| function Int_eq = Int_M_eq3 (L01, L02, m) |
| % MATLAB program for Eq. (38). |
| % L01 represent the zero-order spectral moment for spectra 1 |
| % L02 represent the zero-order spectral moment for spectra 2 |
| % m is fatigue strength exponent |
| error(nargchk(2,3,nargin)) |
| if nargin < 3 || isempty(m) |
| m = 0; |
| end |
| if m < 0 |
| Int_eq = ; |
| Return |
| else |
| if rem(m,1) > 0 |
| Int_eq = ; |
| return |
| end |
| end |
| I0 = sqrt(2*pi)/4+(pi/2-atan(sqrt(L02/L01)))/sqrt(2*pi); |
| I1 = 0.5 + sqrt(L01/(L01+L02))/2; |
| if m == 0 |
| Int_eq = I0; |
| return |
| end |
| if m == 1 |
| Int_eq = I1; |
| return |
| end |
| DoubFac_m = DoubleFactorial(m-1); |
| C1 = DoubFac_m * I1; |
| C2 = DoubFac_m * I0; |
| C3 = sqrt(L01/L02)/2/sqrt(2*pi); |
| C4 = sqrt(2 * L02/(L01+L02)); |
| if mod(m,2)==1 |
| C5 = zeros((m+1)/2,1); |
| for k = 2 : 1 : (m+1)/2 |
| DoubFac_k = DoubleFactorial(2*k-2); |
| C5(k) = C4∧(2*k-1) * gamma((2*k-1)/2)/DoubFac_k; |
| end |
| Int_eq = C1 + C3 * DoubFac_m * sum(C5); |
| else |
| C5 = zeros(m/2,1); |
| for k = 1 : 1 : m/2 |
| DoubFac_k = DoubleFactorial(2*k-1); |
| C5(k) = C4∧(2*k) * gamma(k)/DoubFac_k; |
| end |
| Int_eq = C2 + C3 * DoubFac_m * sum(C5); |
| end |
| return |
| %–subroutine for caculating double factorial. |
| function b = DoubleFactorial(a) |
| % a is a integral number. |
| b = 1; |
| for i = a : -2 : 1 |
| b = b*i; |
| end |
| return |
| %-end- |
