Multi-objective shape optimization of developable Bézier-like surfaces using non-dominated sorting genetic algorithm

IF 1.2 4区工程技术 Q3 ENGINEERING, MECHANICAL Mechanics & Industry Pub Date : 2023-01-01 DOI:10.1051/meca/2023031

Jing Lu, XiaoBo Su, Jingyu Zhong, Gang Hu

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Abstract

The shape optimization design of the developable surface is an important research topic in CAD/CAM, and it is widely used in engineering manufacturing. In this paper, NSGA-II (the elitist non-dominated sorting genetic algorithm) is used to study the multi-objective shape optimization problem of generalized cubic developable Bézier-like surfaces (GCDBLS, for short) to promote the application of GCDBLS in industrial software and engineering design. Firstly, the shape optimization of developable surfaces is transformed into the shape optimization of dyadic curves based on the point-to-plane duality theory. Secondly, a multi-objective shape parameter optimization model is developed based on three surface optimality criteria (the shortest arc length, the smallest energy, and the smallest curvature change rate of the dual curve). Finally, the results of shape parameter optimization of GCDBLS obtained by NSGA-II are compared with MSSA and MOGOA to verify the feasibility and superiority of NSGA-II in solving multi-objective shape optimization problems for developable surfaces and the flexibility of GCDBLS in the construction of developable surfaces.

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基于非支配排序遗传算法的可展bsamzier曲面多目标形状优化

可展曲面的形状优化设计是CAD/CAM中的一个重要研究课题，在工程制造中有着广泛的应用。本文采用NSGA-II(精英非支配排序遗传算法)研究广义三次可展bsamzier -like曲面(GCDBLS，简称GCDBLS)的多目标形状优化问题，促进GCDBLS在工业软件和工程设计中的应用。首先，基于点平面对偶理论，将可展开曲面的形状优化转化为二元曲线的形状优化;其次，基于对偶曲线的最短弧长、最小能量和最小曲率变化率三个曲面优化准则，建立了多目标形状参数优化模型;最后，将NSGA-II获得的GCDBLS形状参数优化结果与MSSA和MOGOA进行了比较，验证了NSGA-II在解决可展曲面多目标形状优化问题中的可行性和优越性，以及GCDBLS在可展曲面构建中的灵活性。

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来源期刊

Mechanics & Industry ENGINEERING, MECHANICAL-MECHANICS

CiteScore

2.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： An International Journal on Mechanical Sciences and Engineering Applications With papers from industry, Research and Development departments and academic institutions, this journal acts as an interface between research and industry, coordinating and disseminating scientific and technical mechanical research in relation to industrial activities. Targeted readers are technicians, engineers, executives, researchers, and teachers who are working in industrial companies as managers or in Research and Development departments, technical centres, laboratories, universities, technical and engineering schools. The journal is an AFM (Association Française de Mécanique) publication.