Optimization • Solver Engine
Lug Optimization Solver & 2D Design Space Exploration
Automated minimum-weight sizing, 2D failure mode mapping, and target margin contouring
1. Overview of the Optimization Challenge
Designing a minimum-weight aerospace lug requires balancing coupled, competing non-linear failure modes. For example:
- Decreasing plate thickness $t$ reduces component weight but drives up the $D/t$ ratio, triggering thin-lug bearing knockdowns (USAF Fig. 9-3) and increasing pin bending moments.
- Increasing bore diameter $D$ increases bearing area $D \cdot t$ and pin strength, but reduces net tensile section $(W - D) \cdot t$ and drives up overall fitting width.
- Increasing width $w$ adds weight rapidly while yielding diminishing returns once bearing or pin shear governs.
The LugCalc™ Optimization Solver eliminates manual trial-and-error by evaluating an exhaustive 2D grid across your design bounds.
2. 2D Design Space Mapping
The user selects two active sweep variables from the primary triad:
| Variable Sweep Pair | Physical Design Scenario | What is Held Constant |
|---|---|---|
| Bore Diameter ($D$) vs. Width ($w$) | Fixed-thickness plate stock or machined forging envelope. | Thickness $t$ held constant |
| Bore Diameter ($D$) vs. Thickness ($t$) | Width constrained by surrounding pocket/clevis envelope. | Width $w$ held constant |
| Lug Width ($w$) vs. Thickness ($t$) | Fixed fastener or standard pin size selected. | Bore diameter $D$ held constant |
3. The Interactive Design Map & Failure Mode Contours
Upon running the solver, LugCalc renders a high-resolution 2D heatmap:
- Target Margin Contour ($MS = MS_{target}$): A solid contour line delineates the boundary between structurally adequate configurations ($MS \ge MS_{target}$) and undersized geometry.
- Failure Mode Color Regions: The 2D map shades every grid coordinate according to which physical failure mode governs at that geometry:
- Bearing / Shear-Out: Dominates when $e/D$ or $t$ is low.
- Net-Section Tension: Dominates when width $w$ is small relative to $D$.
- Transverse Strength: Governs when cross-loads are present and tapers reduce $h_{avg}$.
- Pin Bending (Weak Pin): Dominates in wide female clevises with thin pins.
- Pin Shear: Dominates when high resultant loads shear undersized pins.
- Current Operating Point: Marked with a crosshair, showing exactly where your initial configuration lies within the design space.
- Optimal Minimum-Weight Solution: Highlighted with a star, identifying the exact dimensions that minimize total joint volume while satisfying the target margin.
4. Standard Increment & Manufacturing Constraints
Manufacturing Realism: Aerospace parts are not manufactured with arbitrary infinite precision decimals. The solver includes an Increment Rounding constraint (e.g., $1/16\text{ in}$, $1/32\text{ in}$, or $0.5\text{ mm}$), ensuring recommended optimal dimensions align with standard reamers, drill sizes, and stock sheet gages.