Mathematical modeling and problem statement for thermal topological optimization of additive bimetallic structures accounting for anisotropy and interfacial transition

Аuthors

Kiselev V. P.^*, Ezhov A. D.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: vladimir-kiselev@yandex.ru
**e-mail: ezzhov@gmail.com

Abstract

The design of advanced thermal management components for energy and aerospace systems increasingly relies on additively manufactured bimetallic structures that combine structural strength with tailored heat dissipation pathways. Conventional topology optimization frameworks often simplify thermal conductivity as a scalar property and reduce the intermaterial transition to an ideal surface. This paper formulates a consistent thermal topology optimization model for bimetallic structures accounting for tensor thermal conductivity and an effective interfacial transition region. The model combines a stationary heat conduction problem, finite element discretization, Helmholtz filtering, smoothed Heaviside projection, three-phase material interpolation, KS aggregation of maximum-temperature constraints, adjoint sensitivity analysis and a weakly coupled thermoelastic check. The proposed formulation provides a computational framework for transforming a relaxed density field into a materialized geometry followed by mandatory thermal rechecking.

Keywords:

thermal topology optimization, bimetallic structures, additive manufacturing, tensor thermal conductivity, finite element method, adjoint sensitivity analysis, interfacial transition zone, method of moving asymptotes

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