Two‐scale topology optimization for composite plates with in‐plane periodicity

Abstract

Fig. 1. Our two-scale topology optimization framework allows to optimize continuous material properties mapping to printable microstructures (lee) to fabricate high-resolution functional objects (middle) and minimum compliant structures (right). In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specii-cations. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut-the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set eld. Next, we propose an eecient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially-varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially-varying material properties onto the microstructures with the corresponding properties in order to generate a high-resolution print-able structure. We demonstrate the eecacy of our framework by designing, optimizing, and fabricating objects in diierent material property spaces on the level of a trillion voxels, i.e several orders of magnitude higher than what can be achieved with current systems.

An adaptive mesh‐adjustment strategy for continuum topology optimization to achieve manufacturable structural layout

“…Topology optimization for continuum structures aims at determining the optimal material distribution to achieve desired structural performances under specific constraints. Since the work of Bendsøe and Kikuchi, topology optimization for continuum structures has been extensively studied and achieved remarkable progress in a wide range of fields . At present, various topology optimization methods, broadly classified into two categories: material distribution method and geometry boundary description method, are available.…”

Microscopic design and optimization of hydrodynamically lubricated dissipative interfaces

“…In the context of micro‐texture design, similar optimization problems can be cast in terms of so‐called flow factor tensors , which appear in the formulation of the macroscopic mechanics of hydrodynamic lubrication, and this particular goal has been the subject of research in the work of Waseem et al The second class of problems is macroscopic objective optimization ( MacOO ), where the focus is on quantities of interest which require the solution of a macroscopic boundary value problem and, hence, is intrinsically driven by the two‐scale analysis of homogenization. In structural analysis, minimizing deflection under a prescribed load is a very specific but a practically important example . The counterpart of such an optimization task in hydrodynamic lubrication is the design of a micro‐texture which can maximize the load capacity of the interface, as recently investigated in the work of Waseem et al All of these works presented and investigated homogenization‐based topology optimization approaches, which is the distinguishing feature of the current study as well.…”

“…In structural analysis, minimizing deflection under a prescribed load is a very specific but a practically important example. [12][13][14][15] The counterpart of such an optimization task in hydrodynamic lubrication is the design of a micro-texture which can maximize the load capacity of the interface, as recently investigated in the work of Waseem et al 2 All of these works presented and investigated homogenization-based topology optimization approaches, which is the distinguishing feature of the current study as well. Focusing on hydrodynamic lubrication in the broad field of tribology, there is a limited number of works that addresses microscopic interface design in comparison to material design.…”

Isogeometric topology optimization for continuum structures using density distribution function

“…In recent years, topology optimization has accepted enormous attention and considerable developments due to its capability in finding the optimal material layout in the conceptual design stage of products. 1 Many topology optimization methods have been proposed, such as the homogenization method, 2 the Solid Isotropic Material with Penalization (SIMP) method, 3,4 the Evolutionary Structural Optimization (ESO) method, 5 the Level-Set Method (LSM), [6][7][8] and the Moving Morphable Components (MMC), 9,10 with a wide range of applications, including the frequency responses, [11][12][13] material microstructures, [14][15][16] and multiscale design, [17][18][19][20][21][22][23][24] as well as stress problems, 25,26 etc. 27 Material description models (MDMs) have been widely adopted to describe the structural topology due to its easiness.…”