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member.py
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import numpy as np
class Member:
def __init__(self, member_index, node_i, node_j, shape, dimensions, e_module, yield_strength):
"""constructor of member
Args:
member_index (int): to track the index so as to build whole system equation
node_i (Node): the node who the member is connected with
node_j (Node): the node who the member is connected with
shape (string): cross-section shape of the member
dimensions (list): the parameters to describe the shape
e_module (float): young's modulus
yield_strength (float): yield stress
"""
self.member_index = member_index
self._e_module = e_module
self._yield_strength = yield_strength
self.shape = shape
self._dimensions = dimensions
self.node_i = node_i
self.node_j = node_j
self._length = np.linalg.norm(np.array([node_i.x-node_j.x, node_i.y-node_j.y]))
self._angle = np.arctan2(node_j.y-node_i.y, node_j.x-node_i.x)
self.external_force = None
self.failure = None
def getAngle(self, analysed_joint):
"""compute the bar orientation centered on analysed joint
Raises:
ValueError: wrong connected node
Returns:
angle: relative angle of the member w.r.t analysed joint
"""
if analysed_joint == self.node_i.node_index:
self._angle = np.arctan2(self.node_j.y-self.node_i.y, self.node_j.x-self.node_i.x)
elif analysed_joint == self.node_j.node_index:
self._angle = np.arctan2(self.node_i.y-self.node_j.y, self.node_i.x-self.node_j.x)
else:
raise ValueError('the member does not connect to', analysed_joint)
return self._angle
def fail(self):
"""check if the member fails either because of buckling or yielding
Returns:
failure: if the member fails
"""
# compression
if self.external_force < 0:
# check if buckling
self.critical_force = pow(np.pi, 2)*self._e_module*min(self.inertia_xx, self.inertia_yy)/pow(self._length, 2)
if abs(self.external_force) > self.critical_force:
self.buckling = True
self.failure = True
return self.failure
else:
self.failure = False
return False
elif self.external_force > 0:
# check if yielding because the member is subject to tension force
self.critical_force = self._yield_strength*self.area
if abs(self.external_force) > self.critical_force:
self.yielding = True
self.failure = True
return self.failure
else:
self.failure = False
return False
else:
# no external force
self.buckling = False
self.yielding = False
return self.failure
def getI(self):
"""compute second moment of inertia
"""
pass
def getA(self):
"""compute the cross-sectional area
"""
pass
class CShapedMember(Member):
def __init__(self, member_index, node_i, node_j, shape, dimensions, e_module, yield_strength):
super().__init__(member_index, node_i, node_j, shape, dimensions, e_module, yield_strength)
self.B = self._dimensions[0]
self.H = self._dimensions[1]
self.h = self._dimensions[2]
self.b = self.h
self.centroid_x = (2*self.h*pow(self.B, 2)/2+pow(self.b, 2)*self.H/2)/self.getA()
self.getI()
self.getA()
def getI(self):
self.inertia_yy = pow(self.H, 3)*self.b/12+self.b*self.H*pow(self.centroid_x-self.b/2, 2)+2*pow(self.B, 3)*self.h/12+2*self.B*self.h*pow(self.centroid_x-self.B/2, 2)
self.inertia_xx = pow(self.H, 3)*self.b/12+2*(pow(self.h, 3)*self.B/12+self.h*self.B*pow(self.h+self.H, 2)/4)
return [self.inertia_xx, self.inertia_yy]
def getA(self):
self.area = self.H*self.b+ 2*self.B*self.h
return self.area
class TShapedMember(Member):
def __init__(self, member_index, node_i, node_j, shape, dimensions, e_module, yield_strength):
super().__init__(member_index, node_i, node_j, shape, dimensions, e_module, yield_strength)
self.B = self._dimensions[0]
self.H = self._dimensions[1]
self.h = self._dimensions[2]
self.b = self._dimensions[2]
self.centroid_x = self.B/2
self.centroid_y = ((self.H+self.h/2)*self.h*self.B+pow(self.H, 2)*self.b/2)/self.getA()
self.getI()
self.getA()
def getI(self):
self.inertia_xx = self.b*self.H*pow(self.centroid_y-self.H/2, 2)+self.h*pow(self.H, 3)/12+self.h*self.B*pow(self.H+self.h/2-self.centroid_y, 2)+pow(self.h, 3)*self.B/12
self.inertia_yy = pow(self.b, 3)*self.H/12+pow(self.B, 3)*self.h/12
return [self.inertia_xx, self.inertia_yy]
def getA(self):
self.area = self.B*self.h + self.H*self.b
return self.area
class IShapedMember(Member):
def __init__(self, member_index, node_i, node_j, shape, dimensions, e_module, yield_strength):
super().__init__(member_index, node_i, node_j, shape, dimensions, e_module, yield_strength)
self.B = self._dimensions[0]
self.H = self._dimensions[1]
self.h = self._dimensions[2]
self.b = self.h
self.getI()
self.getA()
def getI(self):
self.inertia_xx = pow(self.H, 3)*self.b/12+2*(pow(self.h, 3)*self.B/12+self.h*self.B*pow(self.H+self.h, 2)/4)
self.inertia_yy = pow(self.b, 3)*self.H/12 + 2*(pow(self.B, 3)*self.h/12)
return [self.inertia_xx, self.inertia_yy]
def getA(self):
self.area = self.H*self.b + 2*self.B*self.h
return self.area
class OShapedMember(Member):
def __init__(self, member_index, node_i, node_j, shape, dimensions, e_module, yield_strength):
super().__init__(member_index, node_i, node_j, shape, dimensions, e_module, yield_strength)
self.d = self._dimensions[0]
self.d1 = self.d - self._dimensions[1]
self.getI()
self.getA()
def getI(self):
self.inertia_xx = np.pi/64*(pow(self.d, 4)-pow(self.d1, 4))
self.inertia_yy = self.inertia_xx
return [self.inertia_xx, self.inertia_yy]
def getA(self):
self.area = pow(self.d/2, 2)*np.pi-pow(self.d1/2, 2)*np.pi
return self.area