In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness and strength. In this sense, Topology Optimization has been extensively used to determine the best topology of structural components from the mechanical point of view. Its main objective is to distribute a given amount of material into a predefined domain to reach the maximum overall stiffness of the component. Besides, high-resolution solutions are essential to define the final distribution of material. Standard Topological Optimization tools are able to propose an optimal topology for the whole component, but when small topological details are required (i.e. trabecular-type structures) the computational cost is prohibitive. In order to mitigate this issue, the present work proposes a two-level topology optimization method to solve high-resolution problems by using density-based methods. The proposed methodology includes three steps: The first one subdivides the whole component in cells and generates a coarse optimized low-definition material distribution assigning one different density to each cell. The second one uses an equilibrating technique that provides tractions continuity between adjacent cells, thus ensuring the material inter-cell continuity after the cells optimization process. Finally, each cell is optimized at fine scale taking as input data the densities and the equilibrated tractions obtained from the macro problem. The main goal of this work is to efficiently solve high-resolution topology optimization problems using density-based methods, which would be unaffordable with standard computing facilities and the current methodologies.

翻译：在当前工业领域，能够满足客户需求的最优化机械部件开发正快速发展。因此，企业需要高效的解决方案来提升产品的刚度和强度。在此背景下，拓扑优化已被广泛用于从力学角度确定结构部件的最佳拓扑。其主要目标是在预定义域内分配给定材料量，以实现部件最大整体刚度。此外，高分辨率解对于确定材料的最终分布至关重要。标准拓扑优化工具能够为整个部件提出最优拓扑，但当需要细小拓扑细节（如小梁状结构）时，计算成本会变得过高。为缓解这一问题，本文提出了一种基于密度方法的两级拓扑优化方法，用于求解高分辨率问题。所提出的方法包括三个步骤：第一步将整个部件划分为单元，并生成粗分辨率最优低分辨率材料分布，为每个单元分配不同的密度；第二步采用平衡技术，提供相邻单元间的牵引力连续性，从而确保单元优化后材料跨单元连续；最后，以宏观问题中获得的密度和平衡牵引力为输入数据，在细尺度上对每个单元进行优化。本研究的主要目标是利用密度方法高效求解高分辨率拓扑优化问题，而此类问题在使用标准计算设施和现有方法时是无法负担的。