def testFrustum_shell(self):
# In limit of thickness approaching radius, should recover regular formulas
self.assertEqual(f.frustumShellVol(rb, rb, rb, h, False),
f.frustumVol(rb, rb, h, False))
self.assertEqual(f.frustumShellVol(2 * rt, 2 * rt, rt, h, True),
f.frustumVol(rt, rt, h, False))
self.assertEqual(f.frustumShellCG(rb, rb, rb, h, False),
f.frustumCG(rb, rb, h, False))
self.assertEqual(f.frustumShellCG(2 * rt, 2 * rt, rt, h, True),
f.frustumCG(rt, rt, h, False))
self.assertEqual(f.frustumShellIzz(rb, rb, rb, h, False),
f.frustumIzz(rb, rb, h, False))
self.assertEqual(f.frustumShellIzz(2 * rt, 2 * rt, rt, h, True),
f.frustumIzz(rt, rt, h, False))
self.assertAlmostEqual(f.frustumShellIxx(rb, rb, rb - eps, h, False),
f.frustumIxx(rb, rb, h, False))
self.assertAlmostEqual(
f.frustumShellIxx(2 * rt, 2 * rt, rt - eps, h, True),
f.frustumIxx(rt, rt, h, False))
def compute(self, inputs, outputs):
# Unpack variables for thickness and average radius at each can interface
twall = inputs["t_full"]
Rb = 0.5 * inputs["d_full"][:-1]
Rt = 0.5 * inputs["d_full"][1:]
zz = inputs["z_full"]
H = np.diff(zz)
rho = inputs["rho"]
coeff = inputs["outfitting_factor"]
coeff = coeff + np.where(coeff < 1.0, 1.0, 0.0)
# Total mass of cylinder
V_shell = frustum.frustumShellVol(Rb, Rt, twall, H)
mass = outputs["mass"] = coeff * rho * V_shell
# Center of mass of each can/section
cm_section = zz[:-1] + frustum.frustumShellCG(Rb, Rt, twall, H)
outputs["section_center_of_mass"] = cm_section
# Center of mass of cylinder
V_shell += eps
outputs["center_of_mass"] = np.dot(V_shell, cm_section) / V_shell.sum()
# Moments of inertia
Izz_section = coeff * rho * frustum.frustumShellIzz(Rb, Rt, twall, H)
Ixx_section = Iyy_section = coeff * rho * frustum.frustumShellIxx(Rb, Rt, twall, H)
# Sum up each cylinder section using parallel axis theorem
I_base = np.zeros((3, 3))
for k in range(Izz_section.size):
R = np.array([0.0, 0.0, cm_section[k] - zz[0]])
Icg = util.assembleI([Ixx_section[k], Iyy_section[k], Izz_section[k], 0.0, 0.0, 0.0])
I_base += Icg + mass[k] * (np.dot(R, R) * np.eye(3) - np.outer(R, R))
outputs["I_base"] = util.unassembleI(I_base)
# Compute costs based on "Optimum Design of Steel Structures" by Farkas and Jarmai
# All dimensions for correlations based on mm, not meters.
R_ave = 0.5 * (Rb + Rt)
taper = np.minimum(Rb / Rt, Rt / Rb)
nsec = twall.size
mshell = rho * V_shell
mshell_tot = np.sum(rho * V_shell)
k_m = inputs["material_cost_rate"] # 1.1 # USD / kg carbon steel plate
k_f = inputs["labor_cost_rate"] # 1.0 # USD / min labor
k_p = inputs["painting_cost_rate"] # USD / m^2 painting
k_e = 0.064 # Industrial electricity rate $/kWh https://www.eia.gov/electricity/monthly/epm_table_grapher.php?t=epmt_5_6_a
e_f = 15.9 # Electricity usage kWh/kg for steel
e_fo = 26.9 # Electricity usage kWh/kg for stainless steel
# Cost Step 1) Cutting flat plates for taper using plasma cutter
cutLengths = 2.0 * np.sqrt((Rt - Rb) ** 2.0 + H ** 2.0) # Factor of 2 for both sides
# Cost Step 2) Rolling plates
# Cost Step 3) Welding rolled plates into shells (set difficulty factor based on tapering with logistic function)
theta_F = 4.0 - 3.0 / (1 + np.exp(-5.0 * (taper - 0.75)))
# Cost Step 4) Circumferential welds to join cans together
theta_A = 2.0
# Labor-based expenses
K_f = k_f * (
manufacture.steel_cutting_plasma_time(cutLengths, twall)
+ manufacture.steel_rolling_time(theta_F, R_ave, twall)
+ manufacture.steel_butt_welding_time(theta_A, nsec, mshell_tot, cutLengths, twall)
