Thermoelasticity: axially restrained bar under uniform ΔT = 80 K
Coupled transient thermoelasticityPASS · 0%A prismatic bar with roller-clamped ends (u_x = 0 on both end faces, free transverse Poisson expansion) starts at a uniform temperature T₀ = 100 °C above the stress-free reference T_ref = 20 °C (ΔT = 80 K). The dynamic solver initializes in static thermoelastic equilibrium without spurious impact waves (kinetic energy < 10⁻²⁷ J) and reproduces the exact uniaxial thermal stress σ_xx = −E·α·ΔT = −192.00 MPa.A prismatic bar with roller-clamped ends (u_x = 0 on both end faces, free transverse Poisson expansion) starts at a uniform temperature T₀ = 100 °C above the stress-free reference T_ref = 20 °C (ΔT = 80 K). The dynamic solver initializes in static thermoelasti… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Prismatic bar 60 × 6 × 6 mm; quadratic tetrahedra (tet10), element size 2 mm (1419 elements).
- Material
- Steel: E = 200 GPa, ν = 0.3, ρ = 7800 kg/m³, α = 1.2 × 10⁻⁵ K⁻¹, k = 40 W/(m·K), c_p = 460 J/(kg·K).
- Boundary conditions
- Axial restraint u_x = 0 on end faces (surface number 1 and surface number 2), rigid-body transverse restraints u_y = 0 on surface number 3 and u_z = 0 on surface number 5. Uniform initial temperature T₀ = 100 °C, reference T_ref = 20 °C (ΔT = 80 K).
- Measured quantity
- Mid-bar axial stress σ_xx at (30, 3, 3) mm compared against −E·α·ΔT = −192.00 MPa and maximum kinetic energy over 100 dynamic steps.
WebCAE Terminal
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units mm
material E=200000000000 nu=0.3 density=7800 kappa=40 specific_heat=460 alpha=0.000012
primitive box dx=60 dy=6 dz=6
mesh tet size=2 order=2
fix surface number 1 component=x
fix surface number 2 component=x
fix surface number 3 component=y
fix surface number 5 component=z
solve thermoelastic transient mode=dynamic dt=1e-6 tend=1e-4 t0=100 tref=20 probes="30,3,3" frames=2 outputs=200
probe transient_stress dir=x id="sxx"
probe transient_energy_max kind=kinetic id="ke"Results comparison
| Reference value | σ_xx = −192.000 MPaE_kin,max = 0 J |
| Our result | σ_xx = −192.000 MPaE_kin,max = 1.32e-28 J |
| Deviation | 0% |
| Tolerance | 5% |
| Status | PASS · 0% |
| Mesh details | tet10, size 2 mm (1419 tets); 100 steps of Δt = 1 µs, linear fast path |
Updated: 2026-10-27 · version not recorded