KinematicConditions package

Module KinematicConditions

This module contains all the kinematics conditions type that are provided by pyHarm. The module is organized around an abstract class ABCKinematic and a FactoryKinematic that is in charge of creating the objects. All kinematic conditions object must comply with the ABCKinematic abstract class. The section below presents the different classes that are available in this module.

ABCKinematic

The ABCKinematic class is an abstract class defining the essential components of any kinematic conditions. Three abstract methods are defined :

Methods	Use
complete_x	Abstract method : From the input of displacement vector x given, provides a vector of same size that completes the displacement vector using the kinematic conditions
complete_R	Abstract method : From the input of residual vector R given, provides a vector of same size that completes the residual vector using the kinematic conditions
complete_J	Abstract method : From the input of the jacobians dRdx & dRdom given, provides jacobians of same size that completes the jacobians vector using the kinematic conditions

Examples of creating an ABCKinematic and adding it into an input dictionary:

To be created, an ABCKinematic subclass needs its abstract methods to be defined :

class FakeKine(ABCKinematic): # inherits from abstract class
    factory_keyword="fakekine" # madatory to define
    def complete_x(self, x) :
        xadd = ... # code that completes x_add array
        return xadd
    def complete_R(self, R, x):
        R_add = ... # code that completes R_add
        return R_add
    def complete_J(self, Jx, Jom, x):
        Jx_add = ... # code that completes Jx_add
        Jom_add = ... # code that completes Jom_add
        return Jx_add, Jom_add


INP = {
    ...,
    "kinematics":{
        "fake_kine_cond":{
            "type":"fakekine",
            "connect":{
                "sub1":[...],
                "sub2":[...]
            },
            "dirs":[...],
            ...,
        }
    },
    ...,
}

FactoryKinematic

This file contains the dictionary of all the kinematics conditions that are available as well as the function generateKinematic that creates the kinematic condition object based on the type of solver desired.

General Order Displacement (GODisplacement) GOdisplacement

This kinematic condition imposes a displacement on a given dof such that :

\[\displaystyle x = \frac{amp}{\omega^{dto}} \cdot l\]

where \(l\) is the unit loading vector containing the ho and phi information.

Parameter	Use	Default
amp	Amplitude of the imposed displacement [float]	✗
ho	Harmonic on which the imposed displacement is made [int]	✓ : 1
dto	Derivative order on the dof [int]	✓ : 0
phi	Phase value [dict]	✓ : 0

AccelImposed AccelImposed

Subclass of GODisplacement with dto=2 such that acceleration is imposed to a given dof.

SpeedImposed SpeedImposed

Subclass of GODisplacement with dto=1 such that speed is imposed to a given dof.

DispImposed DispImposed

Subclass of GODisplacement with dto=0 such that displacement is imposed to a given dof.

Base projection BaseProjection

This kinematic condition imposes a base projection between a master substructure and a slave substructure through a transformation matrix. The residual of the slave substructure is projected back onto the master substructure.

\[\begin{split}\begin{aligned} \displaystyle x_{slave} & = \phi \cdot x_{master} \\ R_{master} & = \phi^{t} \cdot R_{slave}(x_{slave})\end{aligned}\end{split}\]

Parameter	Use	Default
phi	transformation matrix from master to slave [np.ndarray]	✗

References

[1] E. Allgower and K. Georg, *Numerical Continuation Methods – An Introduction. Soc. Ind Appl Math. 2003.

API links

pyHarm.KinematicConditions