objective_function.py

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import math
import numpy as np
from numpy.polynomial.legendre import legval
 
def f(coords, u, stress, strain):
    energy = 0.5*((strain*stress).sum(axis=0)) + 20*np.ones(stress.shape[1])
    return energy; 
 
def f_stress(coords, u, stress, strain):
    return 0.5*strain
 
def f_strain(coords, u, stress, strain):
    return 0.5*stress
 
def f_u(coords, u, stress, strain):
    return np.zeros(u.shape)
 
def number_of_modes(block_id):
    return 1
 
def block_modes(block_id, coords, cenytroid, bbox):
    # print ("block_modes: block_id ", block_id)
    # print ("block_modes: coords ", coords)
    # print ("block_modes: centroid ", cenytroid)
    # print ("block_modes: bbox ", bbox)
 
    nb_points = coords.shape[0]
    M = np.zeros((number_of_modes(block_id), nb_points, 3))
    x0 = coords[:, 0]
    y0 = coords[:, 1]
 
    x = x0 - cenytroid[0]
    y = y0 - cenytroid[1]
    r = np.sqrt(x*x + y*y)
 
    for i in range(number_of_modes(block_id)):
        ksi = x/r
        coeffs = np.zeros(i+1)
        coeffs[-1] = 1
        l = legval(ksi, coeffs)
        n = -l*(ksi+1)*(ksi-1)*np.sign(y)
        M[i] = np.array([np.zeros(nb_points), n, np.zeros(nb_points)]).T
 
    return M