""" MIT License Copyright 2023 David Yang Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ from math import log, pi, sqrt from bessel import integrate_bessel from layer import f_s_all def put_hn(hs): # H(n) sum, hns = 0.0, [] for ih in range(len(hs)): sum += hs[ih] hns.append(sum) return hns def poisson(e): # empirical relationship between modulus of elasticity and poisson's ratio return 0.65 - 0.08 * log(e) / log(10.0) def get_result(params): ij0, psi, rr = params return [-ij0[0][0] * psi, -ij0[1][3] * psi * rr, -ij0[2][2] * psi, -ij0[3][1] * psi * rr, -(ij0[4][0] - ij0[6][1]) * psi, -(ij0[5][0] + ij0[6][1]) * psi] def get_rr(params): xwheel, ywheel, xout, yout = params xrs, yrs, rrs = [], [], [] for i, x in enumerate(xwheel): xr, yr = xout - xwheel[i], yout - ywheel[i] rr = sqrt(xr * xr + yr * yr) if rr > 0.0: xr, yr = xr / rr, yr / rr else: xr, yr = 1.0, 0.0 xrs.append(xr) yrs.append(yr) rrs.append(rr) return [xrs, yrs, rrs] def get_radius(params): opwgt, wgt, psi = params return sqrt(opwgt * wgt / psi / pi) def run_gels(params): vehicle, wheels, output, pavement = params opwgt, wgt, psi = vehicle[0], vehicle[1], vehicle[2] ar = get_radius((opwgt, wgt, psi)) xwheel, ywheel, xout, yout = wheels[0], wheels[1], output[0], output[1] th, ev, ps = pavement[0], pavement[1], pavement[2] hns, rrs, ss = put_hn(th), get_rr((xwheel, ywheel, xout, yout)), [] results = [[0.0 for j in range(7)] for i in range((len(th) - 1) * 2 + 1)] for ir in range(len(xwheel)): xr, yr, rr, lz, iz, z1, z2 = rrs[0][ir], rrs[1][ir], rrs[2][ir], [], 0, [], [] if len(th) > 1: for ln, zz in enumerate(hns[:-1]): # top of layer lz.append(ln + 1) z1.append(zz - th[ln]) z2.append(zz) ij0 = integrate_bessel(f_s_all, (7, ar, rr, zz - th[ln], th, ev, ps, ln + 1, hns)) ssh = get_result((ij0, psi, rr)) # polar to cartesian sxx = ssh[4] * xr * xr + ssh[5] * yr * yr sxy = ssh[4] * xr * yr - ssh[5] * xr * yr syy = ssh[4] * yr * yr + ssh[5] * xr * xr szz, srz, wz, ur = ssh[0], ssh[1], ssh[2], ssh[3] for i, s in enumerate([sxx, sxy, syy, szz, srz, wz, ur]): results[iz][i] += s iz += 1 # bottom of layer lz.append(ln + 1) z1.append(zz) z2.append(zz) ij0 = integrate_bessel(f_s_all, (7, ar, rr, zz, th, ev, ps, ln + 1, hns)) ssh = get_result((ij0, psi, rr)) sxx = ssh[4] * xr * xr + ssh[5] * yr * yr sxy = ssh[4] * xr * yr - ssh[5] * xr * yr syy = ssh[4] * yr * yr + ssh[5] * xr * xr szz, srz, wz, ur = ssh[0], ssh[1], ssh[2], ssh[3] for i, s in enumerate([sxx, sxy, syy, szz, srz, wz, ur]): results[iz][i] += s iz += 1 # top of lowest layer lz.append(len(th)) z1.append(hns[-1] - th[-1]) z2.append(hns[-1]) ij0 = integrate_bessel(f_s_all, (7, ar, rr, hns[-1] - th[-1], th, ev, ps, len(th), hns)) ssh = get_result((ij0, psi, rr)) sxx = ssh[4] * xr * xr + ssh[5] * yr * yr sxy = ssh[4] * xr * yr - ssh[5] * xr * yr syy = ssh[4] * yr * yr + ssh[5] * xr * xr szz, srz, wz, ur = ssh[0], ssh[1], ssh[2], ssh[3] for i, s in enumerate([sxx, sxy, syy, szz, srz, wz, ur]): results[iz][i] += s iz += 1 for ih in range(len(lz)): sxx, sxy, syy, szz, srz, wz, ur = results[ih] ss.append([lz[ih], z1[ih], z2[ih], sxx, sxy, syy, szz, srz, wz, ur]) return ss def print_results(ssa): print('n\tz1\tz2\tsxx\tsxy\tsyy\tszz\tsrz\twz\tur') for sa in ssa: print(sa) print() def print_gels(params): print('Vehicle\tWheels\tOutput\tPavement') for param in params: print(param, '\t', end='') print() results = run_gels(params) print_results(results) return results def hdes(vehicle, wheels, output, pavement, esubs, ths, layer_th, layer_str): results_str = [] results_wz = [] for th in ths: result_str = [] result_wz = [] for es in esubs: # set thickness pavement[0][layer_th - 1] = th # set subgrade modulus of elasticity pavement[1][-1] = es # set subgrade poisson's ratio pavement[2][-1] = poisson(es) results = run_gels((vehicle, wheels, output, pavement)) # quiet mode, else use print_gels # stress at bottom of layer_str at output location, max of sxx, syy result_str.append(max(results[(layer_str - 1) * 2 + 1][3], results[(layer_str - 1) * 2 + 1][5])) # surface deflection at output location result_wz.append(results[0][8]) # save each result for all values of subgrade modulus of elasticity results_str.append(result_str) results_wz.append(result_wz) return results_str, results_wz