A topology optimization method based on element independent nodal density
来源期刊：中南大学学报(英文版)2014年第2期
论文作者：YI Ji-jun(易继军) ZENG Tao(曾韬) RONG Jian-hua(荣见华) LI Yan-mei(李艳梅)
文章页码：558 - 566
Key words：topology optimization; element independent nodal density; Shepard interpolation; parallel computation
Abstract: A methodology for topology optimization based on element independent nodal density (EIND) is developed. Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function. The influence of the diameter of interpolation is discussed which shows good robustness. The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint. The rational approximation for material properties (RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions. Solutions are shown to meet stability, mesh dependence or non-checkerboard patterns of topology optimization without additional constraints. Finally, the computational efficiency is greatly improved by multithread parallel computing with OpenMP.
YI Ji-jun(易继军)1, 2, ZENG Tao(曾韬)1, RONG Jian-hua(荣见华)2, LI Yan-mei(李艳梅)3
(1. School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China;
2. School of Automobile and Mechanical Engineering,
Changsha University of Science and Technology, Changsha 410004, China;
3. Hunan Technical College of Water Resources and Hydro Power, Changsha 410131, China)
Abstract:A methodology for topology optimization based on element independent nodal density (EIND) is developed. Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function. The influence of the diameter of interpolation is discussed which shows good robustness. The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint. The rational approximation for material properties (RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions. Solutions are shown to meet stability, mesh dependence or non-checkerboard patterns of topology optimization without additional constraints. Finally, the computational efficiency is greatly improved by multithread parallel computing with OpenMP.
Key words:topology optimization; element independent nodal density; Shepard interpolation; parallel computation
