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3SPlates.1.0.py
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3SPlates.1.0.py
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import numpy as np
import json
# This code was made by ESAU IDROVO (ESPOL -Ecuador)
def mngen (parity, terms):
numbers=[]
if parity == "even":
for i in range(2,2*terms,2):
numbers.append(i)
elif parity == "odd":
for i in range(1,2*terms,2):
numbers.append(i)
elif parity == "none":
for i in range(1,terms+1):
numbers.append(i)
else:
return(None)
mn=np.array(np.meshgrid(numbers, numbers)).T.reshape(-1, 2)
#Return an array with 2 columns with a combination of all m and n terms
return(mn)
def platecoords(lenghtx, lenghty, subdititions):
x =np.linspace(0, lenghtx, subdititions+1)
y =np.linspace(0, lenghty, subdititions+1)
xx, yy = np.meshgrid(x, y)
coordinates = np.column_stack((xx.ravel(), yy.ravel()))
return (coordinates)
# LOAD DISTRIBUTION #
def load_dist (p, mnterms, platecoords, lenghtx, lenghty):
pxy= np.zeros( np.shape(platecoords)[0])
for xy in enumerate(platecoords):
for mn in mnterms:
Pmn = 16*p/(mn[0]*mn[1]*np.pi**2)
pxy[xy[0]]+= Pmn * np.sin(mn[0]*np.pi*xy[1][0]/lenghtx)* np.sin(mn[1]*np.pi*xy[1][1]/lenghty)
pxy=np.column_stack((platecoords,pxy))
#Return an array with 3 columns [x, y, p]
return(pxy)
def load_point(F, mnterms, platecoords, lenghtx, lenghty,posx,posy):
pxy= np.zeros(np.shape(platecoords)[0])
for xy in enumerate(platecoords):
for mn in mnterms:
Pmn =(4*F/(lenghtx*lenghty))*(np.sin(mn[0]*np.pi*posx/lenghtx))*(np.sin(mn[1]*np.pi*posy/lenghty))
pxy[xy[0]]+= Pmn* np.sin(mn[0]*np.pi*xy[1][0]/lenghtx)* np.sin(mn[1]*np.pi*xy[1][1]/lenghty)
pxy=np.column_stack((platecoords,pxy))
return(pxy)
#DEFLECTION
def deflect_dist (p, mnterms, platecoords, lenghtx, lenghty):
wxy= np.zeros(np.shape(platecoords)[0])
for xy in enumerate(platecoords):
for mn in mnterms:
Pmn=16*p/(mn[0]*mn[1]*np.pi**2)
Wmn = Pmn / (D * np.pi**4 * ((mn[0]/lenghtx)**2+(mn[1]/lenghty)**2)**2)
wxy[xy[0]] += Wmn * np.sin(mn[0]*np.pi*xy[1][0]/lenghtx)* np.sin(mn[1]*np.pi*xy[1][1]/lenghty)
wxy=np.column_stack((platecoords,wxy))
#Return an array with 3 columns [x, y, w]
return(wxy)
def deflect_point (F, mnterms, platecoords, lenghtx, lenghty,posx,posy):
wxy= np.zeros(np.shape(platecoords)[0])
for xy in enumerate(platecoords):
for mn in mnterms:
Pmn =(4*F/(lenghtx*lenghty))*(np.sin(mn[0]*np.pi*posx/lenghtx))*(np.sin(mn[1]*np.pi*posy/lenghty))
Wmn = Pmn / (D * np.pi**4 * ((mn[0]/lenghtx)**2+(mn[1]/lenghty)**2)**2)
wxy[xy[0]]+= Wmn* np.sin(mn[0]*np.pi*xy[1][0]/lenghtx)* np.sin(mn[1]*np.pi*xy[1][1]/lenghty)
wxy=np.column_stack((platecoords,wxy))
#Return an array with 3 columns [x, y, w]
