tmdsimpy.nlforces.NonlinearForce

class tmdsimpy.nlforces.NonlinearForce(Q, T)

Bases: object

Template class for nonlinear forces.

This class does not actually implement any nonlinear force.

Parameters:

Q(Nnl, N) numpy.ndarray

Matrix tranform from the N degrees of freedom (DOFs) of the system to the Nnl local nonlinear DOFs.

T(N, Nnl) numpy.ndarray

Matrix tranform from the local Nnl forces to the N global DOFs.

__init__(Q, T)

Methods

__init__(Q, T)
aft(U, w, h[, Nt, tol, calc_grad])	Implementation of the alternating frequency-time method to extract harmonic nonlinear force coefficients
force(X)	Template force function for evaluating the nonlinear force for a set of global displacements.
nl_force_type()	Method to return a flag for the force type.

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

Implementation of the alternating frequency-time method to extract harmonic nonlinear force coefficients

Parameters:

U(N*Nhc,) numpy.ndarray

displacement harmonic DOFs

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

Tolerance on convergence of force at start and end of AFT. Most cases ignore this tolerance, but it is included to ensure a compatible interface. The default is 1e-7.

calc_gradboolean, optional

Flag for if to calculate the gradients and return them. Fnl should always be returned as the first entry of a tuple regardless of if other returned values are calculated. Flag is ignored in many cases, but in others can significantly decrease computation time. 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

force(X)

Template force function for evaluating the nonlinear force for a set of global displacements.

Parameters:

X(N,) numpy.ndarray

Global displacements

Returns:

F(N,) numpy.ndarray

Global forces

dFdX(N,N) numpy.ndarray

Derivative of global forces with respect to global displacements X

nl_force_type()

Method to return a flag for the force type.

Returns:

int

Value indicates the force type. 0 == Instantaneous Force Type. 1 == Hysteretic Force Type.