At a glance
Material
Aluminum 6061-T6
E 68900 MPa · ν 0.33 · ρ 2.70 g/cm³
Mass
179.8 g
volume 66596 mm³
Size
120.0 × 80.0 × 60.0 mm
13 CAD faces · typical wall ≈ 3.7 mm
First natural frequency
931.0 Hz
free-free · 12 flexible modes analysed
What was analysed
Stiffness & weight
the part's natural vibration, unsupported; 12 regions compared
Finite element model
8,075 elements
16,370 nodes · size 5.21 mm · quality 0.36
Consistency checks
pass
rigid-body modes ≤ 0.00232 Hz · energy balance 1.0000–1.0000 · model volume vs CAD +0.000 %
Want it stiffer? Add material in the regions listed first below (red in the viewer). Want it lighter without losing stiffness? Take material out of the regions listed second (blue in the viewer). The advice does not depend on the material you picked — only the mass does.
The part is analysed unsupported (free-free): its first vibration modes show where it is flexible and where mass is merely riding along. Every suggestion below is independent of the material chosen — only the Hz values and the mass depend on it.
What to change
Ranked by payoff. Click show on part to light the region up in the 3D viewer below; the bar shows each region's payoff relative to the best one.
Derived from the energy split of the first 3 flexible modes (equal weights). First-order sensitivities: reliable for ranking regions, indicative for sizing; a thin wall in bending gains up to 3× the material-scaling number quoted.
Want it stiffer? Add material hereAdd material here — most frequency per gram
- R12 +X end, -Y end, -Z endshow on part
Add a thicker wall, a rib, a gusset or a fillet here. The best place on the part to add material: it does the most work per gram.R12 (+X end, -Y end, -Z end): carries 13 % of the strain energy but only 3 % of the kinetic energy over the first 3 modes. Adding material here is efficient: +1 % of part mass as thickness in this region raises the first modes' frequencies about 0.53 % (first-order; for a thin wall in bending the gain from thickening is up to 3x this). - R1 -X end, -Y end, -Z endshow on part
Add a thicker wall, a rib, a gusset or a fillet here. About 98 % as effective as the best region.R1 (-X end, -Y end, -Z end): carries 13 % of the strain energy but only 3 % of the kinetic energy over the first 3 modes. Adding material here is efficient: +1 % of part mass as thickness in this region raises the first modes' frequencies about 0.52 % (first-order; for a thin wall in bending the gain from thickening is up to 3x this). - R8 +X end, mid Y, -Z endshow on part
Add a thicker wall, a rib, a gusset or a fillet here. About 90 % as effective as the best region.R8 (+X end, mid Y, -Z end): carries 10 % of the strain energy but only 3 % of the kinetic energy over the first 3 modes. Adding material here is efficient: +1 % of part mass as thickness in this region raises the first modes' frequencies about 0.48 % (first-order; for a thin wall in bending the gain from thickening is up to 3x this). - R4 -X end, mid Y, -Z endshow on part
Add a thicker wall, a rib, a gusset or a fillet here. About 83 % as effective as the best region.R4 (-X end, mid Y, -Z end): carries 10 % of the strain energy but only 3 % of the kinetic energy over the first 3 modes. Adding material here is efficient: +1 % of part mass as thickness in this region raises the first modes' frequencies about 0.44 % (first-order; for a thin wall in bending the gain from thickening is up to 3x this).
