Solid cantilever under a tip point force — length-convention consistency

StaticPASS · 2.02%

Closes a specific gap in the corpus: before 2026-07-29 every solid case was loaded by PRESSURE, and pressure on a solid is scale-invariant (delta/L = p/E), which masks a mixed length convention. A force given in newtons is not scale-invariant: geometry in mm with a modulus in Pa moves the deflection by exactly 1e6. The same physical problem is therefore solved twice — in mm/MPa/N and in m/Pa/N — and the two answers must agree after conversion.

Tolerance:: 5%

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Problem statement

Geometry: Cantilever 1600 x 100 x 100, hex8 mesh 96 x 6 x 6, fully fixed at x = 0. Solved twice: (a) L = 1600 mm, E = 200000 MPa, F = 1000 N; (b) L = 1.6 m, E = 200e9 Pa, F = 1000 N.
Material: Isotropic elastic, E = 200 GPa, nu = 0.3.
Boundary conditions: All three translations fixed on the root face x = 0; a total transverse force of 1000 N applied on the free end face in -z, distributed over the face nodes by tributary weights (a total FORCE in newtons, not a pressure).
Measured quantity: Mean |uz| over the free end face against delta = F L^3/(3 E I) + F L/(kappa G A) = 0.821696 mm; and the ratio delta(m)*1000 / delta(mm) = 1 exactly.

WebCAE Terminal

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

units mm
material E=200000 nu=0.3
primitive box dx=1600 dy=100 dz=100
mesh hex size=50
fix surface number 1
load surface number 2 force=-1000 component=z
solve
probe displacement_magnitude at=1600,50,50

Results comparison

Reference value	δ = 0.8216960000000001 мм (Тимошенко)
Our result	0.8050619427865434 мм (мм/МПа/Н), 0.8050619427682074 мм (м/Па/Н → мм)
Deviation	2.02%
Tolerance	5%
Status	PASS · 2.02%
Element family	Solid element
Mesh details	hex8 96×6×6, консоль 1600×100×100 мм, ТОЧЕЧНАЯ сила 1000 Н на свободном торце; одна и та же задача решена в мм/МПа/Н и в м/Па/Н, sparse-путь

Updated: 2026-10-19 · WebCAE solver