Tsallis entropy in dual homogenization of random composites using the stochastic finite element method

Kamiński Marcin

摘要

Summary >This work concerns an application of the Tsallis entropy to homogenization problem of the fiber‐reinforced and also of the particle‐filled composites with random material and geometrical characteristics. Calculation of the effective material parameters is done with two alternative homogenization methods—the first is based upon the deformation energy of the Representative Volume Element (RVE) subjected to the few specific deformations, while the second uses explicitly the so‐called homogenization functions determined under periodic boundary conditions imposed on this RVE. Probabilistic homogenization is made with the use of three concurrent non‐deterministic methods, namely Monte‐Carlo simulation, iterative generalized stochastic perturbation technique as well as the semi‐analytical approach. The last two approaches are based on the Least Squares Method with polynomial basis of the statistically optimized order— this basis serves for further differentiation in the 10th‐order stochastic perturbation technique, while semi‐analytical method uses it in probabilistic integrals. These three approaches are implemented all as the extensions of the traditional Finite Element Method (FEM) with contrastively different mesh sizes, and they serve in computations of Tsallis entropies of the homogenized tensor components as the functions of input coefficient of variation. </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> >这项工作涉及Tsallis熵对具有随机材料和几何特征的纤维增强和颗粒填充复合材料的均匀化问题。用两个替代的均匀化方法进行有效材料参数 - 首先是基于经受少量特定变形的代表体积元素（RVE）的变形能量，而第二种用途明确地确定所谓的均质化函数对此持续的定期边界条件。概率均匀化采用三种并发非确定性方法，即蒙特卡罗仿真，迭代广义随机扰动技术以及半分析方法。最后两种方法基于具有多项式基础的统计上优化的顺序的最小二乘法 - 此基础用于在第10阶随机扰动技术中进一步分化，而半分析方法将其用于概率积分。这三种方法被实施为传统有限元方法（FEM）的延伸，其具有对比不同的网格尺寸，它们在均质张量组件的Tsallis熵的计算中作为输入变异系数的功能。</ 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5期</span><b style="margin: 0 2px;">|</b> <span>共24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=Kamiński Marcin&option=202" target="_blank" rel="nofollow">Kamiński Marcin;</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>Division of Structural Reliability Department of Structural Mechanics Faculty of Civil Engineering Architecture and Environmental Engineering?ód? University of TechnologyAl. Politechniki 6 90‐924 ?ód? Poland;</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=homogenization problem&option=203" rel="nofollow">homogenization problem;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Monte‐Carlo simulation&option=203" rel="nofollow">Monte‐Carlo simulation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=semi‐analytical method&option=203" rel="nofollow">semi‐analytical method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Stochastic Finite Element Method&option=203" rel="nofollow">Stochastic Finite Element Method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=stochastic perturbation technique&option=203" rel="nofollow">stochastic perturbation technique;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Tsallis entropy&option=203" rel="nofollow">Tsallis entropy;</a> </p> <div class="translation"> 机译：均匀化问题;蒙特卡罗模拟;半分析方法;随机有限元法;随机扰动技术;Tsallis熵; </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 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