Rui F. Silva

Topology optimization problem formulations have lately included stresses, besides compliance, to ensure mechanical strength feasibility, which is of utmost importance in structural engineering practice. A mechanically induced stress field has often been considered in optimal structural design. However, one realizes that thermal stresses can also greatly influence efficient designs, especially when addressing highly constrained structures. Moreover, stress mitigation has been achieved by enlarging the design domain to multi-material solutions. This motivates to pursue stress-based topology optimization of thermoelastic structures and the extension of the multi-material setting to Functionally Graded Materials (FGMs), with greater potential in stress mitigation. Two optimization problems are investigated: (1) elastic strain energy minimization and (2) maximum von Mises stress minimization. In the former, the single-material problem is revisited, but in the frame of a multi-objective formulation, weighting mechanical and thermal strain energy terms, as they can be decoupled. Insights into thermal stresses allow to propose a well-posed stress-based formulation for the topology optimization thermoelastic problem. In the latter, stress mitigation is sought on account of optimizing the spatial mixture (composition) of two solids amidst prescribed or predicted voids. It is assumed that the RAMP interpolation scheme has the physical meaning of rendering the thermoelastic properties for the continuous variation of composition. Linear thermoelasticity and plane stress benchmarks are used. In the multi-objective energy-based problem, the trade-offs between the conflicting design objectives, in the Pareto sense, are highlighted. Regarding the stress-based problem, lower stress peaks are obtained in FGM solutions, as stresses are more evenly distributed.

Functionally Graded Materials (FGMs) can outperform their homogeneous counterparts. Advances in digitalization technologies, mainly additive manufacturing, have enabled the synthesis of materials with tailored properties and functionalities. Joining dissimilar metals to attain compositional grading is a relatively unexplored research area and holds great promise for engineering applications. Metallurgical challenges may arise; thus, a theoretical critical analysis is presented in this paper. A multidisciplinary methodology is proposed here to unify optimal design, multi-feed Wire-Arc Additive Manufacturing (WAAM), and image-based characterization methods to create structure-specific oriented FGM parts. Topology optimization is used to design FGMs. A beam under pure bending is used to explore the layer-wise FGM concept, which is also analytically validated. The challenges, limitations, and role of WAAM in creating FGM parts are discussed, along with the importance of numerical validation using full-field deformation data. As a result, a conceptual FGM engineering workflow is proposed at this stage, enabling digital data conversion regarding geometry and compositional grading. This is a step forward in processing in silico data, with a view to experimentally producing parts in future. An optimized FGM beam, revealing an optimal layout and a property gradient from iron to copper along the build direction (bottom–up) that significantly reduces the normal pure bending stresses (by 26%), is used as a case study to validate the proposed digital workflow.