Topology optimization of coupled space–time heat transfer and fluid flow problems
Abstract
This work establishes a space–time topology optimization framework that enables morphable structure design—a fundamentally new capability where optimized topology evolves through time. By treating time as an additional spatial dimension, the method transcends traditional static topology optimization to create structures that adapt their configuration during operation. The framework is applied to transient thermal and thermal flow systems. An additional temporal regularization term is used to control topology evolution when morphability must be limited. The model is formulated with density-based, time-dependent design variables. The transient state equations are solved with a finite element formulation, and the sensitivity is calculated by automatic differentiation via the adjoint method using the unified space–time representation. Four cases are analyzed: minimization of temperature spatial gradient for all instants and at the final time step, minimization of temperature temporal variation, and thermal flow optimization targeting outlet temperature minimization. The effects of temporal regularization with varying weights are also investigated to balance performance objectives with manufacturing (or operational) constraints. Results demonstrate that morphable designs achieve different optimized solutions compared to static topology optimization approaches. This methodology enables the design of structures that adapt their topology during operation to maintain optimized performance throughout transient conditions.