SubstructureMatrixElements package

SubstructureMatrixElement package

The SubstructureMatrixElement subpackage gives implementations of ABCElement that allows to input a whole matrix based residual contribution. It affects a whole substructure.

MatrixElement

The MatrixElement class is the abstract class ruling the definition of an element affecting a whole substructure through a given input matrix. This abstract class inherits from ABCElement but implements some of the abstract methods that are responsible for creating the indices of interest as well as reading properly the input dictionary. Some abstract methods remain to be defined in instantiable classes.

Methods	Use
adim	Abstract method for adimensionalising the characteristics of the element
evalResidual	Abstract method for evaluating the residual contribution of the element
evalJacobian	Abstract method for evaluating the jacobian contribution of the element
_generateMatrices	Abstract method builds the necessary matrices from the input data

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

class GyroMatrix(MatrixElement): # inherits from abstract class
    """
    Gyroscopic matrix
    """
    factory_keyword = 'gyromatrix'

    def _generateMatrices(self, data):
        self.kronG = np.kron(np.linalg.matrix_power(self.nabla,1),data["matrix"]["G"])

    def adim(sel,lc,wc):
        self.kronG = self.kronG * lc * (wc**2)
        self.flag_adim = True

    def evalResidual(self,xg,om):
        x = xg[self.indices]
        self.R = (om**2 * self.kronG) @ x
        return self.R

    def evalJacobian(self,xg,om):
        x = xg[self.indices]
        self.J = om**2 * self.kronG
        self.dJdom = (2 * om * self.kronG) @ x
        return self.J, self.dJdom

GyroMatrixData = np.array([...])

INP = {
    ...,
    'substructure':{
        'sub':{...},
        ...,
    },
    'connectors':{
        'gyro':{
            'type':'gyromatrix',
            'connect':'sub',
            'matrix':{'G':GyroMatrixData}
        },
        ...,
    },
    ...,
    'plugin':[GyroMatrix]
}

GeneralOrderMatrixElement GOMatrix

The GeneralOrderMatrixElement is a general linear matrix element application which takes as input information about the time derivative through dto and the power of angular frequency to be applied through dom.

Parameter	Use	Default
matrix	Contains the matrix to be applied	✗
dto	Order of the derivative in time	✗
dom	Order of the power applied to the angular frequency	✓ : dto

LinearHystMatrixElement linear_hysteretic

The LinearHystMatrixElement is derived from GeneralOrderMatrixElement imposing dto to 1 and dom to 0. It allows taking into account linearized hysteretic damping effects.

Parameter	Use	Default
matrix	contains the matrix to be applied	✗

Substructure substructure

The Substructure class is a MatrixElement that creates residual contribution coming from mass, linear damping, gyroscopic and rigidity matrices.

Parameter	Use	Default
matrix	contains the 4 matrices under the keys (M,C,G,K)	✗

It allows implementing useful methods in the form of get_Mass and get_Rigidity in order to extract initial mass and rigidity matrices.

API links

pyHarm.Elements.SubstructureMatrixElements