analytical_expr.py

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import math
import numpy as np
 
# Analytical displacement wrapper for MoFEM
def analytical_disp(delta_t, t, x, y, z, tx, ty, tz, block_name):
    x = np.asarray(x)
    z = np.asarray(z)
 
    if block_name == "ANALYTICAL_DISPLACEMENT_1":
        c_val_dx = 0.1 * x
    else:
        c_val_dx = np.zeros_like(x)
 
    c_val_dy = np.zeros_like(x)
    c_val_dz = np.zeros_like(z)
 
    return np.hstack([
        c_val_dx.reshape((-1, 1)),
        c_val_dy.reshape((-1, 1)),
        c_val_dz.reshape((-1, 1))
    ])
 
# Analytical traction wrapper for MoFEM
def analytical_traction(delta_t, t, x, y, z, tx, ty, tz, block_name):
    x = np.asarray(x)
    z = np.asarray(z)
 
    # _1 is the legacy block name; _3 is the JSON-applied name for this mesh.
    if block_name in ("ANALYTICAL_TRACTION_1", "ANALYTICAL_TRACTION_3"):
        c_val_dx = np.full_like(x, 0.1)
    elif block_name == "ANALYTICAL_TRACTION_2":
        c_val_dx = np.full_like(x, -0.2)
    else:
        c_val_dx = np.zeros_like(x)
 
    c_val_dy = np.zeros_like(x)
    c_val_dz = np.zeros_like(z)
 
    return np.hstack([
        c_val_dx.reshape((-1, 1)),
        c_val_dy.reshape((-1, 1)),
        c_val_dz.reshape((-1, 1))
    ])
 
def analytical_external_strain(delta_t,t, x, y, z, block_name):
    # ext_strain_val = np.exp(2*x)
    ext_strain_val = t * y * 0.1 
    ext_strain =  np.hstack([ext_strain_val.reshape((-1,1)) ])
    return ext_strain
 
def analytical_elastic(delta_t, t, x, y, z, block_name):
    # Default modulus at the center (x=0)
    E0 = 1000
    x = np.asarray(x)
    youngs_modulus = 1000 * np.exp(0.1 * x)
    # youngs_modulus = 1000 * np.ones_like(x)
    return np.hstack([youngs_modulus.reshape((-1, 1))])