Quarterly Journal of Mechanics and Applied Mathematics最新文献_第10页

The use of complex integral representations for analytical evaluation of three-dimensional BEM integrals - Potential and elasticity problems 复积分表示在三维边界元积分分析评价中的应用——势能和弹性问题

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-08-01 DOI: 10.1093/QJMAM/HBU015

S. Mogilevskaya, D. Nikolskiy

{"title":"The use of complex integral representations for analytical evaluation of three-dimensional BEM integrals - Potential and elasticity problems","authors":"S. Mogilevskaya, D. Nikolskiy","doi":"10.1093/QJMAM/HBU015","DOIUrl":"https://doi.org/10.1093/QJMAM/HBU015","url":null,"abstract":"Summary The article presents a new complex variables-based approach for analytical evaluation of threedimensional integrals involved in boundary element method (BEM) formulations. The boundary element is assumed to be planar and its boundary may contain an arbitrary number of straight lines and/or circular arcs. The idea is to use BEM integral representations written in a local coordinate system of an element, separate in-plane components of the fields involved, arrange them in certain complex combinations, and apply integral representations for complex functions. These integral representations, such as Cauchy–Pompeiu formula (a particular case of Bochner– Martinelli formula) are the corollaries of complex forms of Gauss’s theorem and Green’s identity. They reduce the integrals over the area of the domain to those over its boundary. The latter integrals can be evaluated analytically for various density functions. Analytical expressions are presented for basic integrals involved in the single- and double-layer potentials for potential (harmonic) and elasticity problems.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"67 1","pages":"505-523"},"PeriodicalIF":0.9,"publicationDate":"2014-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBU015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

Scattering by a semi-infinite lattice and the excitation of Bloch waves 半无限晶格的散射和布洛赫波的激发

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-08-01 DOI: 10.1093/QJMAM/HBU014

N. Tymis, Ian Thompson

引用次数: 18

An extended wide-spacing approximation for two-dimensional water-wave problems in infinite depth 无限深度二维水波问题的扩展宽间距近似

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-08-01 DOI: 10.1093/QJMAM/HBU013

P. Mciver

引用次数: 5

The effects of an outer flow on the unsteady free convection boundary layer near a stagnation point in a heat-generating porous medium 外流对热多孔介质中驻点附近非定常自由对流边界层的影响

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-08-01 DOI: 10.1093/QJMAM/HBU012

J. Merkin

引用次数: 7

High frequency homogenisation for elastic lattices 弹性晶格的高频均匀化

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-07-08 DOI: 10.1093/QJMAM/HBV005

D. Colquitt, R. Craster, M. Makwana

{"title":"High frequency homogenisation for elastic lattices","authors":"D. Colquitt, R. Craster, M. Makwana","doi":"10.1093/QJMAM/HBV005","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV005","url":null,"abstract":"AbstractA complete methodology, based on a two-scale asymptotic approach, that enables the ho-mogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distin-guished from scalar lattices in that two or more types of coupled waves exist, even at low frequen-cies. Such a theory enables the determination of e ective material properties at both low and highfrequencies. The theoretical framework is developed for the propagation of waves through latticesof arbitrary geometry and dimension. The asymptotic approach provides a method through whichthe dispersive properties of lattices at frequencies near standing waves can be described; the theoryaccurately describes both the dispersion curves and the response of the lattice near the edges ofthe Brillouin zone. The leading order solution is expressed as a product between the standingwave solution and long-scale envelope functions that are eigensolutions of the homogenised partialdi erential equation. The general theory is supplemented by a pair of illustrative examples fortwo archetypal classes of two-dimensional elastic lattices. The e\u000eciency of the asymptotic ap-proach in accurately describing several interesting phenomena is demonstrated, including dynamicanisotropy and Dirac cones.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"203-230"},"PeriodicalIF":0.9,"publicationDate":"2014-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 20

Plane strain problem in elastically rigid finite plasticity 弹刚有限塑性中的平面应变问题

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-05-01 DOI: 10.1093/QJMAM/HBU007

Anurag Gupta, D. Steigmann

引用次数: 2

Problem of the consolidation of a laterally loaded radially-drained poroelastic cylinder 横向加载径向排水多孔弹性圆柱体的固结问题

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-05-01 DOI: 10.1093/QJMAM/HBU001

A. Suvorov

引用次数: 1

EFFECTIVE ANTIPLANE ELASTIC PROPERTIES OF AN ORTHOTROPIC SOLID WEAKENED BY A PERIODIC DISTRIBUTION OF CRACKS 裂纹周期性分布削弱正交各向异性固体的有效反平面弹性特性

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-05-01 DOI: 10.1093/QJMAM/HBU008

T. Williams, W. Parnell

{"title":"EFFECTIVE ANTIPLANE ELASTIC PROPERTIES OF AN ORTHOTROPIC SOLID WEAKENED BY A PERIODIC DISTRIBUTION OF CRACKS","authors":"T. Williams, W. Parnell","doi":"10.1093/QJMAM/HBU008","DOIUrl":"https://doi.org/10.1093/QJMAM/HBU008","url":null,"abstract":"Summary Using the method of asymptotic homogenization in the low-frequency wave propagation regime we derive the effective antiplane elastic properties of a cracked solid which in the absence of cracks would be orthotropic. The solid is a periodic medium defined by a periodic cell containing N cracks of infinite extent in thez direction but with arbitrary shape and orientation in thexy plane. Effective properties are defined in terms of the solution to a so-called cell problem. We propose two convenient schemes by which the cell problem can be solved, one based on a nearly periodic Green’s function, the other based on doubly periodic multipole expansions. Using these methods we compare results with existing approximate expressions for periodic arrays of straight cracks and discuss their regimes of validity by assessing their departure from the exact results obtained by the present method. We go on to consider more complex distributions such as elliptical cavities, non-straight cracks and effects of an orthotropic host phase. In particular we show that specific types of regular arrays of cracks in an orthotropic host medium can induce a macroscopically isotropic response to antiplane shear waves propagating in the xy plane.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"67 1","pages":"311-342"},"PeriodicalIF":0.9,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBU008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Circumferential stress waves in a non-linear cylindrical annulus in a new class of elastic materials 一类新型弹性材料中非线性圆柱环内的周向应力波

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-05-01 DOI: 10.1093/QJMAM/HBU003

M. Kambapalli, K. Kannan, K. Rajagopal

引用次数: 17

Connections between potentials describing wave scattering by complementary arrangements of vertical barriers 通过垂直屏障的互补排列描述波散射的电位之间的联系

IF 0.9 4区工程技术

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-05-01 DOI: 10.1093/QJMAM/HBU002

R. Porter, D. Evans

引用次数: 4