+ manufacture.steel_butt_welding_time(theta_A, nsec, mshell_tot, 2 * np.pi * Rb[1:], twall[1:])
)
# Cost step 5) Painting- outside and inside
theta_p = 2
K_p = k_p * theta_p * 2 * (2 * np.pi * R_ave * H).sum()
# Cost step 6) Outfitting with electricity usage
K_o = np.sum(1.5 * k_m * (coeff - 1.0) * mshell)
# Material cost with waste fraction, but without outfitting,
K_m = 1.21 * np.sum(k_m * mshell)
# Electricity usage
K_e = np.sum(k_e * (e_f * mshell + e_fo * (coeff - 1.0) * mshell))
# Assemble all costs for now
tempSum = K_m + K_e + K_o + K_p + K_f
# Capital cost share from BLS MFP by NAICS
K_c = 0.118 * tempSum / (1.0 - 0.118)
outputs["cost"] = tempSum + K_c
def compute(self, inputs, outputs):
# Unpack variables for thickness and average radius at each can interface
twall = inputs['t_full']
Rb = 0.5 * inputs['d_full'][:-1]
Rt = 0.5 * inputs['d_full'][1:]
zz = inputs['z_full']
H = np.diff(zz)
rho = inputs['material_density']
coeff = inputs['outfitting_factor']
if coeff < 1.0: coeff += 1.0
# Total mass of cylinder
V_shell = frustum.frustumShellVol(Rb, Rt, twall, H)
outputs['mass'] = coeff * rho * V_shell
# Center of mass of each can/section
cm_section = zz[:-1] + frustum.frustumShellCG(Rb, Rt, twall, H)
outputs['section_center_of_mass'] = cm_section
# Center of mass of cylinder
V_shell += eps
outputs['center_of_mass'] = np.dot(V_shell, cm_section) / V_shell.sum()
# Moments of inertia
Izz_section = frustum.frustumShellIzz(Rb, Rt, twall, H)
Ixx_section = Iyy_section = frustum.frustumShellIxx(Rb, Rt, twall, H)
# Sum up each cylinder section using parallel axis theorem
I_base = np.zeros((3, 3))
for k in range(Izz_section.size):
R = np.array([0.0, 0.0, cm_section[k]])
Icg = assembleI([
Ixx_section[k], Iyy_section[k], Izz_section[k], 0.0, 0.0, 0.0
])
I_base += Icg + V_shell[k] * (np.dot(R, R) * np.eye(3) -
np.outer(R, R))
# All of the mass and volume terms need to be multiplied by density
I_base *= coeff * rho
outputs['I_base'] = unassembleI(I_base)
# Compute costs based on "Optimum Design of Steel Structures" by Farkas and Jarmai
# All dimensions for correlations based on mm, not meters.
R_ave = 0.5 * (Rb + Rt)
taper = np.minimum(Rb / Rt, Rt / Rb)
nsec = twall.size
mplate = rho * V_shell.sum()
k_m = inputs['material_cost_rate'] #1.1 # USD / kg carbon steel plate
k_f = inputs['labor_cost_rate'] #1.0 # USD / min labor
k_p = inputs['painting_cost_rate'] #USD / m^2 painting
# Cost Step 1) Cutting flat plates for taper using plasma cutter
cutLengths = 2.0 * np.sqrt(
(Rt - Rb)**2.0 + H**2.0) # Factor of 2 for both sides
# Cost Step 2) Rolling plates
# Cost Step 3) Welding rolled plates into shells (set difficulty factor based on tapering with logistic function)
theta_F = 4.0 - 3.0 / (1 + np.exp(-5.0 * (taper - 0.75)))
# Cost Step 4) Circumferential welds to join cans together
theta_A = 2.0
# Labor-based expenses
K_f = k_f * (manufacture.steel_cutting_plasma_time(cutLengths, twall) +
manufacture.steel_rolling_time(theta_F, R_ave, twall) +
manufacture.steel_butt_welding_time(
theta_A, nsec, mplate, cutLengths, twall) +
manufacture.steel_butt_welding_time(
theta_A, nsec, mplate, 2 * np.pi * Rb[1:], twall[1:]))
# Cost step 5) Painting- outside and inside
theta_p = 2
K_p = k_p * theta_p * 2 * (2 * np.pi * R_ave * H).sum()
# Cost step 6) Outfitting
K_o = 1.5 * k_m * (coeff - 1.0) * mplate
# Material cost, without outfitting
K_m = k_m * mplate
# Assemble all costs
outputs['cost'] = K_m + K_o + K_p + K_f