Want it lighter without losing stiffness? Remove material hereRemove material here — mass that is riding along
- R3 -X end, -Y end, +Z endshow on part
Thin the wall, pocket it, or add lightening holes here. The mass in this region is mostly riding along: taking some of it out costs essentially no stiffness and can even make the part slightly stiffer.R3 (-X end, -Y end, +Z end): 7.6 % of the part mass, 21 % of the kinetic energy and only 5 % of the strain energy -- it rides along rather than working. Removing 10 % of this region's mass (0.76 % of the part) changes the first modes' frequencies by +0.77 % (first-order): thin it, pocket it, or add lightening holes. - R2 -X end, +Y end, -Z endshow on part
Thin the wall, pocket it, or add lightening holes here. The mass in this region is mostly riding along: taking some of it out costs essentially no stiffness and can even make the part slightly stiffer.R2 (-X end, +Y end, -Z end): 6.7 % of the part mass, 17 % of the kinetic energy and only 3 % of the strain energy -- it rides along rather than working. Removing 10 % of this region's mass (0.67 % of the part) changes the first modes' frequencies by +0.69 % (first-order): thin it, pocket it, or add lightening holes. - R11 +X end, +Y end, -Z endshow on part
Thin the wall, pocket it, or add lightening holes here. The mass in this region is mostly riding along: taking some of it out costs essentially no stiffness and can even make the part slightly stiffer.R11 (+X end, +Y end, -Z end): 6.6 % of the part mass, 17 % of the kinetic energy and only 3 % of the strain energy -- it rides along rather than working. Removing 10 % of this region's mass (0.66 % of the part) changes the first modes' frequencies by +0.69 % (first-order): thin it, pocket it, or add lightening holes. - R9 +X end, -Y end, +Z endshow on part
Thin the wall, pocket it, or add lightening holes here. The mass in this region is mostly riding along: taking some of it out costs essentially no stiffness and can even make the part slightly stiffer.R9 (+X end, -Y end, +Z end): 8.0 % of the part mass, 20 % of the kinetic energy and only 6 % of the strain energy -- it rides along rather than working. Removing 10 % of this region's mass (0.80 % of the part) changes the first modes' frequencies by +0.68 % (first-order): thin it, pocket it, or add lightening holes.
Don't touch — this is where the part bendsLeave alone — the flexible links
- R5 mid X, -Y end, mid Zshow on part
Leave this alone: it is where the part bends. Thinning it would make the whole part noticeably more flexible; if anything, a fillet, rib or doubler here helps.R5 (mid X, -Y end, mid Z): 12 % of the strain energy of the first modes lives here -- the flexible link. Do not thin it; a fillet, rib or doubler here is where stiffness comes from. - R6 mid X, -Y end, -Z endshow on part
Leave this alone: it is where the part bends. Thinning it would make the whole part noticeably more flexible; if anything, a fillet, rib or doubler here helps.R6 (mid X, -Y end, -Z end): 10 % of the strain energy of the first modes lives here -- the flexible link. Do not thin it; a fillet, rib or doubler here is where stiffness comes from. - R7 mid X, +Y end, -Z endshow on part
Leave this alone: it is where the part bends. Thinning it would make the whole part noticeably more flexible; if anything, a fillet, rib or doubler here helps.R7 (mid X, +Y end, -Z end): 7 % of the strain energy of the first modes lives here -- the flexible link. Do not thin it; a fillet, rib or doubler here is where stiffness comes from.
3D viewer
Click the part to identify a region.
Drag to orbit, wheel to zoom, right-drag to pan.
Flexible modes
| Mode | Hz | Character | Motion | Most strain energy | Most kinetic energy | Elements carrying 50 % of ESE | Energy balance |
|---|---|---|---|---|---|---|---|
| 1 | 931.0 | global (3 regions carry half the KE) | Z-dominant (11/21/68 % X/Y/Z) | R6 | R11 | 24.6 % | 1.0000 |
| 2 | 1471.6 | global (3 regions carry half the KE) | Y-dominant (0/58/42 % X/Y/Z) | R8 | R3 | 14.1 % | 1.0000 |
| 3 | 1509.4 | global (2 regions carry half the KE) | Y-dominant (6/68/26 % X/Y/Z) | R1 | R3 | 13.8 % | 1.0000 |
| 4 | 2055.5 | global (3 regions carry half the KE) | Z-dominant (0/16/84 % X/Y/Z) | R7 | R7 | 20.5 % | 1.0000 |
| 5 | 2893.7 | global (3 regions carry half the KE) | Y-dominant (0/62/38 % X/Y/Z) | R8 | R9 | 15.1 % | 1.0000 |
| 6 | 3672.7 | global (4 regions carry half the KE) | Z-dominant (3/13/84 % X/Y/Z) | R4 | R4 | 15.9 % | 1.0000 |
| 7 | 3882.1 | global (4 regions carry half the KE) | Z-dominant (0/37/63 % X/Y/Z) | R5 | R9 | 15.9 % | 1.0000 |
| 8 | 4591.4 | global (2 regions carry half the KE) | Z-dominant (1/2/97 % X/Y/Z) | R2 | R2 | 14.6 % | 1.0000 |
| 9 | 5051.0 | global (2 regions carry half the KE) | Y-dominant (1/95/4 % X/Y/Z) | R9 | R3 | 6.5 % | 1.0000 |
| 10 | 5853.7 | global (5 regions carry half the KE) | Z-dominant (0/34/66 % X/Y/Z) | R5 | R4 | 17.4 % | 1.0000 |
| 11 | 6295.3 | global (3 regions carry half the KE) | Y-dominant (3/78/19 % X/Y/Z) | R10 | R10 | 9.3 % | 1.0000 |
| 12 | 6585.8 | global (4 regions carry half the KE) | Y-dominant (0/59/41 % X/Y/Z) | R5 | R10 | 13.7 % | 1.0000 |
Rigid-body modes found: 6 (|f| ≤ 0.00232 Hz). "Elements carrying 50 % of ESE" = how concentrated the mode's flexibility is — small means one flexible spot, large means a diffuse (global) mode. Energy balance = strain energy over kinetic energy per mode; 1.000 is exact.
