  This paper extends the nonsmooth Relaxed Variational Approach (RVA) to
topology optimization, proposed by the authors in a preceding work, to the
solution of thermal optimization problems. First, the RVA topology optimization
method is briefly discussed and, then, it is applied to a set of representative
problems in which the thermal compliance, the deviation of the heat flux from a
given field and the average temperature are minimized. For each optimization
problem, the relaxed topological derivative and the corresponding adjoint
equations are presented. This set of expressions are then discretized in the
context of the finite element method and used in the optimization algorithm to
update the characteristic function. Finally, some representative (3D) thermal
topology optimization examples are presented to asses the performance of the
proposed method and the Relaxed Variational Approach solutions are compared
with the ones obtained with the level set method in terms of the cost function,
the topology design and the computational cost.
