat, optional: Initial gap between contact due to other. This gap is added to quadrature location of contact element The default is 0

See also

set_aft_initialize: Overrides the value of u0.

Notes

Positive normal displacements are in contact and yield positive normal forces. Negative normal displacements are out of contact and yield zero normal force.

Derivatives are calculated with automatic differentiation using JAX. JAX calculates dense derivative matrices, so the calculation may become very inefficient if more than 1 slider is included in the object (i.e., Nnl > 3).

kt, kn, and mu may work for inputs of (Nnl//3,) numpy.ndarrays. However, this is not tested.

__init__(Q, T, kt, kn, mu, u0=0, meso_gap=0)¶

Methods

`__init__`(Q, T, kt, kn, mu[, u0, meso_gap])
`aft`(U, w, h[, Nt, tol, calc_grad])	Implementation of the alternating frequency-time (AFT) method to extract harmonic nonlinear force coefficients.
`force`(X[, update_hist])	Calculate global nonlinear forces for some global displacement vector.
`init_history`()	Method to initialize history variables to zero force and displacement.
`local_force_history`(unlt, unltdot, h, cst, ...)	Evaluate the local forces for steady-state harmonic motion used in AFT.
`nl_force_type`()	Method to identify the force type as hysteretic.
`reset_real_mu`()	Resets friction coefficient to initial value.
`set_aft_initialize`(X)	Set an initial slider position with zero force for AFT calculation.
`set_prestress_mu`()	Sets friction coefficient to zero while saving initial value in a different variable.
`update_history`(unl, fnl)	Updates hysteretic states to be the input displacement and force.

aft(U, w, h, Nt=128, tol=1e-07, calc_grad=True)¶

Implementation of the alternating frequency-time (AFT) method to extract harmonic nonlinear force coefficients.

Parameters:

U(N*Nhc,) numpy.ndarray: Displacement harmonic DOFs (global)
wfloat: Frequency in rad/s. Needed in case there is velocity dependency.
hnumpy.ndarray, sorted: List of harmonics. The list corresponds to Nhc harmonic components.
Ntint power of 2, optional: Number of time steps used in evaluation. The default is 128.
tolfloat, optional: This argument is ignored, and is included for compatability of interface. The default is 1e-7.
calc_gradboolean: Flag where True indicates that the gradients should be calculated and returned. If False, then returns only (Fnl,) as a tuple. The default is True

Returns:

Fnl(N*Nhc,) numpy.ndarray: Nonlinear hamonic force coefficients
dFnldU(N*Nhc,N*Nhc) numpy.ndarray: Jacobian of Fnl with respect to U
dFnldw(N*Nhc,) numpy.ndarray: Jacobian of Fnl with respect to w

Notes

The tolerance tol is ignored because elastic dry friction converges to steady-state with two cycles of the hysteresis loop. Two cycles of the nonlinear forces are calculated automatically without the option to change this setting. A numpy kron operation is utilized to convert forces back to physical domain. This operation may result in many unnecessary calculations that could be eliminated to speed up AFT.

force(X, update_hist=False)¶

Calculate global nonlinear forces for some global displacement vector.

Parameters:

X(N,) numpy.ndarray: Global displacements
update_histbool: Flag to save displacement and force from the evaluation as history variables for subsequent calls to this function.

Returns:

F(N,) numpy.ndarray: Global nonlinear force
dFdX(N,N) numpy.ndarray: Derivative of F with respect to X.

Notes

If update_hist is True, then update_history is called on the local results of this calculation to save the history.

init_history()¶

Method to initialize history variables to zero force and displacement.

Returns:

None.

tmdsimpy.jax.nlforces.ElasticDryFriction3D¶

Table of Contents

Previous topic

Next topic

This Page