Dynamics: step load on a bar — dynamic amplification factor 2.0

Implicit transient dynamicsPASS · 0.84%

A suddenly applied constant axial force at the free end of a prismatic bar. A continuum bar responds with a sawtooth tip displacement whose peak is exactly twice the static elongation F·L/(E·A) at t = T₁/2 = 2L/c. The 3-D tet10 model with the Newmark trapezoid… show full text

Tolerance:: 5%

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Problem statement

Geometry: Bar L = 1000 mm, section 50 × 50 mm; quadratic tetrahedra (tet10), element size 20 mm.
Material: Steel E = 200 GPa, ν = 0 (the clamped end does not restrain the section), ρ = 7850 kg/m³; consistent mass.
Boundary conditions: One end face fixed; step force 100 kN along the axis on the other face, k(t) ≡ 1 from t = 0, no damping. Newmark β = 1/4, γ = 1/2, Δt = T₁/400, T₁ = 4L/c.
Measured quantity: Maximum tip displacement divided by the static elongation F·L/(E·A) (target 2.0) and the time of the maximum (target T₁/2).

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=0.0 density=7850
primitive box dx=1000 dy=50 dz=50
mesh tet size=20 order=2
fix surface number 1
load surface number 2 force=100000 component=x
solve transient dt=0.000001981161276 tend=0.0009509574123 mass=consistent probes="1000,25,25" outputs=481 frames=0
probe transient_peak dir=x id="peak"
probe transient_peak_time dir=x id="tpeak"
probe transient_displacement dir=x time=0.0009509574123 id="uend"

Results comparison

Reference value	DAF = 2.0000t_пик = T₁/2
Our result	DAF = 1.9839t_пик = 0.3996 мс (T₁/2 = 0.3962 мс)
Deviation	0.84%
Tolerance	5%
Status	PASS · 0.84%
Mesh details	тет10, размер 20 мм (1604 тетр.); 480 шагов (принято 480, резок 0), 480 итераций Ньютона (макс 1/шаг), 2 факторизаций, линейный быстрый путь; ядро 1954 мс, скрипт 10.7 с на нативе

Updated: 2026-10-22 · WebCAE solver