Explicit dynamics: HEX8 cantilever under self-weight (Euler-Bernoulli)
Explicit dynamics (HEX8 bending)PASS · 1.7%A slender cantilever (span/height 20) is meshed with 8 layers of one-point HEX8 elements through the thickness and loaded by its own weight applied as a step. The time average of the tip deflection over four fundamental periods equals the static deflection of a linear system under a step load; it is compared with the Euler-Bernoulli value plus the Timoshenko shear term. The energy of the hourglass control must stay below 10 % of the internal energy (with a single layer the bending is carried by the hourglass control alone and the solver warns).A slender cantilever (span/height 20) is meshed with 8 layers of one-point HEX8 elements through the thickness and loaded by its own weight applied as a step. The time average of the tip deflection over four fundamental periods equals the static deflection of… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Cantilever 1000 × 50 × 50 mm, 60 × 1 × 8 HEX8 elements; the face x = 0 is clamped.
- Material
- Steel: E = 200 GPa, nu = 0.3, rho = 7850 kg/m³.
- Boundary conditions
- Gravity 9.81 m/s² along -z switched on at t = 0 (step load); no damping; time-step factor 0.9 of the strict element limit; end time four fundamental periods.
- Measured quantity
- Time average of the tip z-displacement over [0, 4T1] against w L^4/(8 E I) + w L^2/(2 kappa G A) (kappa = 10(1+nu)/(12+11 nu)); hourglass-to-internal energy ratio (peak to peak).
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=2e11 nu=0.3 density=7850
box dx=1000 dy=50 dz=50
mesh hex nx=60 ny=1 nz=8
explicit endTime=0.098113678 dtScale=0.9 saveStride=700 bulkQ1=0 bulkQ2=0
bc explicit_fixed surface number 1
bc gravity vector="0 0 -9.81"
solve explicit
probe explicit_displacement_z x=1000 time=0 timeEnd=0.098113678 id="tip"
probe explicit_hourglass_ratio id="hg"
probe explicit_steps id="steps"
probe explicit_dt_min id="dt"Results comparison
| Reference value | δ_tip = wL⁴/(8EI) + wL²/(2κGA) = 0.23161 mm |
| Our result | δ_tip = 0.23556 mm (time average over 4 periods), E_hg/E_int = 0.37 % |
| Deviation | 1.7% |
| Tolerance | 5% |
| Status | PASS · 1.7% |
| Element family | Solid element |
| Mesh details | 60×1×8 HEX8 (structured box, native), 103780 steps, Δt = 0.150 µs;: webcae_solve (native) |
Updated: 2026-10-21 · WebCAE solver