Topology Optimisation of Thermomechanical Functionally Graded Materials and Material Interfaces

The work applies topology optimisation to the design of functionally graded materials (FGMs) and materialinterfaces for thermomechanical problems. It is well known, that the mismatch in stiffness and thermal expansioncoefficient of two materials give rise to high stresses at the interface. One way to alleviate this is to use the conceptof FGMs [1]. The FGMs are here designed using topology optimisation, which is a material distribution methodused for finding an optimal structural layout for a given problem subject to design constraints [2]. Density-basedmulti-material topology optimisation is utilised to optimise the material composition and distribution in order toachieve a high thermal throughput, while maintaining an acceptable stress level.The work considers the design of local material microstructures with the objective of optimising themacrostructural response. In contrast to homogenisation techniques, connectivity among the local microstructuralcells is ensured by analysing the full macrostructure with all microstructural details being fully-resolved by thefinite element method. This is computationally challenging and the work will therefore explore the use of acoarse-scale spectral preconditioner [3] to the coupled thermomechanical problems.The problems investigated are inspired by those of plasma facing components (PFCs), thermal barrier coatings(TBCs) and thermal protection systems (TPSs). References[1] F Erdogan, Fracture mechanics of functionally graded materials, MRS Bulletin, 20 (01), 43-44 (1995)[2] MP Bendsøe, O Sigmund, Topology Optimization: Theory, Methods and Applications. Springer (2003)[3] BS Lazarov, Topology optimization using multiscale finite element method for high-contrast media, in:Large-Scale Scientific Computing, Lecture Notes in Computer Science, Springer (2014), in print.