A modified Newton‐type Koiter‐Newton method for tracing the geometrically nonlinear response of structures

Liang Ke; Abdalla Mostafa M.; Sun Qin

摘要

Summary >The Koiter‐Newton (KN) method is a combination of local multimode polynomial approximations inspired by Koiter's initial postbuckling theory and global corrections using the standard Newton method. In the original formulation, the local polynomial approximation, called a reduced‐order model, is used to make significantly more accurate predictions compared to the standard linear prediction used in conjunction with Newton method. The correction to the exact equilibrium path relied exclusively on Newton‐Raphson method using the full model. >In this paper, we proposed a modified Newton‐type KN method to trace the geometrically nonlinear response of structures. The developed predictor‐corrector strategy is applied to each predicted solution of the reduced‐order model. The reduced‐order model can be used also in the correction phase, and the exact full nonlinear model is applied only to calculate force residuals. Remainder terms in both the displacement expansion and the reduced‐order model are well considered and constantly updated during correction. The same augmented finite element model system is used for both the construction of the reduced‐order model and the iterations for correction. Hence, the developed method can be seen as a particular modified Newton method with a constant iteration matrix over the single KN step. This significantly reduces the computational cost of the method. As a side product, the method has better error control, leading to more robust step size adaptation strategies. Numerical results demonstrate the effectiveness of the method in treating nonlinear buckling problems. </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：id =“nme5709-abs-abs-0001”xml：lang =“en”> <标题类型=“main” >摘要</标题> > Koiter-Newton（kn）方法是由Koiter的初始出现理论和使用标准Newton方法的全局校正启发的本地多模多项式近似的组合。在原始配方中，与与牛顿方法结合使用的标准线性预测相比，使用称为阶阶模型的局部多项式近似用于显着更准确的预测。使用完整型号的牛顿Raphson方法校正了精确的平衡路径。</ p> >在本文中，我们提出了一种改进的牛顿型KN方法来追踪结构的几何非线性响应。将开发的预测器校正器策略应用于减少阶模型的每个预测解决方案。还可以在校正阶段中使用阶阶模型，并且仅应用精确的全非线性模型以计算力残差。在校正期间，位移扩展和减少阶模型的剩余术语在换置阶段和下降阶模型中得到了很好的考虑和不断更新。相同的增强有限元模型系统用于降低阶模型的构造和校正的迭代。因此，开发方法可以被视为具有在单个KN步骤上具有恒定迭代矩阵的特定修改的牛顿方法。这显着降低了方法的计算成本。作为侧面产品，该方法具有更好的错误控制，导致更强大的步长适应策略。数值结果证明了该方法治疗非线性屈曲问题的有效性。</ p> </摘要> </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10期</span><b style="margin: 0 2px;">|</b> <span>共20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=Liang Ke&option=202" target="_blank" rel="nofollow">Liang Ke;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Abdalla Mostafa M.&option=202" target="_blank" rel="nofollow">Abdalla Mostafa M.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Sun Qin&option=202" target="_blank" rel="nofollow">Sun Qin;</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>School of AeronauticsNorthwestern Polytechnical UniversityYouyi Western Road 127 Xi'an 710072 PR China;</p> <p>Aerospace Structures and Computational MechanicsDelft University of TechnologyKluyverweg 1 2629 HS Delft The Netherlands;</p> <p>School of AeronauticsNorthwestern Polytechnical UniversityYouyi Western Road 127 Xi'an 710072 PR 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=adaptation strategy&option=203" rel="nofollow">adaptation strategy;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=geometrically nonlinear analysis&option=203" rel="nofollow">geometrically nonlinear analysis;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Koiter‐Newton method&option=203" rel="nofollow">Koiter‐Newton method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=modified Newton method&option=203" rel="nofollow">modified Newton method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=reduced‐order model&option=203" rel="nofollow">reduced‐order model;</a> </p> <div class="translation"> 机译：适应策略;几何非线性分析;Koiter-Newton方法;改进的牛顿方法;减少阶模型; </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="/academic-journal-cn_journal-southeast-university-english-edition_thesis/0201235276743.html">一种用于空间框架结构几何非线性分析的切线刚度矩阵</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=顾建新&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">顾建新,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=陈绍礼&option=202" target="_blank" rel="nofollow" class="tuijian_auth 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