A superconvergent hybridisable discontinuous Galerkin method for linear elasticity

Sevilla Ruben; Giacomini Matteo; Karkoulias Alexandros; Huerta Antonio

摘要

Summary >The first superconvergent hybridisable discontinuous Galerkin method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is the strong imposition of the symmetry of the stress tensor by means of the well known and extensively used Voigt notation, circumventing the use of complex mathematical concepts to enforce the symmetry of the stress tensor either weakly or strongly. A novel procedure to construct element by element a superconvergent postprocessed displacement is proposed. Contrary to other hybridisable discontinuous Galerkin formulations, the methodology proposed here is able to produce a superconvergent displacement field for low‐order approximations. The resulting method is robust and locking‐free in the nearly incompressible limit. An extensive set of numerical examples is utilised to provide evidence of the optimality of the method and its superconvergent properties in two and three dimensions and for different element types. </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”xml：id =“nme5916-abs-abs-0001”> <标题类型=“main” >概述</标题> >呈现了第一种超要变压杂交的不连续的持续的Galerkin方法，用于使用相同的原始和混合变量的相同近似程度的线性弹性问题。该方法的关键特征是通过众所周知的和广泛使用的voIGT符号来强调应力张量对称性的对称性，避免使用复杂的数学概念来强弱或强烈地强制应力张量的对称性。用元素构建元件的新方法提出了一种超级验光后处理位移。与其他杂交的不连续的Galerkin制剂相反，此处提出的方法能够生产用于低位近似的超级电容位移场。所得到的方法在几乎不可压缩的极限中是鲁棒和无锁定的。利用广泛的数值示例来提供两种和三维的方法的最优性及其超级聚合物性能的证据，以及不同的元素类型。</ 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2期</span><b style="margin: 0 2px;">|</b><span>共26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=Sevilla Ruben&option=202" target="_blank" rel="nofollow">Sevilla Ruben;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Giacomini Matteo&option=202" target="_blank" rel="nofollow">Giacomini Matteo;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Karkoulias Alexandros&option=202" target="_blank" rel="nofollow">Karkoulias Alexandros;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Huerta Antonio&option=202" target="_blank" rel="nofollow">Huerta Antonio;</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>Zienkiewicz Centre for Computational Engineering College of EngineeringSwansea UniversitySwansea United Kingdom;</p> <p>Laboratori de Càlcul Numèric (LaCàN) ETS de Ingenieros de Caminos Canales y PuertosUniversitat Politècnica de CatalunyaBarcelona Spain;</p> <p>Laboratori de Càlcul Numèric (LaCàN) ETS de Ingenieros de Caminos Canales y PuertosUniversitat Politècnica de CatalunyaBarcelona Spain;</p> <p>Laboratori de Càlcul Numèric (LaCàN) ETS de Ingenieros de Caminos Canales y PuertosUniversitat Politècnica de CatalunyaBarcelona Spain;</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=elasticity&option=203" rel="nofollow">elasticity;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=hybridisable discontinuous Galerkin&option=203" rel="nofollow">hybridisable discontinuous Galerkin;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=locking‐free&option=203" rel="nofollow">locking‐free;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=mixed formulation&option=203" rel="nofollow">mixed formulation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=superconvergence&option=203" rel="nofollow">superconvergence;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Voigt notation&option=203" rel="nofollow">Voigt notation;</a> </p> <div class="translation"> 机译：弹性;杂交的不连续的Galerkin;无锁定;混合配方;超级介质;voigt表示法; 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