Aspects are presented of a general approach based on constrained optimisation for the analysis of processes involving heat deposition, such as welding processes. The methodology of the present approach entails generating functions and subdomain elliptic solvers useful for the practical application of constrained optimisation for the calculation of thermal histories. The emphasis in the present work is on the general properties associated with the methodology of this approach as these properties relate to its application. In addition, prototype weld analyses are presented that serve to demonstrate many of the details associated with the practical application of this methodology.
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