Explicit dynamics: longitudinal wave speed in a HEX8 bar
Explicit dynamics (wave propagation)PASS · 0%A velocity step travels along a 1 m steel bar meshed with 100 one-point HEX8 elements. The wave speed is found from the arrival times of the half-height of the front at two sections and compared with the 1D bar speed sqrt(E/rho). Poisson ratio is zero, so the 3D element sound speed sqrt((K + 4/3 G)/rho) equals the bar speed.A velocity step travels along a 1 m steel bar meshed with 100 one-point HEX8 elements. The wave speed is found from the arrival times of the half-height of the front at two sections and compared with the 1D bar speed sqrt(E/rho). Poisson ratio is zero, so the… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Bar 1000 × 40 × 40 mm, 100 × 1 × 1 HEX8 elements (structured), hourglass control on (stiffness form, default coefficient).
- Material
- Steel: E = 200 GPa, nu = 0, rho = 7850 kg/m³.
- Boundary conditions
- The face x = 0 moves along x with a velocity ramp over 20 elements to 1 m/s; the far end and lateral faces are free; time-step factor 0.9 of the strict element limit.
- Measured quantity
- Arrival times of the level 0.5 m/s of the x-velocity at x = 250 and 750 mm; c = 500 mm / (t2 - t1).
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 density=7850
box dx=1000 dy=40 dz=40
mesh hex nx=100 ny=1 nz=1
explicit endTime=0.00021198426 dtScale=0.9 saveStride=1 bulkQ1=0 bulkQ2=0
bc explicit_motion surface number 1 direction 1 0 0 velocity="0:0;0.000039623226:1000;0.00021198426:1000"
solve explicit
probe explicit_arrival_time_x x=250 level=0.5 id="t1"
probe explicit_arrival_time_x x=750 level=0.5 id="t2"
probe explicit_steps id="steps"
probe explicit_dt_min id="dt"Results comparison
| Reference value | c = √(E/ρ) = 5047.54 m/s |
| Our result | c = 5044.94 m/s |
| Deviation | 0% |
| Tolerance | 5% |
| Status | PASS · 0% |
| Element family | Solid element |
| Mesh details | 100×1×1 HEX8 (structured box, native), 119 steps, Δt = 1.585 µs;: webcae_solve (native) |
Updated: 2026-10-21 · WebCAE solver