return(wxy)
#Moments
#dist
def momentx_dist(p, mnterms, platecoords, lenghtx, lenghty):
Mx= np.zeros(np.shape(platecoords)[0])
for xy in enumerate(platecoords):
for mn in mnterms:
Pmn=16*p/(mn[0]*mn[1]*np.pi**2)
Wmn = Pmn / (D * np.pi**4 * ((mn[0]/lenghtx)**2+(mn[1]/lenghty)**2)**2)
Mx[xy[0]]+= Wmn * ((mn[0]*np.pi**2/lenghtx)+pois*(mn[1]*np.pi/lenghty)**2) * np.sin(mn[0]*np.pi*xy[1][0]/lenghtx)* np.sin(mn[1]*np.pi*xy[1][1]/lenghty)
Mx = D * Mx
Mx=np.column_stack((platecoords,Mx))
#Return an array with 3 columns [x, y, Mx]
return(Mx)
def momenty_dist(p, mnterms, platecoords, lenghtx, lenghty):
My= np.zeros(np.shape(platecoords)[0])
for xy in enumerate(platecoords):
for mn in mnterms:
Pmn=16*p/(mn[0]*mn[1]*np.pi**2)
Wmn = Pmn / (D * np.pi**4 * ((mn[0]/lenghtx)**2+(mn[1]/lenghty)**2)**2)
My[xy[0]]+= Wmn * ((mn[1]*np.pi**2/lenghtx)+pois*(mn[0]*np.pi/lenghty)**2) * np.sin(mn[0]*np.pi*xy[1][0]/lenghtx)* np.sin(mn[1]*np.pi*xy[1][1]/lenghty)
My = D * My
My=np.column_stack((platecoords,My))
#Returns an array with 3 columns [x, y, My]
return(My)
#point
def momentx_point(F, mnterms, platecoords, lenghtx, lenghty,posx,posy):
Mx= np.zeros(np.shape(platecoords)[0])
for xy in enumerate(platecoords):
for mn in mnterms:
Pmn=(4*F/(lenghtx*lenghty))*(np.sin(mn[0]*np.pi*posx/lenghtx))*(np.sin(mn[1]*np.pi*posy/lenghty))
Wmn = Pmn / (D * np.pi**4 * ((mn[0]/lenghtx)**2+(mn[1]/lenghty)**2)**2)
Mx[xy[0]]+= Wmn * ((mn[0]*np.pi**2/lenghtx)+pois*(mn[1]*np.pi/lenghty)**2) * np.sin(mn[0]*np.pi*xy[1][0]/lenghtx)* np.sin(mn[1]*np.pi*xy[1][1]/lenghty)
Mx = D * Mx
Mx=np.column_stack((platecoords,Mx))
#Returns an array with 3 columns [x, y, Mx]
return(Mx)
def momenty_point(F, mnterms, platecoords, lenghtx, lenghty,posx,posy):
My= np.zeros(np.shape(platecoords)[0])
for xy in enumerate(platecoords):
for mn in mnterms:
Pmn=(4*F/(lenghtx*lenghty))*(np.sin(mn[0]*np.pi*posx/lenghtx))*(np.sin(mn[1]*np.pi*posy/lenghty))
Wmn = Pmn / (D * np.pi**4 * ((mn[0]/lenghtx)**2+(mn[1]/lenghty)**2)**2)
My[xy[0]]+= Wmn * ((mn[1]*np.pi**2/lenghtx)+pois*(mn[0]*np.pi/lenghty)**2) * np.sin(mn[0]*np.pi*xy[1][0]/lenghtx)* np.sin(mn[1]*np.pi*xy[1][1]/lenghty)
My = D * My
My=np.column_stack((platecoords,My))
#Returns an array with 3 columns [x, y, My]
return(My)
#Normal stresses
def normalstresx(factor, momentx):
sigmax = np.copy(momentx)
sigmax[:,2] *= factor
#Return an array with 3 columns [x, y, sigmax]
return(sigmax)
def normalstresy(factor, momenty):
sigmay = np.copy(momenty)
sigmay[:,2] *= factor
#Return an array with 3 columns [x, y, sigmay]
return(sigmay)
# IMPORT DATA
data = json.load(open('plate.json'))
E = data["E"]
Yield = data["yield"]
pois = data["pois"]
lenghtx = data ["lenghtx"]
