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Glossary

CAE & Engineering Glossary

Definitions of key terms in FEM, CFD, thermal analysis, control engineering, and numerical methods, with links to related tools.

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B
BEM
Boundary Element Method
A numerical method that discretizes only the boundary of a domain. Useful for acoustics, elastodynamics, and electromagnetics.
Bode Plot
Bode Plot
A frequency-response plot showing gain and phase versus frequency on logarithmic axes.
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Buckling
Buckling
An instability in which a compressed structure suddenly deflects laterally after a critical load is exceeded.
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C
CAE
Computer-Aided Engineering
Engineering analysis performed with computers, including structural, fluid, thermal, electromagnetic, and control simulations.
CFD
Computational Fluid Dynamics
Numerical simulation of fluid flow and heat transfer, usually by solving the Navier-Stokes equations.
Convergence
Convergence
The tendency of a numerical solution to approach the true solution as the mesh, timestep, or tolerance is refined.
Crack Propagation
Crack Propagation
Growth of a crack under fatigue loading, often modeled by Paris law.
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E
Eigenvalue Problem
Eigenvalue Problem
A problem used to find natural frequencies, mode shapes, and buckling loads.
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Elastoplastic Analysis
Elastoplastic Analysis
Analysis that accounts for plastic deformation after yield.
Euler Buckling
Euler Buckling
The elastic buckling load of a slender column, Pcr = pi^2 EI/(KL)^2.
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F
FEM
Finite Element Method
A numerical method that divides a continuum into finite elements and solves approximate field equations.
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FFT
Fast Fourier Transform
A fast algorithm for converting time-domain signals into frequency-domain spectra.
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Fracture Toughness
Fracture Toughness
A material resistance to crack-driven fracture, commonly represented by KIC.
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G
Goodman Diagram
Goodman Diagram
A fatigue design diagram for alternating stress and mean stress.
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Green's Function
Green's Function
The response of a linear system to a point source.
H
Heat Transfer Coefficient
Heat Transfer Coefficient
Coefficient h [W/m^2K] that quantifies convective heat transfer between a surface and a fluid.
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Hertzian Contact
Hertz Contact
Contact stress generated when elastic bodies touch.
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L
Linear Elasticity
Linear Elasticity
Material behavior in which stress is proportional to strain.
LMTD
Log Mean Temperature Difference
The effective temperature difference used in heat-exchanger calculations, Q = UA LMTD.
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M
Material Mechanics
Mechanics of Materials
The mechanics of stress, strain, and deformation in solid members.
Modal Analysis
Modal Analysis
Analysis used to find natural frequencies, mode shapes, and damping characteristics.
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Mohr's Circle
Mohr's Circle
A graphical method for finding principal stresses and maximum shear stress.
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N
Navier-Stokes Equations
Navier-Stokes Equations
Partial differential equations governing viscous fluid motion.
Nonlinear Analysis
Nonlinear Analysis
Analysis where geometry, material behavior, or contact conditions make response nonlinear.
Nusselt Number
Nusselt Number
Dimensionless number Nu = hL/k for convective versus conductive heat transfer.
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P
Paris Law
Paris Law
An empirical fatigue-crack-growth relation, da/dN = C(Delta K)^m.
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PID Control
PID Control
A feedback control law combining proportional, integral, and derivative terms.
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Poisson's Ratio
Poisson's Ratio
The ratio of lateral strain to axial strain in a loaded material.
R
Reynolds Number
Reynolds Number
Dimensionless ratio Re = rho V L / mu between inertial and viscous forces in a fluid.
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S
Safety Factor
Safety Factor
A design margin that divides reference strength by allowable stress or load.
S-N Curve
S-N Curve
A fatigue curve relating stress amplitude S to cycles to failure N.
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Stiffness Matrix
Stiffness Matrix
The FEM matrix [K] relating nodal displacements to nodal forces.
Stress Concentration
Stress Concentration
Local stress amplification near holes, notches, shoulders, and other discontinuities.
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T
Topology Optimization
Topology Optimization
A design method that uses numerical optimization to determine material placement.
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Truncation Error
Truncation Error
Error introduced by approximating derivatives, integrals, or series with finite terms.
V
V&V
Verification & Validation
Verification asks whether equations were solved correctly; validation asks whether the model represents the real system.
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von Mises Stress
von Mises Stress
An equivalent stress used to evaluate yielding under multiaxial stress states.
W
Warping Function
Warping Function
A function describing cross-section warping in torsion problems.
Y
Young's Modulus
Young's Modulus
Elastic modulus E, the ratio of normal stress to normal strain in the linear elastic range.

How to Use

  1. Search or navigate by discipline: FEM (Finite Element Method), CFD (Computational Fluid Dynamics), structural mechanics, or control systems
  2. Select a term to display its definition, standard notation, and typical SI/imperial units (e.g., stress in MPa, deflection in mm, pressure in Pa)
  3. Click embedded links to jump to related glossary entries or access companion calculators for strain energy, natural frequency, or Navier-Stokes validation

Worked Example

Query: "Von Mises stress." Result shows definition of equivalent stress tensor used in yield criteria, formula σ_vm = √[(σ₁−σ₂)² + (σ₂−σ₃)² + (σ₃−σ₁)²]/2, and an FEM case: aluminum alloy 6061-T6 bracket under 50 kN axial + 30 kN shear load yields Von Mises = 215 MPa (yield strength 276 MPa, safety factor = 1.28). Links to stress concentration calculator and fatigue analysis glossary entry.

Practical Notes

  1. Glossary distinguishes between numerical methods (FEA, BEM, meshfree) and physics domains (structural, thermal, multiphase flow) to clarify solver selection
  2. Each term includes industrial context: e.g., "aspect ratio" definition clarifies 2D quad vs. 3D tetrahedral element quality thresholds (target AR < 100 for convergence)
  3. Cross-references link CFD terms (Reynolds number, turbulence models k-epsilon vs. k-omega) to practical simulation setup for pump or heat exchanger design
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Theory & Key Formulas

$$\sigma = E\varepsilon$$

フックの法則（弾性域）：応力 $\sigma$（Pa）はひずみ $\varepsilon$（無次元）とヤング率 $E$（Pa）の積。

$$Re = \frac{\rho v L}{\mu}$$

レイノルズ数（流体力学）：慣性力 vs 粘性力の比。配管では $Re \gt 4000$ で乱流。

$$Nu = \frac{h L}{k}$$

ヌッセルト数（熱伝達）：対流熱伝達率 $h$（W/m²K）と熱伝導率 $k$（W/mK）の比。