Energy by region (% of each mode's total)
Red bars = element strain energy (ESE), green bars = element kinetic energy (EKE). A region high in both carries a local mode of its own; a mode whose strain energy is spread across many regions is global.
Element strain energy (ESE) % by region
| Mode | Hz | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | R9 | R10 | R11 | R12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 931 | 11.6 | 5.3 | 3.1 | 10.6 | 8.5 | 16.2 | 9.4 | 10.5 | 3.5 | 5.0 | 5.2 | 11.2 |
| 2 | 1472 | 10.4 | 1.4 | 3.4 | 15.4 | 12.9 | 11.0 | 7.1 | 16.7 | 5.1 | 5.0 | 1.4 | 10.1 |
| 3 | 1509 | 18.1 | 2.7 | 9.0 | 4.3 | 13.7 | 4.2 | 4.7 | 4.1 | 10.2 | 10.0 | 2.6 | 16.5 |
| 4 | 2055 | 11.1 | 8.3 | 3.2 | 11.1 | 4.5 | 3.7 | 21.3 | 10.8 | 3.9 | 3.6 | 7.8 | 10.7 |
| 5 | 2894 | 9.2 | 3.6 | 11.4 | 11.8 | 9.4 | 4.2 | 4.6 | 12.5 | 12.3 | 9.6 | 3.6 | 7.8 |
| 6 | 3673 | 12.9 | 9.5 | 2.3 | 14.2 | 4.0 | 2.8 | 12.2 | 13.4 | 2.4 | 4.9 | 9.4 | 12.0 |
| 7 | 3882 | 6.9 | 7.8 | 4.0 | 10.5 | 20.1 | 6.5 | 6.2 | 10.2 | 5.2 | 9.1 | 7.7 | 5.8 |
| 8 | 4591 | 4.0 | 20.5 | 0.2 | 15.8 | 0.9 | 5.0 | 13.5 | 15.4 | 0.2 | 0.7 | 19.5 | 4.1 |
| 9 | 5051 | 7.0 | 0.5 | 26.3 | 0.7 | 15.4 | 1.9 | 0.6 | 0.6 | 27.2 | 14.0 | 0.5 | 5.3 |
| 10 | 5854 | 8.5 | 10.8 | 4.8 | 8.7 | 15.9 | 3.5 | 6.5 | 8.6 | 6.2 | 7.3 | 10.7 | 8.5 |
| 11 | 6295 | 11.0 | 3.2 | 12.0 | 3.3 | 18.0 | 4.2 | 1.7 | 3.2 | 10.8 | 19.8 | 3.3 | 9.6 |
| 12 | 6586 | 9.8 | 4.9 | 10.6 | 5.9 | 15.4 | 6.2 | 5.5 | 5.9 | 9.6 | 12.6 | 4.9 | 8.6 |
Element kinetic energy (EKE) % by region
| Mode | Hz | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | R9 | R10 | R11 | R12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 931 | 2.8 | 23.5 | 13.3 | 4.6 | 4.5 | 0.4 | 2.4 | 4.4 | 12.6 | 5.6 | 23.6 | 2.2 |
| 2 | 1472 | 2.8 | 15.7 | 20.6 | 2.8 | 2.5 | 4.5 | 6.4 | 2.8 | 20.6 | 3.1 | 15.6 | 2.8 |
| 3 | 1509 | 4.1 | 11.6 | 27.9 | 1.7 | 3.8 | 0.9 | 1.7 | 1.5 | 26.3 | 5.2 | 11.4 | 3.9 |
| 4 | 2055 | 2.2 | 18.1 | 5.1 | 8.7 | 2.8 | 1.5 | 25.9 | 8.1 | 5.3 | 2.2 | 18.0 | 2.2 |
