{"title":"Plane-Strain Elastic Problem for a Square Array of Disks. I. Elastic Field in a Composite with Soft Inclusions","authors":"P. Drygaś, N. Rylko","doi":"10.1134/s0021894424020172","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The stress-strain elastic field in a square array of <i>N</i> non-overlapping circular inclusions is described by approximate analytical formulas. In particular, soft inclusions are studied by an asymptotic analysis. The case with <i>N</i> = 1 yields a regular square array of disks of radius r embedded in an elastic matrix. The computations of Natanzon and Filshtinsky are based on an infinite system of linear algebraic equations solved by the truncation method. The infinite system determines the Taylor series coefficients of the Kolosov–Muskhelishvili complex potentials. A method of functional equations is used to write the series coefficients in symbolic form up to terms of the order of <i>O</i>(<i>r</i><sup>2<i>s</i></sup>) at a fixed value of <i>s</i>. Approximate analytical formulas for local elastic fields are derived.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"59 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics and Technical Physics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1134/s0021894424020172","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The stress-strain elastic field in a square array of N non-overlapping circular inclusions is described by approximate analytical formulas. In particular, soft inclusions are studied by an asymptotic analysis. The case with N = 1 yields a regular square array of disks of radius r embedded in an elastic matrix. The computations of Natanzon and Filshtinsky are based on an infinite system of linear algebraic equations solved by the truncation method. The infinite system determines the Taylor series coefficients of the Kolosov–Muskhelishvili complex potentials. A method of functional equations is used to write the series coefficients in symbolic form up to terms of the order of O(r2s) at a fixed value of s. Approximate analytical formulas for local elastic fields are derived.
摘要 由 N 个非重叠圆形夹杂物组成的正方形阵列中的应力-应变弹性场是用近似分析公式描述的。特别是通过渐近分析研究了软夹杂物。在 N = 1 的情况下，会产生一个嵌入弹性矩阵的半径为 r 的规则方形圆盘阵列。Natanzon 和 Filshtinsky 的计算基于截断法求解的线性代数方程的无限系统。这个无限系统决定了 Kolosov-Muskhelishvili 复势的泰勒级数系数。利用函数方程的方法，以符号形式写出了在 s 的固定值下直到 O(r2s)阶项的系列系数。
期刊介绍：
Journal of Applied Mechanics and Technical Physics is a journal published in collaboration with the Siberian Branch of the Russian Academy of Sciences. The Journal presents papers on fluid mechanics and applied physics. Each issue contains valuable contributions on hypersonic flows; boundary layer theory; turbulence and hydrodynamic stability; free boundary flows; plasma physics; shock waves; explosives and detonation processes; combustion theory; multiphase flows; heat and mass transfer; composite materials and thermal properties of new materials, plasticity, creep, and failure.
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