Non-parametric shape optimization method for thin-walled structures under strength criterion

机译：强度准则下薄壁结构非参数形状优化方法

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摘要

This paper presents a numerical optimization method for shape design to improve the strength of thin-walled structures. A solution to maximum stress minimization problems subject to a volume constraint is proposed. With this solution, the optimal shape is obtained without any parameterization of the design variables for shape definition. It is assumed that the design domain is varied in the in-plane direction to maintain the curvatures of the initial shape. The problem is formulated as a non-parametric shape optimization problem. The shape gradient function is theoretically derived using the Lagrange multiplier method and the adjoint variable method. The traction method, which was proposed as a gradient method in Hilbert space, is applied to determine the smooth domain variation that minimizes the objective functional. The calculated results show the effectiveness and practical utility of the proposed solution in solving minmax shape optimization problems for the design of thin-walled structures under a strength criterion.

机译：本文提出了一种用于形状设计的数值优化方法，以提高薄壁结构的强度。提出了解决受体积约束的最大应力最小化问题的解决方案。通过该解决方案，无需对形状定义的设计变量进行任何参数化即可获得最佳形状。假定设计域在平面内方向上变化以维持初始形状的曲率。该问题被公式化为非参数形状优化问题。理论上，形状梯度函数是使用拉格朗日乘数法和伴随变量法导出的。在希尔伯特空间中作为梯度方法提出的牵引方法被用于确定使目标函数最小化的平滑域变化。计算结果表明，所提出的解决方案在解决强度准则下的薄壁结构设计的最小最大形状优化问题时是有效的和实用的。

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来源
《International Conference on Computer Aided Optimum Design in Engineering; 2007; Myrtle Beach,SC(US)》|2007年|P.179-188|共10页
会议地点 Myrtle BeachSC(US)
作者
M. Shimoda; J. Tsuji; H. Azegami;
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作者单位

Department of Mechanical Design Engineering, Shonan Institute of Technology, Japan;

Mitsubishi Automotive Engineering Co., Ltd., Japan;

Nagoya University, Japan;

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会议组织
原文格式 PDF
正文语种 eng
中图分类 TH122.5;
关键词
shell; shape optimization; traction method; structural optimization; optimal shape; non-parametric optimisation; minmax; adjoint variable;

机译：壳体;形状优化;牵引方法;结构优化;最佳形状;非参数优化;最小最大;伴随变量;

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Non-parametric shape optimization method for thin-walled structures under strength criterion

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