| 5 | 2894 | 1.3 | 5.0 | 23.5 | 6.0 | 8.6 | 2.6 | 10.4 | 5.8 | 25.0 | 5.7 | 4.8 | 1.1 |
| 6 | 3673 | 8.0 | 15.9 | 5.5 | 16.8 | 2.2 | 0.5 | 2.8 | 15.8 | 5.4 | 3.1 | 16.0 | 7.9 |
| 7 | 3882 | 5.8 | 11.6 | 14.0 | 9.7 | 5.5 | 1.2 | 5.1 | 9.2 | 14.8 | 6.5 | 11.5 | 5.0 |
| 8 | 4591 | 1.3 | 27.8 | 0.4 | 13.3 | 0.4 | 1.5 | 13.4 | 12.9 | 0.4 | 0.4 | 26.9 | 1.4 |
| 9 | 5051 | 1.3 | 0.8 | 36.9 | 0.7 | 10.3 | 0.2 | 0.2 | 0.7 | 35.1 | 12.4 | 0.9 | 0.5 |
| 10 | 5854 | 4.3 | 7.2 | 8.5 | 13.1 | 8.0 | 7.5 | 12.0 | 12.7 | 8.5 | 6.3 | 7.2 | 4.4 |
| 11 | 6295 | 5.7 | 4.8 | 15.6 | 3.7 | 19.9 | 0.7 | 0.9 | 3.6 | 15.0 | 22.2 | 4.8 | 3.2 |
| 12 | 6586 | 7.9 | 4.8 | 13.0 | 8.5 | 10.9 | 1.2 | 8.3 | 8.3 | 13.0 | 13.3 | 4.6 | 6.0 |
Average (ESE+EKE)/2 % by region — self-contained modes stand out
| Mode | Hz | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | R9 | R10 | R11 | R12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 931 | 7.2 | 14.4 | 8.2 | 7.6 | 6.5 | 8.3 | 5.9 | 7.4 | 8.1 | 5.3 | 14.4 | 6.7 |
| 2 | 1472 | 6.6 | 8.5 | 12.0 | 9.1 | 7.7 | 7.7 | 6.7 | 9.7 | 12.9 | 4.0 | 8.5 | 6.5 |
| 3 | 1509 | 11.1 | 7.1 | 18.5 | 3.0 | 8.8 | 2.5 | 3.2 | 2.8 | 18.2 | 7.6 | 7.0 | 10.2 |
| 4 | 2055 | 6.6 | 13.2 | 4.2 | 9.9 | 3.6 | 2.6 | 23.6 | 9.5 | 4.6 | 2.9 | 12.9 | 6.4 |
| 5 | 2894 | 5.2 | 4.3 | 17.4 | 8.9 | 9.0 | 3.4 | 7.5 | 9.2 | 18.7 | 7.7 | 4.2 | 4.5 |
| 6 | 3673 | 10.4 | 12.7 | 3.9 | 15.5 | 3.1 | 1.7 | 7.5 | 14.6 | 3.9 | 4.0 | 12.7 | 10.0 |
| 7 | 3882 | 6.3 | 9.7 | 9.0 | 10.1 | 12.8 | 3.9 | 5.7 | 9.7 | 10.0 | 7.8 | 9.6 | 5.4 |
| 8 | 4591 | 2.7 | 24.2 | 0.3 | 14.5 | 0.6 | 3.2 | 13.5 | 14.2 | 0.3 | 0.5 | 23.2 | 2.8 |
| 9 | 5051 | 4.2 | 0.7 | 31.6 | 0.7 | 12.8 | 1.1 | 0.4 | 0.6 | 31.1 | 13.2 | 0.7 | 2.9 |
| 10 | 5854 | 6.4 | 9.0 | 6.6 | 10.9 | 12.0 | 5.5 | 9.3 | 10.7 | 7.3 | 6.8 | 9.0 | 6.5 |
| 11 | 6295 | 8.3 | 4.0 | 13.8 | 3.5 | 19.0 | 2.4 | 1.3 | 3.4 | 12.9 | 21.0 | 4.1 | 6.4 |
| 12 | 6586 | 8.9 | 4.8 | 11.8 | 7.2 | 13.2 | 3.7 | 6.9 | 7.1 | 11.3 | 13.0 | 4.8 | 7.3 |
