Multi-Scale Topology Optimization of Bodies with TPMS-based Lattice Structures and Mortar Contact Interfaces

Abstract

The combination of topology optimization, lattice structures and 3D printing has quickly emerged as a potential alternative for the design and manufacturing of lightweight components. However, the size of the building chamber restricts the size of this kind of lightweight designs. A possibility to overcome this limitation is to design assemblies of 3D printed lightweight components put together with contact interfaces. To design such an optimal lightweight assembly, the components should not be optimized separately, but the wholeassembly should be optimized simultaneously with all components including their unilateralcontact interfaces. This is the topic of the following work. In this paper, a framework formulti-scale topology optimization of assemblies of bodies with triply periodic minimal surfaces(TPMS)-based lattice structures and unilateral contact interfaces is developed and implementedin 3D. The contact interfaces are formulated for finite element bodies with non-matching meshesusing the mortar approach which in turn is solved by the augmented Lagrangian formulationand Newton’s method. The multi-scale topology optimization formulation, suggested in [1],is set up by defining two density variables for each finite element: one macro density variablegoverned by RAMP (Rational Approximation of Material Properties), and a micro densityvariable governed by representative orthotropic elastic properties obtained by numerical finiteelement homogenization of representative volume elements of the TPMS-based lattice structure. Thus, the macro density variable defines if an element should be treated as a void or be filled with lattice structure, and the micro density variable sets the local grading of the lattice. The potential energy of the system is maximized with respect to the design variables, in such manner no extra adjoint equation is needed for the sensitivity analysis. Both density variables are treated with a density filter, and the macro density variable is also passed a Heaviside filter. The final optimal assembly design is realized by transforming the optimal density fields to implicit surface-based geometries using a support vector machine and Shepard’s interpolation method, which then can be 3D printed as the corresponding stl-file obtained by applying the marching cube algorithm. The implemented framework is demonstrated for three-dimensional benchmark problems.

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