Abstract
In the structural topology optimization approaches, the Moving Morphable Component (MMC) is a new method to obtain the optimized structural topologies by optimizing shapes, sizes, and locations of components. However, the optimized structure boundary usually generates local nonsmooth areas due to incomplete connection between components. In the present paper, a topology optimization approach considering nonsmooth structural boundaries in the intersection areas of the components based on the MMC is proposed. The variability of components’ shape can be obtained by constructing the topology description function (TDF) with multiple thickness and length variables. The shape of components can be modified according to the structural responses during the optimization process, and the relatively smooth structural boundaries are generated in the intersection areas of the components. To reduce the impact of the initial layout on the rate of convergence, this method is implemented in a hierarchical variable calling strategy. Compared with the original MMC method, the advantage of the proposed approach is that the smoothness of the structural boundaries can be effectively improved and the geometric modeling ability can be enhanced in a concise way. The effectiveness of the proposed method is demonstrated for topology optimization of the minimum compliance problem and compliant mechanisms.
Highlights
Structural topology optimization aims to find the best distribution of materials within a prescribed design domain using an optimization algorithm in order to achieve some exceptional structural performance [1]
It is worth noting that the topology optimization process using the variability of components’ shape based on the Moving Morphable Component (MMC) framework is somewhat similar to the level set method (TDF has been used to represent the geometry of components), the proposed method can possibly give an explicit description of the boundary and geometric features of components, which cannot be achieved in the level set method that uses the free transformation of the level set functions to represent the boundary of a structure
A topology optimization method based on the MMC to solve the local nonsmooth problem of components connection areas is proposed
Summary
Structural topology optimization aims to find the best distribution of materials within a prescribed design domain using an optimization algorithm in order to achieve some exceptional structural performance [1]. In order to overcome the above problems, recently, Guo et al [27] proposed a more accurate and geometric topology optimization method based on the topology optimization framework, a so-called Moving Morphable Component (MMC) In this framework, a series of components with movable and deformable capabilities are used as building blocks of the topology optimization, and the optimal structural topology that meets specific performance can be obtained by varying the lengths, thickness, tilt angle, and center coordinates of these components. Erefore, based on the MMC framework, this paper mainly studies how to use the variability of components’ shape to solve the local nonsmooth problem in the intersection areas of the components For this purpose, we control the length of components by adding new design variables in the TDF of the quadratically varying thicknesses. Considering the influence of the initial layout with more components on the rate of the convergence, the hierarchical variables calling strategy is proposed to optimize the layout of components in the initial stage. e effectiveness of the proposed method is verified by several numerical examples
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