Regions
| Region | Where | CAD faces (by boundary area) | Elements | Mass % | Wall proxy mm | Extent mm |
|---|---|---|---|---|---|---|
| R1 show | -X end, -Y end, -Z end centre (19.46, 10.54, 4.61) | F3 (1068.5), F5 (928.0), F2 (697.7) | 553 | 9.8 | 3.8 | 40.8 × 29.0 × 20.5 |
| R2 show | -X end, +Y end, -Z end centre (22.32, 63.81, 2.0) | F5 (1115.7), F3 (1114.8), F4 (175.0) | 860 | 6.7 | 3.42 | 41.8 × 30.8 × 3.6 |
| R3 show | -X end, -Y end, +Z end centre (26.87, 2.04, 49.82) | F2 (1271.5), F6 (1259.8), F7 (235.0) | 445 | 7.6 | 3.53 | 57.1 × 3.0 × 24.6 |
| R4 show | -X end, mid Y, -Z end centre (30.97, 42.25, 1.93) | F3 (1363.4), F5 (1341.0), F1 (70.5) | 1060 | 8.1 | 3.82 | 58.3 × 30.2 × 5.1 |
| R5 show | mid X, -Y end, mid Z centre (40.25, 3.17, 27.66) | F2 (1492.1), F6 (1410.4), F11 (219.4) | 520 | 9.9 | 3.81 | 67.7 × 19.9 × 28.7 |
| R6 show | mid X, -Y end, -Z end centre (59.89, 14.63, 5.11) | F3 (1194.9), F5 (962.3), F2 (573.7) | 716 | 11.7 | 3.84 | 42.7 × 34.0 × 19.6 |
| R7 show | mid X, +Y end, -Z end centre (60.92, 62.34, 1.95) | F5 (1170.5), F3 (1153.6), F4 (140.0) | 705 | 7.0 | 3.77 | 38.6 × 35.1 × 3.0 |
| R8 show | +X end, mid Y, -Z end centre (88.26, 41.93, 1.97) | F5 (1318.8), F3 (1302.2), F8 (65.5) | 1030 | 7.9 | 3.84 | 59.4 × 30.5 × 5.8 |
| R9 show | +X end, -Y end, +Z end centre (88.76, 2.02, 49.89) | F2 (1332.1), F6 (1327.1), F7 (245.0) | 449 | 8.0 | 3.58 | 61.5 × 3.0 × 22.6 |
| R10 show | +X end, -Y end, mid Z centre (95.76, 2.0, 26.13) | F2 (1295.7), F6 (1241.3), F8 (100.9) | 370 | 7.6 | 3.82 | 51.3 × 3.0 × 26.0 |
| R11 show | +X end, +Y end, -Z end centre (98.79, 63.45, 1.98) | F3 (1114.5), F5 (1075.2), F4 (165.0) | 840 | 6.6 | 3.41 | 40.2 × 31.9 × 3.6 |
| R12 show | +X end, -Y end, -Z end centre (100.39, 11.85, 3.46) | F3 (1135.0), F5 (947.4), F2 (537.2) | 527 | 9.1 | 3.79 | 40.2 × 30.1 × 13.7 |
Regions are automatic clusters of the finite element model (k = 12); "CAD faces" are the STEP face numbers with the boundary area each contributes (mm²).
