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strength-of-ship.py
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"""
Created on Fri Nov 19 20:11:05 2021
@author: nedir ymamov
"""
import numpy as np
from scipy.interpolate import interp1d
from scipy.integrate import cumtrapz
import matplotlib.pyplot as plt
def newtonDifMethod(x, b, value): # NEWTON DIFFERANCE METODUNU FONKSİYONU
def proterm(i, value, x):
pro = 1
for j in range(i):
pro *= (value - x[j])
return pro
def dividedDifTable(x, y, n):
for i in range(1, n):
for j in range(n - i):
y[j, i] = ((y[j, i - 1] - y[j + 1, i - 1]) / (x[j] - x[i + j]))
return y
def applyFormula(value, x, y, n):
sum = y[0, 0]
for i in range(1, n):
sum += (proterm(i, value, x) * y[0, i])
return sum
y = np.zeros((len(x), len(x)))
for i in range(len(b)):
y[i, 0] = b[i]
y = dividedDifTable(x, y, len(x))
return applyFormula(value, x, y, len(x))
def bonjeanAlani(offset, posta0, posta, suhatti):
offset_new = np.zeros((101, 8))
for i in range(8):
f = interp1d(posta0, offset[:, i], kind = "cubic")
offset_new[:, i] = f(posta)
alan = np.zeros((101, 8)) # BON-JEAN ALANLARI
for i in range(101):
alan[i, 1:] = 2 * cumtrapz(offset_new[i, :], suhatti[:])
return alan
def prohaskaDagilimi(boy, deplasman):
qx = np.zeros(101) # TOPLAM GEMİ AĞIRLIK DAĞILIMI (PROHASKA YÖNTEMİ)
a = .68 * deplasman / boy
b = 1.185 * deplasman / boy
c = .58 * deplasman / boy
n = 1
for i in range(101):
if i < 34:
qx[i] = a + i * (b - a) / 34
if i > 33 and i < 68:
qx[i] = b
if i > 67:
qx[i] = b - n * (b - c) / 33
n += 1
return qx
def ataletDagilimi(boy, posta):
Ix = np.zeros(101) # ATALET MOMENT DAĞILIMI
Wmax = .193
Iy = 3 * Wmax * boy / 100 # ORTA KESİT ATALET MOMENTİ [m4]
for i in range(100):
if posta[i] <= boy / 20:
Ix[i] = 5 * Iy * posta[i] / boy
if boy / 20 < posta[i] <= 7 * boy / 20:
Ix[i] = .25 * Iy + (15 * Iy) * (posta[i] - boy / 20) / (6 * boy)
if 7 * boy / 20 < posta[i] <= 15 * boy / 20:
Ix[i] = Iy
if 15 * boy / 20 < posta[i] <= 19 * boy / 20:
Ix[i] = Iy - 2.5 * (Iy / boy) * (posta[i] - 15 * boy / 20)
if posta[i] > 19 * boy / 20:
Ix[i] = .5 * Iy - 10 * (Iy / boy) * (posta[i] - 19 * boy / 20)
return Ix
def dalgaKaydirma(boy, draft, deplasman, H, alan, posta, suhatti, dalga_katsayi, yogunluk):
posta1 = np.array([0, .5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5]) * boy / 10
c = np.interp(posta[:51], posta1, dalga_katsayi) # YARI DALGA DEĞERLERİ
c = np.concatenate((np.delete(c, -1), np.flipud(c)), axis = 0) # YARI DALGAYI TAM YAPMA
ksi = draft - H / 2 + H * c
ax = np.zeros(101) # DALGAYI DİKEY KAYDIRARAK a(x) BULMAK
for i in range(200):
for j in range (101):
ax[j] = yogunluk * newtonDifMethod(suhatti, alan[j, :], ksi[j])
if round(deplasman) < round(np.trapz(ax, posta)):
ksi -= .004
elif round(deplasman) > round(np.trapz(ax, posta)):
ksi += .004
else: break
return ax
def gerilmeHesabi(name, boy, w, ax, qx, Ix, posta, ymax):
