Analogy of thermal and structural compliance
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When dealing with the structure subjected to the thermal loading, one terms comes very frequently and that is thermal compliance. But term is rarely defined in any literature, what we frequently see is the mathematical expression -
\[Thermal -Compliance = \frac{1}{2} P \times T\]where, P is the power i.e. heat and T is temperature.
Thermal compliance is analogous to the structural compliance i.e. strain energy stored in the structure which can be defined as
\[Structural- Compliance = \frac{1}{2} \sigma \times \epsilon \,= \frac{1}{2}P \times \delta\]where, P is the force and \(\delta\) is the displacement
When force P is applied to the structure then, the displacement \(\delta\) is produced similarly, when heat P is applied to the structure then temperature T will be produced.
Structures which are subjected to mechanical loading are designed such that the displacement (strain) produced in the structure is within the design limit and to do that we generally consider the strain energy while designing. Similarly, when any structure is subjected to the thermal loading then our main aim remains that the temperature within the structure doesn’t exceed the certain limit, and to do that we design on the basis of thermal compliance.