Sensitivity by region
"Add material" = first-mode frequency gain per +1 % of part mass added in the region (efficiency). "Remove 10 %" = first-mode frequency change when 10 % of the region's mass is removed (positive = frequency rises). Weighted columns use the first 3 modes equally.
| Region | Mass % | ESE % (m1) | EKE % (m1) | Add material: Δf % per +1 % mass (m1) | Add material (weighted) | Remove 10 %: Δf % (m1) | Remove 10 % (weighted) | Mass saved % |
|---|---|---|---|---|---|---|---|---|
| R1 -X end, -Y end, -Z end | 9.8 | 11.6 | 2.8 | +0.45 | +0.52 | -0.44 | -0.51 | 0.98 |
| R2 -X end, +Y end, -Z end | 6.7 | 5.3 | 23.5 | -1.36 | -1.03 | +0.91 | +0.69 | 0.67 |
| R3 -X end, -Y end, +Z end | 7.6 | 3.1 | 13.3 | -0.67 | -1.02 | +0.51 | +0.77 | 0.76 |
| R4 -X end, mid Y, -Z end | 8.1 | 10.6 | 4.6 | +0.37 | +0.44 | -0.30 | -0.35 | 0.81 |
| R5 mid X, -Y end, mid Z | 9.9 | 8.5 | 4.5 | +0.20 | +0.41 | -0.20 | -0.41 | 0.99 |
| R6 mid X, -Y end, -Z end | 11.7 | 16.2 | 0.4 | +0.67 | +0.36 | -0.79 | -0.43 | 1.17 |
| R7 mid X, +Y end, -Z end | 7.0 | 9.4 | 2.4 | +0.50 | +0.25 | -0.35 | -0.18 | 0.70 |
| R8 +X end, mid Y, -Z end | 7.9 | 10.5 | 4.4 | +0.38 | +0.48 | -0.30 | -0.38 | 0.79 |
| R9 +X end, -Y end, +Z end | 8.0 | 3.5 | 12.6 | -0.57 | -0.84 | +0.46 | +0.68 | 0.80 |
| R10 +X end, -Y end, mid Z | 7.6 | 5.0 | 5.6 | -0.04 | +0.13 | +0.03 | -0.10 | 0.76 |
| R11 +X end, +Y end, -Z end | 6.6 | 5.2 | 23.6 | -1.40 | -1.05 | +0.92 | +0.69 | 0.66 |
| R12 +X end, -Y end, -Z end | 9.1 | 11.2 | 2.2 | +0.49 | +0.53 | -0.45 | -0.48 | 0.91 |
Strain-energy hot spots
Per mode, the smallest set of elements that carries 50 % and 80 % of the strain energy. Elements in the 80 % set of every one of the first 3 modes form the core stiffness zone (18.2 % of elements, 28.1 % of mass) — change several modes at once by working there.
| Mode | Hz | Elements for 50 % ESE | Elements for 80 % ESE |
|---|---|---|---|
| 1 | 931.0 | 1986 (24.6 %) | 4302 (53.3 %) |
| 2 | 1471.6 | 1142 (14.1 %) | 3006 (37.2 %) |
| 3 | 1509.4 | 1111 (13.8 %) | 2783 (34.5 %) |
| 4 | 2055.5 | 1657 (20.5 %) | 3986 (49.4 %) |
| 5 | 2893.7 | 1216 (15.1 %) | 3119 (38.6 %) |
| 6 | 3672.7 | 1283 (15.9 %) | 3453 (42.8 %) |
| 7 | 3882.1 | 1281 (15.9 %) | 3529 (43.7 %) |
| 8 | 4591.4 | 1180 (14.6 %) | 3058 (37.9 %) |
| 9 | 5051.0 | 526 (6.5 %) | 1251 (15.5 %) |
| 10 | 5853.7 | 1402 (17.4 %) | 3562 (44.1 %) |
| 11 | 6295.3 | 747 (9.3 %) | 2166 (26.8 %) |
| 12 | 6585.8 | 1104 (13.7 %) | 3276 (40.6 %) |
Scope and limits
- One solid body, one isotropic linear material, no supports or loads (free-free), no damping. The part's STEP geometry is converted to mm and meshed automatically; a mesh-size policy keeps run time bounded, so very large or very intricate parts are coarsened.
- Results come from a finite element normal-modes analysis and energy methods (element strain and kinetic energy per mode). Sensitivities are first-order: exact for infinitesimal changes, indicative for real ones. Nothing here replaces a re-analysis of the changed part.
- Thin-walled parts are analysed with solid elements; the report notes when that approximation is coarse.