root_bisect = bisection(deflection, 0, 1.5) root_newton = newton_raphson(deflection, d_deflection, 2.5)
[ EI \fracd^4ydx^4 = w ]
def d_deflection(x): return 3 x**2 - 12 x + 11 Numerical Methods In Engineering With Python 3 Solutions
slope = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x**2) intercept = (sum_y - slope * sum_x) / n return slope, intercept def poly_fit(x, y, degree): coeffs = np.polyfit(x, y, degree) return np.poly1d(coeffs) strain = np.array([0.0, 0.05, 0.10, 0.15, 0.20]) stress = np.array([0.0, 35.2, 68.4, 99.7, 128.5]) root_bisect = bisection(deflection, 0, 1
Boundary conditions: ( y(0)=0, y(L)=0, y''(0)=0, y''(L)=0 ). root_bisect = bisection(deflection