Design Analysis and Modeling
Models Are Arguments, Not Answers
Analysis exists to predict behavior before you build. Candidates should recognize the main families: closed-form analytical models (equations from physics), empirical models (fits to test data), numerical models (finite element, computational fluid dynamics), and physical scale models.
Core principles:
- Free-body diagrams are the foundation of any structural or mechanical analysis. If a question describes forces, sketch them.
- Conservation laws - mass, energy, momentum - bound every answer. Sanity-check results against them.
- Factor of safety = failure strength ÷ expected stress (or allowable load ÷ applied load). A factor below 1 means predicted failure.
- Units and dimensional consistency catch more errors than any other single check.
- Model validity - every model has a domain. A linear model fails past yield; a lumped thermal model fails when internal gradients are large.
Traps
- Confusing stress (force per area) with force, and strength (a material property) with stress (a response to load).
- Applying a factor of safety to the load versus the strength - both are common conventions, but the question usually states which; read it.
- Treating a simulation as ground truth. Unvalidated models are hypotheses; mesh convergence and boundary-condition sensitivity matter.
- Ignoring worst-case combinations: maxima rarely coincide, but the design must survive the cases the requirements name.
Rule of Thumb
Estimate first, compute second. A back-of-envelope answer (order of magnitude) tells you whether the detailed result is plausible. If your FEA says 3 MPa and your hand calculation says 300 MPa, believe neither until reconciled.
Worked example: A bracket carries 2 kN over a 100 mm² cross-section → stress = 2000 N / 100 mm² = 20 MPa. If the material yields at 200 MPa, the factor of safety is 200/20 = 10. If the requirement is a factor of 3, the design passes with margin - but check buckling and fatigue separately, since static yield is only one failure mode.