This paper deals with the computation of the shakedown load of engineering systems subjected to varying loads. In particular, we focus on thermal loading and the resulting heat conduction problem in combination with shakedown analysis. The analysis is based on the lower bound shakedown theorem by Melan. The calculation is carried out by use of an interior-point algorithm. Emphasis is placed on the presentation of theoretical derivations whereas numerical aspects are out of scope and will be presented elsewhere. The methodology is illustrated by the application to a simplified model of a tube sheet in heat exchangers.

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