考虑嵌入移动孔洞的多相材料布局优化

王选; 胡平; 龙凯

doi:10.6052/0459-1879-18-327

考虑嵌入移动孔洞的多相材料布局优化

doi: 10.6052/0459-1879-18-327

王选^*,
胡平^*2), ,,
龙凯^**

* 大连理工大学工业装备结构分析国家重点实验室,大连 116023
† 合肥工业大学土木与水利工程学院,合肥 230009
** 华北电力大学新能源电力系统国家重点实验室, 北京 102206

基金项目: 1) 国家自然科学基金( 11872017)和北京市自然科学基金(2182067)资助项目.

详细信息

通讯作者:
胡平

中图分类号: O342;
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- 被引次数: 0
出版历程
- 收稿日期: 2018-10-08
- 刊出日期: 2019-05-18

MULTIPHASE MATERIAL LAYOUT OPTIMIZATION CONSIDERING EMBEDDING MOVABLE HOLES

Xuan Wang^*,
Ping Hu^{*2)
, ,},
Kai Long^**

* State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China
† College of Civil Engineering, Hefei University of Technology, Hefei 230009, China
** State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University,Beijing 102206, China

摘要

摘要: 工程结构设计问题中经常需要预先嵌入一个或多个固定形状的孔洞以满足某些功能性或者制造性设计要求.为了有效求解这种带有嵌入可移动孔洞的多相材料连续体结构布局优化问题,通常需要同时优化这些嵌入孔洞的位置和方向及多相材料结构的拓扑构型,以改善结构的整体性能.为此,本文采用参数化的水平集函数描述嵌入孔洞的几何形状,并将定义多相材料结构拓扑的材料密度以及描述嵌入孔洞的位置和方向的几何参数视为所考虑优化问题的设计变量.为了避免由于孔洞移动造成的重新划分网格的繁琐及改善计算效率,使用平滑化的Heaviside函数将所有嵌入孔洞映射为固定网格上的密度场.同时,提出了一种在有限元水平上调用的类SIMP材料插值格式,用于优化问题的材料参数化,进而实现多相材料结构拓扑构型和嵌入孔洞位置和方向的同步优化.这种材料插值格式便于几何变量的解析灵敏度分析,使得当前的优化问题可以用基于梯度的优化算法求解.优化算例证明所提方法可以有效地处理带有多个嵌入孔洞的多相材料结构布局优化问题.
- 布局优化 /
- 移动孔洞 /
- 多相材料 /
- SIMP方法 /
- 拓扑优化
Abstract: In structural engineering design, it is often necessary to embed one or more fixed-shaped holes to meet certain functional or manufacturing design requirements. To effectively solve the multi-phase material layout optimization problem of continuum structure with embedded movable holes, it is usually necessary to simultaneously optimize the position and orientation of these embedded holes and the topology configuration of the multi-phase material structure to improve the overall performance of the structure. To this end, parameterized level set functions are used to describe the geometry of the embedded holes. The material densities defining the structural topology of multiphase materials, and the geometric parameters used to describe the position and orientation of the embedded holes, are considered as design variables of the optimization problem considered here. To avoid the cumbersome of re-meshing the grids caused by the movement of holes and improve the efficiency of computation, the embedded holes are mapped into a density field on a fixed grid using a smoothed Heaviside function. Meanwhile, a SIMP-like material interpolation invoked at the finite element level is introduced for material parameterization of the optimization problem, and then the simultaneous optimization of the topology configuration of the multi-phase material structure and the position and orientation of the embedded hole can be realized. The material interpolation scheme supports full analytical sensitivity analysis, which allows the current optimization problem to be solved using gradient-based optimization algorithms. Numerical examples illustrate that the proposed method can effectively deal with the layout optimization problem of multiphase material embedded with multiple embedded holes.
- layout optimization /
- movable holes /
- multi-material /
- SIMP method /

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