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An adaptive refinement approach for topology optimization based on separated density field description

机译:基于分离密度场描述的拓扑优化自适应细化方法

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This paper presents an adaptive density point refinement approach for continuum topology optimization on the basis of an analysis-mesh separated material density field description based on nodal design variables. The Shepard interpolants are used to construct a strictly range-restricted density field over the design domain with the density design variables defined on a density point grid. Since the density points are defined independent of the finite element mesh, it is easy to refine the density point grid without remeshing the finite element model. A refinement criterion is given to identify the gray transitional regions to be adaptively refined in the subsequent optimization iterations. With such a refinement scheme, the topology optimization can start from a relatively coarse density point grid but still yields a desired higher resolution of the structural boundaries in the final design. Because refinements are only performed when and where necessary, this method is able to improve the boundary description quality of the optimal result with much less design variables as compared with the case of global refinement, and therefore can greatly reduce the computational burden involved in the sensitivity analysis and optimization process. Moreover, the percentage of transitional regions in the final solutions can also be reduced. Compared with using a uniformly globally-dense density point arrangement, this approach can achieve similar optimal designs but with much less computational cost. Numerical examples are given to demonstrate the effectiveness and efficiency of the present approach.
机译:本文在基于节点设计变量的分析网格分离材料密度场描述的基础上,提出了一种用于连续体拓扑优化的自适应密度点细化方法。 Shepard插值用于在设计域上构造一个严格范围受限的密度场,并在密度点网格上定义密度设计变量。由于密度点的定义独立于有限元网格,因此无需重新定义有限元模型就可以轻松优化密度点网格。给出了一个优化标准,以识别要在后续优化迭代中进行自适应优化的灰色过渡区域。利用这种改进方案,拓扑优化可以从相对粗略的密度点网格开始,但是在最终设计中仍可以产生结构边界的所需的更高分辨率。由于仅在必要时和必要时执行细化,因此与全局细化的情况相比,该方法能够以更少的设计变量来改善最佳结果的边界描述质量,因此可以大大降低灵敏度所涉及的计算负担分析和优化过程。此外,最终解决方案中过渡区域的百分比也可以降低。与使用统一的全局密集密度点布置相比,此方法可以实现类似的最佳设计,但计算成本却低得多。数值例子说明了该方法的有效性和效率。

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