Three-Dimensional Stress and Strain States
Mathematical foundations of continuous media, Cauchy stress tensor, principal stresses, traction vectors, invariants, spherical & deviatoric stress,compatibility equations.
Elastic Yield Criteria & Limit Analysis
Multi-axial yielding criteria (von Mises, Tresca, Rankine, Mohr-Coulomb). Plastic hinges, collapse mechanisms, and shape factors.
Advanced Fatigue Analysis — Stress-Life (S-N) Approach
Endurance limits, Marin size/surface/load correction factors, mean stress corrections (Goodman, Soderberg, Gerber), Miner's cumulative damage rule.
Strain-Life (ε-N) Approach & Cyclic Material Behavior
Low-cycle fatigue, Coffin-Manson relationship, cyclic plasticity, strain hardening, Bauschinger effect, Neuber's rule, local strain approach.
Linear Elastic Fracture Mechanics (LEFM)
Griffith energy balance, Irwin energy release rate, Mode I/II/III crack displacement, stress intensity factors (K), plastic zone corrections.
Elastic-Plastic Fracture Mechanics (EPFM) & Crack Propagation
J-integral formulations, crack tip opening displacement (CTOD), Paris Law cycle integration, threshold stress intensity, environmental cracking.
Contact Mechanics & Hertzian Stresses
Hertz contact of spheres, cylinders, and ellipsoids. Contact pressure profiles, subsurface shear stresses, location of peak shear, and spalling fatigue.
Tribology, Friction, and Wear Mechanisms
Stribeck curve regimes (boundary, mixed, hydrodynamic), adhesive/abrasive/fretting wear, Archard wear equation, surface roughness parameters (Ra, Rz).
Hydrodynamic & Hydrostatic Lubrication
Reynolds equation derivation, journal bearing analysis, Sommerfeld number, oil film thickness, eccentricity, oil whirl/whip dynamic instability.
Rotor Dynamics & Critical Speeds
Jeffcott rotor model, critical speeds, dynamic magnification, gyroscopic effects, Campbell diagrams, single and two-plane dynamic balancing.
Design of High-Performance Gears
Spur, helical, and bevel gear forces. Gear kinematics, AGMA bending strength and contact stress formulas, overload/dynamic factors, scuffing failure.
Threaded Fasteners, Bolted Joints & Preload Dynamics
Thread torque-preload relationship, bolt and member stiffness, joint constant, fatigue load sharing, bolt preload relaxation, thread stripping.
Compliant Mechanisms & Flexure Design
Pseudo-Rigid-Body Model (PRBM), flexure pivots, parallel guider mechanisms, parasitic motion, fatigue life of compliant springs.
Failure Analysis Methodology & Case Studies
Forensic engineering, failure analysis steps, fractography features (striations, dimples, beach marks), creep rupture, hydrogen embrittlement.