Three‐dimensional shape optimization
Three‐dimensional shape optimization
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DOI：
10.1002/nme.1620180504
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发表时间：
1982-05
影响因子：
2.9
通讯作者：
M. Imam
中科院分区：
文献类型：
--
作者：
M. Imam
结构优化设计通常涉及框架或壳体结构，其中优化仅限于优化结构构件以获得最佳截面或厚度。形状优化解决了另一类涉及连续结构部件的问题，其中确定了最佳形状（部件的边界和表面的形状）。本报告描述了三维结构部件的形状优化。采用20节点等参单元进行有限元分析。目标函数，质量，最小化的直接使用非线性数学规划，具体的可行方向法。数值形状表示和设计变量的选择是问题的最重要的方面。这个问题是从一个实用的角度来解决和技术，以尽量减少desingn变量的数量。讨论了曲面的等参表示和形状的数值叠加。这些技术进行了比较，并证明了简单的悬臂梁和他们的最小质量设计。在一个例子中，非均匀横截面梁的最佳形状是在应力约束下获得的。最终设计的横截面形状在梁的长度上变化，这不能用梁的弯曲理论来预测。在某些问题中遇到的一个主要困难是，在优化过程中的形状变化可能需要改变有限元网格，因为有限元网格的初始配置可能导致新形状的非常扭曲的元素。使用包含扭曲元素的网格进行分析可能根本不可能，或者分析结果可能不准确。
Optimal structural desingn generally deals with frame or shell structures where the optimization is limited to resizing of structural members to obtain optimum cross‐sections or thicknesses. Shape optimization solves another class of problems involving continuous structural components where the optimum shape (the shape of the boundaries and the surfaces of the components) is determined. This report describes shape optimization of three‐dimensional structural components. The finite element method of analysis is used employing the 20‐noded isoparametric element. The objective function, mass, is minimized by the direct use of nonlinear mathematical programming, specifically the feasible direction method. Numerical shape representation and the selection of design variables are the most important aspects of the problem. The problem is addressed from a practical standpoint and techniques are presented to minimize the number of desingn variables. Isoparametric representation of the surfaces and the numerical superposition of shapes are discussed. These techniques are compared and demonstrated on simple cantilever beams and their minimum mass designs are obtained. In one example, the optimum shape of a non‐uniform cross‐sectinal beam is obtained under stress constraint. The final design has a crosssectional shape varying over the length of the beam which could not be predicted using the bending theory of beams. One major difficulty encountered in some problems was that the shape changes during the optimization process may require a change in the finite element mesh because the initial configuration of the finite element mesh may result in very distorted elements for the new shape. The analyis with a mesh containing distorted elements may not be possible at all or the results of the analysis may be inaccurate.