Thermal Coupling
Thermal loads in structural FEM — temperature fields, thermal expansion, and thermo-mechanical analysis.
Temperature changes cause structures to expand or contract. When that expansion is constrained — by supports, by adjacent parts, or by a temperature gradient within the part itself — thermal stresses develop. Thermal coupling in FEM accounts for this effect.
Why thermal stresses matter
A structure that is stress-free at room temperature can develop significant stresses when heated or cooled — even with no external mechanical load. Common situations:
- Engine components cycling between ambient and operating temperature
- Welded joints where the heat-affected zone shrinks on cooling
- Electronics where the PCB and housing have different thermal expansion rates
- Pipe systems constrained at both ends
Two approaches
Uniform temperature change
The simplest case: the entire structure changes temperature by ΔT uniformly. No heat transfer analysis is needed — just specify the reference temperature and the operating temperature in the structural solver.
The thermal strain is:
ε_thermal = α × ΔT
where α is the coefficient of thermal expansion (CTE) of the material.
This approach is correct when the part reaches thermal equilibrium and the temperature is uniform throughout.
Temperature field from heat transfer analysis
When the temperature varies across the structure — due to a heat source, convection, or a transient process — you need to compute the temperature field first with a thermal analysis, then import it into the structural solver as a load.
This two-step process is called sequentially coupled thermo-mechanical analysis (or one-way coupling). The temperature field drives thermal strains; the structural solver computes the resulting stress and deformation.
Material properties needed
For thermal analysis, you need:
- Coefficient of thermal expansion (α) — how much the material expands per degree. Typical values: steel ≈ 12×10⁻⁶ /°C, aluminium ≈ 23×10⁻⁶ /°C.
- Thermal conductivity (λ) — for heat transfer analysis
- Specific heat capacity (c) — for transient thermal analysis
CTE is temperature-dependent for many materials. If you are analyzing a wide temperature range (e.g., cryogenic to 500 °C), use temperature-dependent material data rather than a room-temperature average.
Reference temperature
The reference temperature is the temperature at which the structure has zero thermal stress — typically the manufacturing or assembly temperature. Stresses develop relative to this reference. Getting the reference temperature wrong is a common modelling error that shifts all thermal stresses by a constant offset.
Practical checklist
- Define CTE for all materials in the model
- Set the correct reference temperature
- For non-uniform temperatures: run the thermal analysis first, then import the temperature field
- Check that boundary conditions allow thermal expansion where it should occur — over-constraining a thermally expanding structure produces artificially high stresses
- Validate against simple hand calculations (uniform expansion of a restrained bar) before running complex models