Transient, Phase Dependent Temperature Constraints in Topology Optimization with Design-Driven Heat Source and One-Step Adjoint Sensitivity Calculation
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Topology optimization enables the integration of diverse component requirements while generating optimal, manufacturable designs efficiently. Besides many others, thermal constraints are often relevant, particularly for cast components. Special challenges include temperature limits outside the part, transient behavior, and heat sources that depend on the part design. For instance, during the casting of components, the mold temperature must remain within limits throughout the cooling phase. This talk presents a method for topology optimization to constrain region-specific temperatures during cooling. The region of interest is defined as a function of the design variables. The approach is based on a thermal heat‑conduction simulation and an adjoint sensitivity analysis, incorporated by a design-driven heat source. To address the high computational cost and memory requirements of transient temperature fields, the adjoint equation is approximated by a transient solution using only one single time step. Through this approach, cast components with critical manufacturability requirements can be optimized effectively. In particular, for sand casting the method enables the limitation of maximum temperatures within the sand mold, thereby preventing critical surface defects caused by sintering. It is especially relevant for the optimization of large forming tools manufactured with lost foam casting and high process temperatures. The method is validated on two‑ and three‑dimensional examples of sand‑cast forming tools using the Three‑Field SIMP approach. Results show that targeted geometric modifications satisfy temperature limits at low computational cost. This enables temperature constraints in phase‑dependent regions to be considered in parallel with structural optimization to meet the requirements of a feasible design.
