tensoes_induzidas_interior_macico.py

import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter

# Dados do problema
gama = 19
m = 0.5
k = 0.5
P = 1500
ti = 0
r_arr = z_arr = np.arange(0.5, 3.5, 0.5)

# configuracoes para o araquivo csv
file_name = "tensoes_geostaticas.csv"
delimiter = ";"
fmt = "%.2f"

# Parte 0: definicao de utilidades
def get_R(r, z):
    return np.sqrt(np.power(r,2) + np.power(z,2))

def get_phi(k):
    return np.degrees(np.arcsin(1 - k))

def get_vi(gama, z):
    return gama * z

def get_hi(k, vi):
    return k * vi

def get_delta_v(P, R, z):
    return (3 * P * np.power(z,3)) / (2 * np.pi * np.power(R, 5))

def get_delta_h(P, R, z, r, m):
    return P / (2 * np.pi) * ((3 * np.power(r, 2) * z) / np.power(R, 5) - (1 - 2 * m) / (R * (R + z)))

def get_delta_t(P, R, z, r):
    return (3 * P * r * np.power(z, 2)) / (2 * np.pi * np.power(R, 5))

def get_vf(vi, delta_v):
    return vi + delta_v

def get_hf(hi, delta_h):
    return hi + delta_h

def get_tf(ti, delta_t):
    return ti + delta_t


# Parte 1: Gráficos
fig = plt.figure(figsize=plt.figaspect(0.5))
fig.subplots_adjust(hspace=0.5)
X = r_arr
Y = z_arr
X, Y = np.meshgrid(X, Y)
R = get_R(X,Y)
strains = [
    get_vf(get_vi(gama, Y), get_delta_v(P,R,Y)),
    get_hf(get_hi(k, get_vi(gama, Y)), get_delta_h(P, R, Y, X, m)),
    get_tf(ti, get_delta_t(P, R, Y, X)),
]
titles = [
    "Tensões Verticais",
    "Tensões Horizontais",
    "Tensões Cisalhantes",
]
for index, Z in enumerate(strains):
    ax = fig.add_subplot(2, 2, index + 1, projection='3d')
    ax.view_init(30, 45)
    surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm, linewidth=0, antialiased=False)
    ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
    ax.set_xlabel('Distancia horizontal (r)')
    ax.set_ylabel('Profundidade (z)')
    ax.set_title(titles[index])
plt.show()


# Parte 2: Arquvio pro excel
result = []
for r in r_arr:
    for z in z_arr:
        R = get_R(r, z)
        vi = get_vi(gama, z)
        hi = get_hi(k, vi)
        delta_v = get_delta_v(P, R, z)
        delta_h = get_delta_h(P, R, z, r, m)
        delta_t = get_delta_t(P, R, z, r)
        vf = get_vf(vi, delta_v)
        hf = get_hf(hi, delta_h)
        tf = get_tf(ti, delta_t)
        result.append((r,z,vi,hi,delta_v, delta_h, delta_t,vf,hf,tf))
file = np.asarray(result)
np.savetxt(
    file_name,
    file,
    delimiter=delimiter,
    fmt=fmt,
    header="r;z;vi;hi;delta_v; delta_h; delta_t;vf;hf;tf"
)