def getTangentStiffness ( self, elemdat ):
#Compute the current state vector
a = toElementCoordinates( elemdat.state , elemdat.coords )
Da = toElementCoordinates( elemdat.Dstate , elemdat.coords )
#Compute the elongation of the spring
elong = a[2]-a[0]
#Compute the force in the spring
Fs = elong * elemdat.props.k
#Compute the element internal force vector in the element coordinate system
elFint = array([-Fs,0.,Fs,0])
#Determine the element tangent stiffness in the element coordinate system
elKbar = zeros( (4,4) )
elKbar[:2,:2] = elemdat.props.k*eye(2)
elKbar[:2,2:] = -elemdat.props.k*eye(2)
elKbar[2:,:2] = elKbar[:2,2:]
elKbar[2:,2:] = elKbar[:2,:2]
#Rotate element tangent stiffness to the global coordinate system
elemdat.stiff = toGlobalCoordinates( elKbar, elemdat.coords )
elemdat.fint = toGlobalCoordinates( elFint, elemdat.coords )
def getInternalForce ( self, elemdat ):
#Compute the current state vector
a = toElementCoordinates( elemdat.state , elemdat.coords )
Da = toElementCoordinates( elemdat.Dstate, elemdat.coords )
a0 = a - Da
#Compute l0 and strains
self.l0 = norm( elemdat.coords[1]-elemdat.coords[0] )
( epsilon , Depsilon ) = self.getStrain( a , a0 )
#Compute the stress increment (multiplied
#with the undeformed cross-sectional area)
Dsigma = elemdat.props.E * Depsilon
#Compute the current stress (multiplied
#with the undeformed cross-sectional area)
sigma = self.getHistoryParameter('sigma') + Dsigma
#Update the history parameter
self.setHistoryParameter( 'sigma', sigma )
#Compute BL in the parent element coordinate system
BL = self.getBL( a )
#Compute the element internal force vector in the element coordinate system
elFint = self.l0 * sigma * elemdat.props.Area * BL
#Rotate element fint to the global coordinate system
elemdat.fint = toGlobalCoordinates( elFint, elemdat.coords )
def getInternalForce(self, elemdat):
#Compute the current state vector
a = toElementCoordinates(elemdat.state, elemdat.coords)
Da = toElementCoordinates(elemdat.Dstate, elemdat.coords)
a0 = a - Da
#Compute l0 and strains
self.l0 = norm(elemdat.coords[1] - elemdat.coords[0])
(epsilon, Depsilon) = self.getStrain(a, a0)
#Compute the stress increment (multiplied
#with the undeformed cross-sectional area)
Dsigma = elemdat.props.E * Depsilon
#Compute the current stress (multiplied
#with the undeformed cross-sectional area)
sigma = self.getHistoryParameter('sigma') + Dsigma
#Update the history parameter
self.setHistoryParameter('sigma', sigma)
#Compute BL in the parent element coordinate system
BL = self.getBL(a)
#Compute the element internal force vector in the element coordinate system
elFint = self.l0 * sigma * elemdat.props.Area * BL
#Rotate element fint to the global coordinate system
elemdat.fint = toGlobalCoordinates(elFint, elemdat.coords)
def getTangentStiffness(self, elemdat):
#Compute the current state vector
a = toElementCoordinates(elemdat.state, elemdat.coords)
Da = toElementCoordinates(elemdat.Dstate, elemdat.coords)
#Compute the elongation of the spring
elong = a[2] - a[0]
#Compute the force in the spring
Fs = elong * elemdat.props.k
#Compute the element internal force vector in the element coordinate system
elFint = array([-Fs, 0., Fs, 0])
#Determine the element tangent stiffness in the element coordinate system
elKbar = zeros((4, 4))
elKbar[:2, :2] = elemdat.props.k * eye(2)
elKbar[:2, 2:] = -elemdat.props.k * eye(2)
elKbar[2:, :2] = elKbar[:2, 2:]
elKbar[2:, 2:] = elKbar[:2, :2]
#Rotate element tangent stiffness to the global coordinate system
elemdat.stiff = toGlobalCoordinates(elKbar, elemdat.coords)
elemdat.fint = toGlobalCoordinates(elFint, elemdat.coords)
def getInternalForce ( self, elemdat ):
#Compute the current state vector
a = toElementCoordinates( elemdat.state , elemdat.coords )
Da = toElementCoordinates( elemdat.Dstate , elemdat.coords )
#Compute the elongation of the spring
elong = a[2]-a[0]
#Compute the force in the spring
Fs = elong * elemdat.props.k
#Compute the element internal force vector in the element coordinate system
elFint = array([-Fs,0.,Fs,0])
#Rotate element fint to the global coordinate system
elemdat.fint = toGlobalCoordinates( elFint, elemdat.coords )
def getInternalForce(self, elemdat):
#Compute the current state vector
a = toElementCoordinates(elemdat.state, elemdat.coords)
Da = toElementCoordinates(elemdat.Dstate, elemdat.coords)
#Compute the elongation of the spring
elong = a[2] - a[0]
#Compute the force in the spring
Fs = elong * elemdat.props.k
#Compute the element internal force vector in the element coordinate system
elFint = array([-Fs, 0., Fs, 0])
#Rotate element fint to the global coordinate system
elemdat.fint = toGlobalCoordinates(elFint, elemdat.coords)