Staged construction: a column built in layers under its own weight
Birth and death of elements (staged analysis)PASS · 0.12%A 4 m column is erected as four stacked 1 m layers (separate bodies). Each layer is born stress-free on the already settled configuration of the layers below and carries its own weight from then on; the soft-element algorithm keeps unborn layers in the mesh at 1e-6 of their stiffness. On every stage the settlement of the column equals the closed form for a column of the current height, and the displacements are cumulative from stage to stage.A 4 m column is erected as four stacked 1 m layers (separate bodies). Each layer is born stress-free on the already settled configuration of the layers below and carries its own weight from then on; the soft-element algorithm keeps unborn layers in the mesh at… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Four 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 (free sides, uniaxial stress), ρ = 2400 kg/m³; gravity 9.81 m/s² along −z, acting on a body only while it is active.
- Boundary conditions
- Stage 1: body 1. Stages 2–4: bodies 2, 3, 4 are born at the start of their stage. Dead pressure, geometric nonlinearity on, native solver.
- Measured quantity
- Vertical displacement of the plane z = z₀ (mean of its nodes) at the end of each stage against −(ρg/E)(H·z₀ − z₀²/2), H the current height of the column.
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
primitive box dx=500 dy=500 dz=1000 oz=3000
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=L1
stage add name=L2 activate=body2
stage add name=L3 activate=body3
stage add name=L4 activate=body4
solve static
stage view 1
probe displacement_z at z=1000 id="u1_1000"
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=2000 id="u3_2000"
probe displacement_z at z=3000 id="u3_3000"
stage view 4
probe displacement_z at z=1000 id="u4_1000"
probe displacement_z at z=4000 id="u4_4000"Results comparison
| Reference value | u_z (мм), стадии 1–4: -0.0005886-0.001766-0.002354-0.004709-0.005297-0.00412-0.009418 |
| Our result | -0.0005879-0.001765-0.002353-0.004707-0.005295-0.004119-0.009415 (худшее отклонение 0.118 %) |
| Deviation | 0.12% |
| Tolerance | 5% |
| Status | PASS · 0.12% |
| Mesh details | тет4 (P1), размер 125 мм (2492 тетр.), сборка из склеенных тел; 4 стадий, 24 шагов, 24 итераций Ньютона; мягкость неактивных элементов 1e-6; 10.2 с на скрипт (сетка + расчёт) на нативе |
Updated: 2026-10-22 · WebCAE solver