Abstract
This paper develops a robust framework for the multiscale design of three-dimensional lattices with macroscopically tailored thermal and thermo-structural characteristics. A multiscale approach is implemented where the discrete evaluations of small-scale lattice unit cell characteristics are converted to response surface models so that the properties exist as continuous functions of the lattice micro-parameters. The derived framework constitutes free material optimization in the space of manufacturable lattice micro-architecture. The optimization of individual lattice member dimensions is enabled by the adjoint method and the explicit expressions of the response surface material property sensitivities. The approach is demonstrated by solving thermal and thermo-structural optimization problems, significantly extending previous work which focused on linear structural response. The thermal optimization solution shows a design with improved optimality compared to the SIMP methodology. The thermo-structural optimization solution demonstrates the method’s capability for attaining a prescribed displacement in response to temperature gradients.
Highlights
The advent of additive manufacturing and its rapid evolution is increasingly offering flexibility and precision to the physical realization of advanced materials, potentially expanding the capabilities of some structural and thermal optimization techniques (Sigmund and Maute 2013; Wu et al 2017; Li et al 2018; Cheng et al 2019)
The realization of optimal structural design was limited to manufacturing techniques such as casting and machining processes which constrained the complexity and precision of realizable designs (Brackett et al 2011)
The goal of the work described in this paper is to demonstrate a multiscale approach for mechanically and thermally optimized structures using a spatially varying lattice design
Summary
The advent of additive manufacturing and its rapid evolution is increasingly offering flexibility and precision to the physical realization of advanced materials, potentially expanding the capabilities of some structural and thermal optimization techniques (Sigmund and Maute 2013; Wu et al 2017; Li et al 2018; Cheng et al 2019). The mechanics of advanced materials have defined a class of optimization techniques that allow free variations of the material properties tailored to meet prescribed macroscale objectives. This concept of freely varying material properties in the domain of a structure towards fulfiling functional objectives, with the capacity. The FMO framework employs the components of the constitutive material tensor as design variables which are free to vary spatially throughout the domain of the structure. Though optimization using the unrestricted set of components of the constitutive material tensor as design variables makes no considerations for the physical realization of local structure,
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