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频带约束下刚架结构优化问题可行域研究
  • ISSN号：1000-8608
  • 期刊名称：大连理工大学学报
  • 时间：2014.7
  • 页码：384-390
  • 分类：O39[理学—工程力学;理学—力学] TU323.5[建筑科学—结构工程]
  • 作者机构：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024, [2]大连理工大学工程力学系辽宁大连116024
  • 相关基金：国家自然科学基金资助项目（重点项目11372060;91216201,11326005）;“九七三”国家重点基础研究发展计划资助项目（2011CB610304）.
  • 相关项目：近空间高超声速飞行器结构多学科优化理论与方法研究
作者： 倪长辉|阎军|程耿东|郭旭|
关键词： 奇异性, 优化, 可行域, W-W算法, singularity, optimization, feasible domain, W-W algorithm
中文摘要：

研究频带约束下刚架结构轻量化设计问题的可行域基本性质。刚架结构中梁的断面积取为设计变量，采用欧拉-伯努利梁的动力刚度法及 W-W 算法精确求解结构的固有频率值。利用 W-W算法的特征值计数原理，研究了前述优化问题的可行域的形状和联通性，发现可行域呈现复杂的形状，由多块非联通子域组成，并且部分可行域子域可以是低维的。还以三杆梁的尺寸优化和拓扑优化为例，给出了可行域的具体形状，展示了这一优化问题的可行域具有“强奇异性”。可行域的这一特点给基于梯度类的优化算法带来了极大的困难，需要采用其他手段处理，也使这类问题有望用于测试各类优化软件算法。

英文摘要：

The feasible domain of minimum weight designs of rigid frame structures with frequency band constraints is studied,in which the cross sectional area of beam is chosen as design variable.The natural frequencies of frame structures are solved with the dynamic stiffness method and W-W algorithm for Euler-Bernoulli beam.Then,the shape and connectivity of the feasible domain of the optimization problem are described exactly by eigenvalue counting technology.It is found that the feasible domain of the optimization problem is complex and disj ointed,and some disj ointed domains are low dimensional.The shape and connectivity of the feasible domain of the size and topology optimization problem of 3-beam model are studied,and results show that the singularity is very strong,which brings about great difficulties for the process of classical gradient-based optimization searching algorithm,and other way is needed.It also provides a bench mark problem for the test of soft optimum algorithm.

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频率约束下复合材料支撑骨架结构多尺度优化设计及其奇异最优现象研究
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材料结构拓扑优化中的数学问题
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近空间高超声速飞行器结构多学科优化理论与方法研究
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期刊信息
  • 《大连理工大学学报》
  • 中国科技核心期刊
  • 主管单位:教育部
  • 主办单位:大连理工大学
  • 主编：程耿东
  • 地址：大连理工大学学报编辑部
  • 邮编：116024
  • 邮箱：xuebao@dlut.edu.cn
  • 电话：0411-84708608
  • 国际标准刊号：ISSN：1000-8608
  • 国内统一刊号：ISSN：21-1117/N
  • 邮发代号:8-82
  • 获奖情况:
  • 国家“双百”期刊,1997年获首届中国期刊奖提名奖、获第二届全国优秀...,1992年获全国优秀科技期刊评比三等奖
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  • 被引量:15881