Optimization — Let the Computer Find the Shape

You say where loads come in and supports attach; the computer removes material that isn't earning its keep.

Method	Plain-language identity	Question it answers
Topology (SIMP)	carves material away where stress is low	"What's the lightest skeleton that carries this load?"
Size	scales thicknesses/areas up or down	"How thin can this plate be at the same safety?"
Shape	moves boundary points via mesh morphing	"Can this hole shape cut the peak stress?"
Parameter sweep	tries a list of design points	"Which of these five thicknesses is best?"

Use when	Don't use for
Weight reduction — aerospace, automotive, any moving part	When geometry is fixed (use Static Structural)
Design exploration — find good starting shapes before detailing	Final detailed analysis (use other domains)
Comparing options — parameter sweep over discrete choices	Single deterministic check (use Static Structural)

Problem Type	Industry	Example
Lightweight design	Aerospace	Bracket topology optimization
Structural redesign	Automotive	Engine mount weight reduction
Support structure	Additive Manufacturing	Optimal print orientation
Thermal optimization	Electronics	Heat sink shape optimization
Material distribution	Civil/Structural	Truss layout optimization

Result	Meaning
Material layout	Where material should remain
Volume fraction	Target % of original volume
Compliance	Inverse of stiffness (lower = stiffer)

Result	Meaning
Parameter values	Each design point tested
Max stress	Peak stress for each point
Max deflection	Peak deflection for each point

Case	Reference	Error
Cantilever topology	Published	< 5%
Parameter sweep	Exact	Machine precision

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