Exact response bound analysis of truss structures via linear mixed 0‐1 programming and sensitivity bounding technique

机译：通过线性混合0-1编程和灵敏度边界技术的桁架结构的精确响应响应分析

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Summary > In the present paper, finding the <fi>exact bound</fi> of structural response for truss structures is considered under bounded interval type uncertainty. This problem is challenging since seeking the <fi>exact bound</fi> corresponds to locating the <fi>global optima</fi> of a multivariate function (generally nonconvex). Traditional treatment of this problem involves the solution of a linear mixed 0‐1 programming problem, which is a highly computationally demanding task especially when large‐scale structures are taken into consideration. In order to alleviate the computational effort, a sensitivity bounding technique is developed in this work using the tools from convex analysis to disclose the monotonicity of concerned structural response function with respect to 0‐1 variables. It is shown that this technique can not only reduce the number of 0‐1 variables substantially but also change the computational complexity of the considered problem from nondeterministic polynomial–hard to nondeterministic polynomial–hard in some cases. The proposed approach provides the possibility of finding the <fi>exact bound</fi> of structural response for large‐scale truss structures within a reasonable time, and its effectiveness is demonstrated through several numerical examples. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：lang =“en”> <title type =“main”>摘要</ title> >本文在界限间隔类型不确定性下，考虑了桁架结构的结构响应的<fi>精确束缚</ fi>。此问题是具有挑战性，因为寻找<fi>精确绑定</ fi>对应于定位多变量函数的<fi>全局Optima </ fi>（通常是非凸不透射）。传统治疗该问题涉及线性混合的0-1编程问题的解，这是一种高度计算要求的任务，特别是当考虑大规模结构时。为了减轻计算工作，在这项工作中使用来自凸分析的工具开发了灵敏度限定技术，以揭示关于0-1变量的相关结构响应函数的单调性。结果表明，该技术不能仅降低0-1变量的数量，而且还在一些情况下将所考虑的多项式 - 难以非必要的多项式 - 难以改变所考虑的问题的计算复杂度。所提出的方法提供了在合理的时间内找到对大型桁架结构的结构响应的<fi>精确束缚</ fi>，其有效性通过几个数值例子来证明。 </ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-20801/'>《International Journal for Numerical Methods in Engineering》</a> <b style="margin: 0 2px;">|</b><span>2018年第1期</span><b style="margin: 0 2px;">|</b><span>共22页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Du Jianming&option=202" target="_blank" rel="nofollow">Du Jianming;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Du Zongliang&option=202" target="_blank" rel="nofollow">Du Zongliang;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wei Yihai&option=202" target="_blank" rel="nofollow">Wei Yihai;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Zhang Weisheng&option=202" target="_blank" rel="nofollow">Zhang Weisheng;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Guo Xu&option=202" target="_blank" rel="nofollow">Guo Xu;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics International Research Center for Computational MechanicsDalian University of TechnologyDalian China;</p> <p>State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics International Research Center for Computational MechanicsDalian University of TechnologyDalian China;</p> <p>State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics International Research Center for Computational MechanicsDalian University of TechnologyDalian China;</p> <p>State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics International Research Center for Computational MechanicsDalian University of TechnologyDalian China;</p> <p>State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics International Research Center for Computational MechanicsDalian University of TechnologyDalian China;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/6940.html" title="工程数学">工程数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=bounds of structural response&option=203" rel="nofollow">bounds of structural response;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=global optimization&option=203" rel="nofollow">global optimization;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=interval uncertainty&option=203" rel="nofollow">interval uncertainty;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=linear mixed 0‐1 programming&option=203" rel="nofollow">linear mixed 0‐1 programming;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=sensitivity bounding&option=203" rel="nofollow">sensitivity bounding;</a> </p> <div class="translation"> 机译：结构响应的界限;全局优化;间隔不确定性;线性混合0-1编程;灵敏度束缚; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704022970273.html">Exact response bound analysis of truss structures via linear mixed 0‐1 programming and sensitivity bounding technique</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Du Jianming&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Du Jianming,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Du 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