NeuralBlitz Mechanical Engineering
What I Do
I provide comprehensive mechanical engineering tools including statics and dynamics analysis, machine design calculations, heat transfer analysis, fluid mechanics, stress analysis, and manufacturing optimization for engineering applications.
When to Use Me
- Structural analysis and design
- Machine component sizing
- Heat transfer calculations
- Fluid flow analysis
- Stress and strain analysis
- Manufacturing process planning
Core Concepts
- Statics: Force equilibrium, free body diagrams
- Dynamics: Kinematics, kinetics, vibrations
- Mechanics of Materials: Stress, strain, deformation
- Machine Design: Bearings, gears, shafts
- Heat Transfer: Conduction, convection, radiation
- Fluid Mechanics: Bernoulli, Navier-Stokes
- Thermodynamics: Energy, entropy, efficiency
- Manufacturing: Machining, forming, additive
Code Examples
Statics Analysis
import numpy as np
def equilibrium_2d(forces_x, forces_y, moments, distances):
sum_fx = sum(f[0] for f in forces_x) + sum(f[0] for f in forces_y)
sum_fy = sum(f[1] for f in forces_y)
sum_m = sum(m + r * f[1] for m, r, f in zip(moments, distances, forces_y))
return {'Fx': sum_fx, 'Fy': sum_fy, 'M': sum_m}
def beam_reactions(w, L, support_type='simply_supported'):
if support_type == 'simply_supported':
RA = w * L / 2
RB = w * L / 2
max_moment = w * L**2 / 8
return {'RA': RA, 'RB': RB, 'Mmax': max_moment}
elif support_type == 'cantilever':
RA = w * L
M_base = w * L**2 / 2
return {'RA': RA, 'Mmax': M_base}
w = 10 # kN/m
L = 5 # m
reactions = beam_reactions(w, L, 'simply_supported')
print(f"Beam reactions: {reactions}")
Stress Analysis
def normal_stress(P, A):
return P / A
def shear_stress(V, Q, I, b):
return V * Q / (I * b)
def moment_of_inertia_rectangle(b, h):
return b * h**3 / 12
def section_modulus_rectangle(b, h):
return b * h**2 / 6
def von_mises_stress(sigma_x, sigma_y, tau_xy):
return np.sqrt(sigma_x**2 - sigma_x*sigma_y + sigma_y**2 + 3*tau_xy**2)
def stress_transformation(sigma_x, tau_xy, theta):
sigma_x_prime = (sigma_x + sigma_y)/2 + (sigma_x - sigma_y)/2 * np.cos(2*theta) + tau_xy * np.sin(2*theta)
return sigma_x_prime
sigma_x, sigma_y, tau_xy = 100, 50, 25
vm_stress = von_mises_stress(sigma_x, sigma_y, tau_xy)
print(f"von Mises stress: {vm_stress:.2f} MPa")
Heat Transfer
k_copper = 401 # W/m·K
k_steel = 43 # W/m·K
h_air = 10 # W/m²·K
def conduction_resistance(L, k, A):
return L / (k * A)
def convection_resistance(h, A):
return 1 / (h * A)
def overall_heat_transfer(U, A):
return 1 / (1/(h_air*A) + L/(k*A))
def heat_flux(q, A):
return q / A
def fourier_law(k, dT, dx):
return -k * dT / dx
def newton_cooling(h, Ts, Tinf):
return h * (Ts - Tinf)
L, A = 0.01, 0.1 # m, m²
R_cond = conduction_resistance(L, k_steel, A)
R_conv = convection_resistance(h_air, A)
print(f"Total thermal resistance: {R_cond + R_conv:.4f} K/W")
Fluid Mechanics
rho_water = 1000 # kg/m³
mu_water = 0.001 # Pa·s
def reynolds_number(rho, v, D, mu):
return rho * v * D / mu
def pressure_drop_darcy(ρ, L, v, D, f):
return f * (L/D) * (ρ * v**2 / 2)
def bernoulli_equation(p1, v1, z1, p2, v2, z2, rho=1000):
return p1 + 0.5*rho*v1**2 + rho*9.81*z1 - (p2 + 0.5*rho*v2**2 + rho*9.81*z2)
def drag_force(CD, A, rho, v):
return 0.5 * CD * A * rho * v**2
def pump_power(Q, H, rho=1000, efficiency=0.8):
return rho * 9.81 * Q * H / efficiency
v, D = 2, 0.05
Re = reynolds_number(rho_water, v, D, mu_water)
print(f"Reynolds number: {Re:.0f}")
print(f"Flow regime: {'laminar' if Re < 2300 else 'turbulent'}")
Vibration Analysis
def natural_frequency(k, m):
return np.sqrt(k / m) / (2 * np.pi)
def damped_frequency(wn, zeta):
return wn * np.sqrt(1 - zeta**2)
def magnification_factor(wn, wd, zeta):
r = wd / wn
return 1 / np.sqrt((1 - r**2)**2 + (2*zeta*r)**2)
def modal_mass(m, mode_shape):
return np.sum(m * mode_shape**2)
def response_to_impulse(F0, m, c, k, t):
wd = damped_frequency(np.sqrt(k/m), c/(2*m*np.sqrt(k*m)))
zeta = c/(2*np.sqrt(k*m))
if zeta < 1:
return (F0/m/wd) * np.exp(-zeta*np.sqrt(k/m)*t) * np.sin(wd*t)
k, m = 10000, 100
fn = natural_frequency(k, m)
print(f"Natural frequency: {fn:.2f} Hz")
Best Practices
- Units: Use consistent units throughout
- Safety Factors: Apply appropriate factors of safety
- Material Selection: Consider strength, cost, manufacturability
- Fatigue: Account for cyclic loading
- Failure Modes: Consider all potential failure modes
Common Patterns
# Factor of safety
def factor_of_syntax(stress, allowable_stress):
return allowable_stress / stress
# Kinematic analysis
def velocity_analysis(r1, omega1, r2):
return r1 * omega1 / r2
# Power transmission
def belt_power_transmission(T1, T2, v):
return (T1 - T2) * v
Core Competencies
- Statics and dynamics analysis
- Stress and strain calculations
- Heat transfer analysis
- Fluid mechanics applications
- Machine design principles