lenghty = data ["lenghty"]
thickness = data ["thickness"]
z=data ["z"]
F = data["F"]
XF = data["XF"]
YF = data["YF"]
resolution = data["Resolution"]
parity = data["parity"]
terms = data["terms"]
typeofforce= data["type"]
#Flexural Rigidity
D = E*thickness**3/(12*(1-pois**2))
#Factor for normal stress
factor= 12*z/thickness**3
mn=mngen(parity, terms)
coords=platecoords(lenghtx,lenghty,resolution)
if typeofforce == "distributed":
load = load_dist(F, mn, coords, lenghtx,lenghty)
deflection= deflect_dist(F, mn, coords,lenghtx, lenghty)
momentx = momentx_dist(F, mn, coords, lenghtx, lenghty)
momenty = momenty_dist(F, mn, coords, lenghtx, lenghty)
sigmax = normalstresx(factor, momentx)
sigmay = normalstresx(factor, momenty)
# With this values you can check if the plate satisfies the allowable values or not making an if or something extra
maxdefl = np.max(np.abs(deflection[:,2]))
maxsigmax = np.max(np.abs(sigmax[:,2]))
maxsigmay = np.max(np.abs(sigmay[:,2]))
## this array contains the results x, y, pxy, mx, my, sigmx, sigmy in this order.
outputarray = np.column_stack((coords,load[:,2], momentx[:,2],momenty[:,2],sigmax[:,2], sigmay[:,2]))
np.savetxt('output.log',
outputarray,
newline='\n',
delimiter=',',
header='''
Output.
EIIS (2023)- ESPOL
https://github.com/eiidrovo/3SPLATES
Max deflection [m] = {}
Max stress in x [N/m2] = {}
Max stress in y [N/m2] = {}
x[m] y[m] P[N/m2] Mx[N] My[N] Sigma x[N/m2] Sigma y [Nm/m2] \n
'''.format(maxdefl, maxsigmax, maxsigmay))
elif typeofforce == "point":
load = load_point(F, mn, coords, lenghtx,lenghty, XF, YF)
deflection= deflect_point(F, mn, coords, lenghtx,lenghty, XF, YF)
momentx = momentx_point(F, mn, coords, lenghtx,lenghty, XF, YF)
momenty = momenty_point(F, mn, coords, lenghtx,lenghty, XF, YF)
sigmax = normalstresx(factor, momentx)
sigmay = normalstresx(factor, momenty)
# With this values you can check if the plate satisfies the allowable values or not making an if or something extra
maxdefl = np.max(np.abs(deflection[:,2]))
maxsigmax = np.max(np.abs(sigmax[:,2]))
maxsigmay = np.max(np.abs(sigmay[:,2]))
## this array contains the results x, y, pxy, mx, my, sigmx, sigmy
outputarray = np.column_stack((coords,load[:,2], momentx[:,2],momenty[:,2],sigmax[:,2], sigmay[:,2]))
np.savetxt('output.log',
outputarray,
newline='\n',
delimiter=',',
header='''
Output.
EIIS (2023)- ESPOL
https://github.com/eiidrovo/3SPLATES
Max deflection [m] = {}
Max stress in x [N/m2] = {}
Max stress in y [N/m2] = {}
x[m] y[m] P[N/m2] Mx[N] My[N] Sigma x[N/m2] Sigma y [Nm/m2] \n
'''.format(maxdefl, maxsigmax, maxsigmay))
else:
print("Cannot being calculated anything, review your spelling in the plate.json file")
exit()