Staged excavation: removing layers of a loaded column — elastic rebound
Birth and death of elements (staged analysis)PASS · 0.17%A 3 m column stands under its own weight; its top layer is excavated (the body dies), then the next one. The force each dying body exerted on the rest is released gradually inside the stage, and the lower bodies rebound: the displacements after each excavation equal the closed form for the shorter column, i.e. the process is elastically reversible.A 3 m column stands under its own weight; its top layer is excavated (the body dies), then the next one. The force each dying body exerted on the rest is released gradually inside the stage, and the lower bodies rebound: the displacements after each excavation… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Three bodies 500 × 500 × 1000 mm stacked along z, tetrahedral mesh (P1) of size 125 mm glued into one conformal mesh; base face fixed.
- Material
- E = 20 GPa, ν = 0, ρ = 2400 kg/m³; gravity 9.81 m/s² along −z.
- Boundary conditions
- Stage 1: all three bodies. Stage 2: body 3 dies. Stage 3: body 2 dies. Dead pressure, geometric nonlinearity on, native solver.
- Measured quantity
- Vertical displacement of the planes z = 1 m and z = 2 m (mean of their nodes) at the end of each stage against −(ρg/E)(H·z − z²/2), H the remaining height.
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=2e10 nu=0 density=2400
primitive box dx=500 dy=500 dz=1000
primitive box dx=500 dy=500 dz=1000 oz=1000
primitive box dx=500 dy=500 dz=1000 oz=2000
mesh tet size=125 bonding=1 glue=full
fix surface number 5
load accel=-9.81 component=z
nlgeom on pressure=dead
stage add name=initial
stage add name=excavation1 deactivate=body3
stage add name=excavation2 deactivate=body2
solve static
stage view 1
probe displacement_z at z=1000 id="u1_1000"
probe displacement_z at z=2000 id="u1_2000"
stage view 2
probe displacement_z at z=1000 id="u2_1000"
probe displacement_z at z=2000 id="u2_2000"
stage view 3
probe displacement_z at z=1000 id="u3_1000"Results comparison
| Reference value | u_z (мм): -0.002943-0.004709-0.001766-0.002354-0.0005886 |
| Our result | -0.002942-0.004708-0.001765-0.002354-0.0005876 (худшее отклонение 0.169 %) |
| Deviation | 0.17% |
| Tolerance | 5% |
| Status | PASS · 0.17% |
| Mesh details | тет4 (P1), размер 125 мм (1805 тетр.), сборка из склеенных тел; 3 стадий, 18 шагов, 18 итераций Ньютона; мягкость неактивных элементов 1e-6; 5.0 с на скрипт (сетка + расчёт) на нативе |
Updated: 2026-10-22 · WebCAE solver