px = ax - qx
dpx0 = np.array([0, *cumtrapz(px, posta)])
dpx = dpx0 - dpx0[-1] * posta / boy # LİNEER DÜZELTME (%0.03dpx.son<dpx.max [M. Savcı])
ddpx = np.array([0, *cumtrapz(dpx, posta)])
if name == "cukur": # ARTIK MOMENT DÜZELTME [M. Savcı 1980]
C = 1 - np.cos(2 * np.pi * posta / boy)
d1Qx = -(ddpx[-1] * C) / boy
Qx = dpx - d1Qx
Mx = ddpx + np.array([0, *cumtrapz(d1Qx, posta)])
else:
dax = np.array([0, *cumtrapz(ax, posta)])
Qx = dpx + (-ddpx / w) * ax
Mx = ddpx + (-ddpx[-1] / w) * dax
W = Ix / ymax # SECTİON MODULUS
gerilme = np.array([0, *(9.81 * Mx[1 : -1]) / (W[1 : -1] * 1000), 0]) # 1[ton] = 9.81[kN]
return Qx, Mx, gerilme
def grafikCizimi(name, ax, qx, Qx, Mx, gerilme, posta):
plt.figure(figsize = (10, 4), facecolor = "seagreen")
plt.title(name, fontweight = "bold") # GRAFİĞİN BAŞLIĞI
plt.xlabel("Gemi Boyu [m]", fontweight = "bold")
plt.plot(posta, ax, posta, qx, posta, Qx, posta, Mx, posta, gerilme)
plt.legend(["a [ton/m]", "q [ton/m]", "Q [ton]", "M [ton.m]", "σ [MPa]"], loc = "best")
plt.plot([-1, boy + 1], [0, 0])
plt.grid(color = "green", linestyle = "--", linewidth = .5)
plt.show()
def hesapla(offset, boy, genislik, draft, yogunluk):
H = boy / 20 # DALGA YÜKSEKLİĞİ
blok_katsayi = .7
deplasman = boy * genislik * draft * blok_katsayi * yogunluk
posta0 = np.array([0, .5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9.5, 10]) * boy / 10
posta = np.linspace(0, boy, 101)
suhatti = np.array([0, .3, 1, 2, 3, 4, 5, 6]) * draft / 4
ymax = 1.5 * draft - .4 * 1.5 * draft # TARAFSIZ EKSEN KABULU [İ. Bayer]
alan = bonjeanAlani(offset, posta0, posta, suhatti)
qx = prohaskaDagilimi(boy, deplasman) # GEMİNİN AĞITLIK DAĞILIMI
Ix = ataletDagilimi(boy, posta) # GEMİNİN ATALET DAĞILIMI
# SAKİN SU
ax = alan[:, 5] * yogunluk
Qx, Mx, gerilme = gerilmeHesabi("sakin", boy, deplasman, ax, qx, Ix, posta, ymax)
# BURADA Qx, Mx VE gerilme 'Yİ BELİRLİ BİR ORAN İLE BÖLÜNÜR
# BU ORANLARI KENDİ DEĞERLERİNİZ İLE DEĞİŞTİRMEYİ UNUTMAYINIZ
grafikCizimi("SAKİN SU", ax, qx, Qx / 5, Mx / 60, gerilme / 6, posta)
# DALGA ÇUKURU
dalga_katsayi = [1, .966, .871, .795, .578, .422, .28, .16, .072, .018, 0]
ax = dalgaKaydirma(boy, draft, deplasman, H, alan, posta, suhatti, dalga_katsayi, yogunluk)
Qx, Mx, gerilme = gerilmeHesabi("cukur", boy, deplasman, ax, qx, Ix, posta, ymax)
grafikCizimi("DALGA ÇUKURU", ax, qx, Qx / 5, Mx / 20, gerilme / 2, posta)
# DALGA TEPESİ
dalga_katsayi = np.flipud(dalga_katsayi) # DALGA KATSAYISININ LİSTESİNİ TERSİNE ÇEVİRME
ax = dalgaKaydirma(boy, draft, deplasman, H, alan, posta, suhatti, dalga_katsayi, yogunluk)
Qx, Mx, gerilme = gerilmeHesabi("tepe", boy, deplasman, ax, qx, Ix, posta, ymax)
grafikCizimi("DALGA TEPESİ", ax, qx, Qx / 7, Mx / 110, gerilme / 10, posta)
boy = 87
genislik = 10.88
draft = 4.35
yogunluk = 1.025
offset = np.loadtxt("s60.txt", dtype = float) * genislik / 2
hesapla(offset, boy, genislik, draft, yogunluk)