Dynamics: seismic base acceleration and RBE2 kinematic constraints in 3D solids

Implicit transient dynamicsPASS · 0.05%

Implicit Newmark transient dynamics of a 3D solid cantilever under step base acceleration a₀ = 1 m/s² (−M·ι·a₀(t)) and under remote tip force/moment transmitted through an RBE2 rigid spider (projected via T₀ᵀ M T₀ and T₀ᵀ K T₀). Both web WASM and native solver… show full text

Tolerance:: 5%

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Problem statement

Geometry: Prismatic cantilever 1000 × 50 × 50 mm; quadratic tetrahedra (tet10), element size 50 mm (150 elements).
Material: Steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³.
Boundary conditions: Root face (surface number 1) fixed; step base acceleration a_z = 1.0 m/s² (and companion RBE2 remote load F_z = −100 N at tip centroid 1000, 25, 25 mm on surface number 2). Newmark β = 1/4, γ = 1/2, Δt = 0.5 ms, t_end = 50 ms.
Measured quantity: Peak relative tip deflection divided by static deflection u_st = ρA·a₀·L⁴/(8EI) (analytical continuum step DAF ≈ 1.945) and energy balance drift.

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=200000000000 nu=0.3 density=7850
primitive box dx=1000 dy=50 dz=50
mesh tet size=50 order=2
fix surface number 1
solve transient dt=0.0005 tend=0.05 base_accel="0,0,1" rayleigh b=1e-4 probes="1000,25,25" outputs=101 frames=4
probe transient_peak dir=z id="peak"
probe transient_energy_drift id="drift"

Results comparison

Reference value	DAF = 1.945 (u_st = 2.355e-5 м)energy drift ≤ 1e-8
Our result	DAF = 1.946 (u_peak = −4.583e-5 м)energy drift 1.2e-10
Deviation	0.05%
Tolerance	5%
Status	PASS · 0.05%
Mesh details	tet10, size 50 mm (150 tets); 101 steps of Δt = 0.5 ms, проекция связей T₀ (10 метрик constraintStats)

Updated: 2026-10-27 · version not recorded