Topology Optimization Algorithms for Improved Manufacturability and Cellular Material Design
Carstensen, Josephine V
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Topology optimization is a free-form approach to structural design in which a formal optimization problem is posed and solved using mathematical programming. It has been widely implemented for design at a range of length scales, including periodic cellular materials. Cellular materials in this context refer to porous materials with a representative unit cell that is repeated in all directions. For cellular material design an upscaling law is required to connect the unit cell topology to the bulk material properties. This has limited most work on topology optimization of cellular materials to linear properties, such as elastic moduli or thermal conduction, where numerical homogenization can be used. Although topology-optimized materials are often shown to outperform conventional cellular material designs, the optimized designs are often complex and can therefore be di cult to fabricate. This is true despite the rapid development of manufacturing technologies that have provided radically new capabilities. Although such technologies have reduced the manufacturing constraints, there are still limitations. This thesis looks to advance topology optimization of cellular materials on two fronts: (i) by more formally integrating manufacturing constraints and capabilities into topology optimization methodology, and (ii) by moving beyond linear properties to consider the nonlinear response of cellular materials. In this work we propose to implicitly integrate manufacturing considerations into the topology optimization formulation by using projection based approaches. We seek to improve the manufacturability of topology-optimized structures by providing the designer minimum length scale control of both the design’s solid and void phases. The new two-phase projection algorithm is demonstrated on benchmark examples and uses nonlinear weighting functions to let the design variable magnitude determine if solid or void should be actively projected. In addition, we utilize a multi-phase cellular design approach that can leverage the new capability of deposition of multiple solids that is o ered by current 3D printing technologies. These multi-phase designs generally outperform two-phase topologies and potentially o er new functionalities. Our algorithm is based on an existing multimaterial formulation and used to design cellular topologies for various elastic properties, including negative Poisson’s ratio, and for multiobjectives including mechanical and thermal properties. Expanding topology optimization to cellular design governed by nonlinear mechanics enables designing e ective materials with a range of new improved properties such as energy absorption. However, considering material– and/or geometric nonlinearities in cellular design faces the challenge of the lack of a recognized upscaling technique. Previous works have turned to nite periodicity. This thesis will explore the necessary steps in developing a topology optimization algorithm for cellular design governed by nonlinear mechanics. Further, the forward homogenization problem of how the unit cell topology e ects the e ective material’s energy absorption will be numerically investigated for a range of conventional and topology-optimized unit cells.