Undergraduate Thesis
ASME JMD
ANSYS FEA
FGM Connecting Rod Optimization & Spatial Gradation
Coupled thermo-mechanical FEA optimization (82,500+ nodes) across 45 material combinations using Wärtsilä 20 engine geometry. Implements 5 spatial gradation laws across an 8.85 mm transition layer, achieving +14.88% SF gain and -12.39% stress reduction.
V₁(x) = (e^{βx/h} - 1)/(e^β - 1), J = Σ w_i (R_i/R_{ref})²
ANSYS Workbench
SolidWorks
Python
SSE Optimization
Cloud Simulation
RK4 ODE
Atwood Machine Physics Lab
Interactive cloud-deployed simulator modeling coupled multi-body kinematics, string tension dynamics, pulley rotational inertia, and axle viscous friction via continuous 4th-order Runge-Kutta numerical integration.
a = [(m₂ - m₁)g - μ(m₁ + m₂)g] / [m₁ + m₂ + I/R²]
Vanilla JS
HTML5 Canvas
Vercel
RK4 Integration
Aerospace Mechanics
Variable Mass
Rocket Propulsion & Variable Mass Dynamics
Computational model simulating variable mass dynamics, fuel burn rates $\dot{m}(t)$, instantaneous thrust vectoring, atmospheric drag profiles, and multi-stage payload optimization based on the Tsiolkovsky rocket equation.
Δv = v_e · ln(m₀ / m_f) - ∫ g·sin(θ) dt
JavaScript
Physics Engine
Numerical ODE
Rotational Dynamics
Inertia Tensors
Rolling Motion Race on Inclined Planes
Visual simulation comparing velocity and acceleration of diverse geometric bodies (Solid Sphere, Solid Cylinder, Hollow Sphere, Hoop) rolling without slipping down an inclined plane. Demonstrates kinetic energy partitioning into translational vs rotational modes.
a = (g · sin θ) / [1 + I / (m · R²)]
JavaScript
Rigid Body Mechanics
Kinematics
Non-Linear Dynamics
Phase Space
Vertical Circular Motion of Non-Linear Pendulum
Complete dynamical modeling of a constrained pendulum in a vertical plane. Computes instantaneous tension, tangential acceleration, radial centripetal forces, and energy balance between kinetic and gravitational potential energy across 360 degrees.
T(θ) = m · [g · cos θ + v(θ)² / L], v_min = √(5gR)
Canvas Engine
Vector Calculus
Energy Diagnostics
Classical Mechanics
Path Independence
Tracking Energy in Arbitrary Potential Wells
Numerical verification demonstrating mechanical energy conservation across diverse curvilinear paths. Validates path-independent work in conservative gravitational fields and characterizes non-conservative dissipation under Rayleigh dissipation functions.
dE/dt = 0 ⇒ ∮ F_c · dr = 0
Python
NumPy
Numerical Solvers
Vector Calculus
Field Theory
Conservative & Non-Conservative Force Fields
Analytical and numerical tests verifying force field curl conditions $\nabla \times \vec{F} = \vec{0}$. Evaluates closed-contour line integrals for inverse-square, electrostatic, spring, and viscous frictional damping fields.
∇ × F = 0 ⇔ F = -∇U
Vector Fields
Line Integrals
Scientific Python
Numerical Quadrature
Work-Energy
Work Done by Complex Force Fields
Engineered algorithms computing work done by spatially and temporally variable forces using adaptive Simpson's and trapezoidal numerical quadrature. Evaluates work performed under nonlinear spring stiffness $F(x) = k_1 x + k_2 x^3$ and magnetic repulsion.
W = ∫_{x₁}^{x₂} F(x) dx = ΔK
Numerical Methods
Simpson's Rule
JavaScript
Transportation Mechanics
Friction Limits
Dynamics of Banked Curved Roadways
Parametric engineering model evaluating super-elevation angle $\theta$, lateral tire friction limits $\mu_s$, and maximum non-skid vehicle velocity envelopes. Simulates slip vs skid instability regimes for highway curve geometry design.
v_{max} = √[r · g · (tan θ + μ) / (1 - μ · tan θ)]
Dynamics
Geometric Modeling
Friction Envelopes