Coupled Thermal-Structural Analysis

What Is It?

Coupled thermal-structural analysis is the process of linking the thermal analysis (which predicts the temperature field) with the structural analysis (which predicts the stress and deformation) to assess the structural consequences of the thermal response. The temperature field from the thermal model becomes a load in the structural model — the thermal strain drives the stress and distortion. The coupling may be one-way (thermal results feed into structural, but structural does not affect thermal) or two-way (thermal and structural affect each other). Understanding the coupling approach and when each is appropriate is essential for credible thermal-structural analysis.

Why It Matters

The temperature field is a structural load when thermal expansion matters. A thermal analysis that produces a temperature field but does not feed it into a structural analysis is incomplete — it answers "what is the temperature?" but not "what does the temperature do to the structure?" The coupled thermal-structural analysis connects the two — the temperature becomes a thermal strain, the thermal strain becomes a stress, and the stress is assessed against the structural capability. The coupling must be done correctly — the temperature mapping, the reference temperature, the material properties and the boundary conditions must all be consistent between the thermal and structural models.

The temperature field is a structural load when thermal expansion matters. The thermal analysis produces the load; the structural analysis predicts the response. The coupling between them — the mapping, the reference temperature, the properties — must be correct.

Sequential (One-Way) Coupling

In sequential (one-way) coupling, the thermal analysis is run first, producing the temperature field. The temperature field is then mapped onto the structural model as a thermal load. The structural analysis is run with the temperature load, producing the thermal stress and distortion. The structural deformation does not feed back into the thermal analysis. This is the standard approach for most thermal-structural analyses — it is appropriate when the structural deformation does not significantly affect the heat transfer. Most thermal stress and distortion problems are adequately handled by one-way coupling.

One-way (sequential) coupling:

Thermal analysis → Temperature field T(x,y,z)
                        ↓ (mapping)
Structural analysis → Thermal strain ε = α(T − T_ref)
                     → Stress σ and deformation u

No feedback: structural deformation does not affect thermal

When One-Way Coupling Is Sufficient

• The structural deformation is small — does not change the geometry enough to affect the heat transfer
• The thermal contact resistance does not change significantly with deformation
• The convection and radiation boundaries are not significantly altered by the deformation
• The thermal analysis is steady state (no time-dependent coupling needed)
• The temperature-dependent properties are not affected by the stress state

Two-Way Coupling

In two-way coupling, the thermal and structural analyses are solved simultaneously, with each affecting the other. The structural deformation changes the geometry, which changes the heat transfer. The thermal contact resistance changes with the contact pressure, which changes with the deformation. The convection or radiation boundary may change if the surface moves. Two-way coupling is needed when the structural deformation is large enough to affect the thermal response. Examples: thermal contact problems where the contact pressure changes, radiation problems where the view factors change with deformation, convection problems where the gap changes. Two-way coupling is more expensive and more complex than one-way but may be necessary for strongly coupled problems.

Temperature Mapping

The temperature field from the thermal model must be mapped onto the structural model. If the thermal and structural models use the same mesh, the mapping is direct — the temperature at each node is used directly in the structural analysis. If the meshes differ (which is common — the thermal mesh may be coarser or finer than the structural mesh), the temperature must be interpolated from the thermal mesh to the structural mesh. The interpolation should preserve the temperature distribution accurately — errors in the mapping produce errors in the thermal strain and therefore in the stress. The mapping should be verified — the total thermal strain in the structural model should be consistent with the temperature field from the thermal model.

Coordinate and Mesh Mapping

The thermal and structural models must use consistent coordinate systems. The temperature at a point in the structural model must correspond to the temperature at the same physical point in the thermal model. If the models use different coordinate systems (e.g. the thermal model uses a cylindrical system and the structural uses Cartesian), the mapping must account for the transformation. The mesh resolution may differ — the thermal mesh may be fine in regions of high gradient (near heat sources) and coarse elsewhere; the structural mesh may be fine in regions of high stress (near constraints, holes) and coarse elsewhere. The mapping must handle the different resolutions without losing accuracy.

Time Synchronisation in Transient Coupling

For transient thermal-structural analysis, the time stepping must be synchronised between the thermal and structural models. The thermal time step may be different from the structural time step — the thermal time step is determined by the thermal diffusion, while the structural time step is determined by the dynamic response. The temperature at each structural time step must be obtained from the thermal solution at the corresponding time. If the thermal and structural time steps differ, the temperature must be interpolated in time. The time synchronisation must be verified — the temperature history at critical points should be consistent between the two models.

Temperature-Dependent Properties in Coupled Analysis

In a coupled thermal-structural analysis, the structural material properties may be temperature-dependent — Young's modulus, yield strength and CTE may vary with temperature. The structural analysis must use the properties evaluated at the local temperature, not at a uniform reference temperature. This means the structural stiffness varies spatially — the hot region is more compliant than the cold region. The analysis must handle the temperature-dependent properties correctly — the solver must read the local temperature, look up the properties at that temperature, and use them in the structural computation. This is a standard capability of most FEA solvers but must be set up correctly.

Key Takeaways

• Coupled thermal-structural analysis links the temperature field to the structural stress and deformation
• One-way coupling (thermal → structural) is sufficient for most problems where deformation does not affect heat transfer
• Two-way coupling is needed when deformation changes geometry, contact pressure or view factors
• Temperature mapping — transferring the temperature field to the structural mesh — must be verified
• Reference temperature, material properties and coordinate systems must be consistent between models