Physics Fundamentals for CAE Engineers
You've seen Newton's Second Law in high school. But did you know it's also the FEM equation of motion — [M]ü + [C]u̇ + [K]u = F? This section bridges the physics you already know to the simulation tools you're learning, one concept at a time. No prerequisite beyond curiosity.
Recommended Learning Pathway
Forces and Motion — The Foundation
Start here. These three topics together explain what FEM is computing at every node.
Energy and Material Response
How energy flows and how materials resist deformation — the heart of structural FEM.
Dynamics and Vibration
Time-dependent behavior: impacts, oscillations, resonance. Required for dynamic analysis.
Fluid, Thermal, and Wave Physics
Multi-physics fundamentals: heat transfer, fluid mechanics, and acoustic waves.
Coupled Physics — Modern Engineering
Where multiple physical phenomena interact. Essential for EV, aerospace, and electronics CAE.
All Articles — Physics Fundamentals
Newton's Laws of Motion
The three laws of motion explained for CAE engineers. From F=ma to the full FEM equation of motion [M]ü+[C]u̇+[K]u=F. Crash test worked example: 1500 kg car at 50 km/h.
F = ma → [M]ü+[K]u=FKinematics: Velocity & Acceleration
Position, velocity, and acceleration relationships. Setting initial conditions for drop test FEM. Newmark-β time integration for implicit dynamic analysis.
v = √(2gh) for drop testsWork and Energy
W=F·d, elastic strain energy, and the virtual work principle — why FEM uses weak forms instead of strong-form Newton. Hourglass energy checks in explicit FEM.
δW_int = δW_ext → [K]u=FMomentum and Impulse
p=mv, J=FΔt=Δp, conservation of momentum. Airbag design physics: same impulse, longer contact time → lower peak force. Explicit FEM and SPH for impacts.
J = Δp = FΔtSprings & Hooke's Law
F=kx, Young's modulus, springs in series/parallel. The FEM stiffness matrix [K] explained as a system of springs. Spring-back in UHSS sheet metal forming.
[K] = ∫ BᵀDB dVSimple Harmonic Motion
ωn=√(k/m), damped oscillation, resonance, MDOF eigenvalue problem, FEM modal analysis. Why the Tacoma Narrows Bridge collapsed — and how to prevent resonance.
[K]φ = ω²[M]φWave Properties
Transverse and longitudinal waves, superposition, Snell's law, acoustic impedance. How ultrasonic NDT detects cracks. Acoustic FEM and BEM for NVH analysis.
∇²p + k²p = 0Heat and Temperature
Q=mcΔT, Fourier's law, thermal resistance networks. FEM thermal analysis equation [C]Ṫ+[K]T=Q. EV battery pack thermal management: 10 kW heat rejection during fast charging.
q = -k∇T (Fourier)Fluid Pressure and Buoyancy
p=ρgh, Pascal's principle, Archimedes, Bernoulli. How deep can a submarine dive? Pressure buckling FEM analysis. CFD connection and hydrostatic initialization.
p = p₀ + ρghStress and Strain Basics
σ=F/A, ε=ΔL/L, full stress tensor, von Mises yield criterion. What von Mises stress really means physically. Stress concentration factors and when to use fracture mechanics.
σ_vM = √(½[(σ₁-σ₂)²+...])Circular Motion & Centrifugal Force
ac=ω²r, centrifugal stress in turbine blades (200+ MPa at 10,000 RPM), flywheel hoop stress, gyroscopic bearing loads, Campbell diagram for resonance avoidance.
σ_root = ½ρω²(R²-r²)Statics and Equilibrium
ΣF=0, ΣM=0, FBD, determinate vs indeterminate structures, truss analysis. When is linear static FEM valid? Symmetry exploitation and boundary condition selection.
[K]u = F (linear static)Thermal Expansion
ΔL=αLΔT, constrained thermal stress σ=EαΔT, bimetal actuators, CTE mismatch in PCB solder joints. Bridge expansion joints and railway sun kink. Thermo-structural FEM coupling.
σ_thermal = EαΔTElectric Current, Voltage & Resistance
V=IR, P=I²R Joule heating, skin effect at high frequency, FEM electro-thermal coupling. EV fast-charging cable design: why 200A doesn't melt the cable.
∇·(σ∇φ) = 0 + Joule heatAfter Physics Fundamentals
Once you're comfortable with these physics fundamentals, the next step is the advanced theory sections — which go deeper into the mathematics and numerical methods behind each domain: