Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences最新文献_第7页

The mass of cylindrical systems in general relativity 广义相对论中圆柱形系统的质量

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-02-08 DOI: 10.1098/rspa.1990.0012

H. Bondi

引用次数: 18

The effective boundary conditions for a perforated elastic sandwich panel in a compressible fluid 可压缩流体中多孔弹性夹层板的有效边界条件

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-02-08 DOI: 10.1098/rspa.1990.0019

F. G. Leppington

引用次数: 17

Singularities, interfaces and cracks in dissimilar anisotropic media 不同各向异性介质中的奇点、界面和裂缝

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-02-08 DOI: 10.1098/rspa.1990.0016

Z. Suo

{"title":"Singularities, interfaces and cracks in dissimilar anisotropic media","authors":"Z. Suo","doi":"10.1098/rspa.1990.0016","DOIUrl":"https://doi.org/10.1098/rspa.1990.0016","url":null,"abstract":"For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"18 1","pages":"331 - 358"},"PeriodicalIF":0.0,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89865892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 705

Conservation and non-conservation in general relativity 广义相对论中的守恒和不守恒

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-02-08 DOI: 10.1098/rspa.1990.0011

H. Bondi

引用次数: 97

Horizontal free convection 水平自由对流

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-02-08 DOI: 10.1098/rspa.1990.0018

N. Amin, N. Riley

引用次数: 16

The analysis of interlaminar fracture in uniaxial fibre-polymer composites 单轴纤维-聚合物复合材料层间断裂分析

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0007

S. Hashemi, A. Kinloch, J. M. Williams

{"title":"The analysis of interlaminar fracture in uniaxial fibre-polymer composites","authors":"S. Hashemi, A. Kinloch, J. M. Williams","doi":"10.1098/rspa.1990.0007","DOIUrl":"https://doi.org/10.1098/rspa.1990.0007","url":null,"abstract":"One of the most important mechanical properties of a fibre-polymer composite is its resistance to delamination. The presence of delaminations may lead not only to complete fracture but even partial delaminations will lead to a loss of stiffness, which can be a very important design consideration. Because delamination may be regarded as crack propagation then an obvious scheme for characterizing this phenomenon has been via a fracture mechanics approach. There is, therefore, an extensive literature on the use of fracture mechanics to ascertain the interlaminar fracture energies, Gc, for various fibre-polymer composites using different test geometries to yield mode I, mode II and mixed mode I/II values of Gc. Nevertheless, problems of consistency and discussions on the accuracy of such results abound. This paper describes a detailed study of the methods of analysing the experimental data obtained from fracture mechanics tests using double-cantilever beam, end loaded split and end notched flexure specimens. It is shown that to get consistent and accurate values of Gc it is necessary to consider aspects of the tests such as the end rotation and deflection of the crack tip, the effective shortening of the beam due to large displacements of the arms, and the stiffening of the beam due to the presence of the end blocks bonded to the specimens. Analytical methods for ascertaining the various correction constants and factors are described and are successfully applied to the results obtained from three different fibre-polymer composites. These composites exhibit different types of fracture behaviour and illustrate the wide range of effects that must be considered when values of the interlaminar fracture energies, free from artefacts from the test method and the analysis method, are required.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"1 1","pages":"173 - 199"},"PeriodicalIF":0.0,"publicationDate":"1990-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78429995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 389

The scattering of sound by two semi-infinite parallel staggered plates. II. Evaluation of the velocity potential for an incident plane wave and an incident duct mode 两个半无限平行交错板对声音的散射。2对入射平面波和入射管道模式的速度势的评估

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0006

I. Abrahams, G. R. Wickham

{"title":"The scattering of sound by two semi-infinite parallel staggered plates. II. Evaluation of the velocity potential for an incident plane wave and an incident duct mode","authors":"I. Abrahams, G. R. Wickham","doi":"10.1098/rspa.1990.0006","DOIUrl":"https://doi.org/10.1098/rspa.1990.0006","url":null,"abstract":"In a recent paper Abrahams & Wickham showed how to exactly solve the diffraction problem for two parallel semi-infinite plates that are arranged to form a duct. The edges of the plates are misaligned so that the geometry is asymmetric with respect to the central line of the duct. In this paper we examine in detail the effect of this asymmetry on the field radiated from the duct when a fundamental travelling mode is excited within it, and the scattered field when a plane wave is excited at infinity. To evaluate the field in either case it is first necessary to solve the integral equations derived in our paper. Here we show how this is effected using the expansion theorem also enunciated in that paper. This solution is then used to calculate a number of physically interesting quantities such as the variation of the energy capture by the duct (when irradiated by an incident plane wave) as the stagger is increased and the asymmetric radiation pattern from an incident duct mode. The numerical computations are checked using an energy balance argument and, finally, a simple heuristic approximation is given for the scattering problem that in many situations accurately reproduces the essential physical characteristics of the solution.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"12 1","pages":"139 - 171"},"PeriodicalIF":0.0,"publicationDate":"1990-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90059870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 22

Heat transport into a shear flow at high Peclet number 高佩莱特数剪切流的热输运

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0002

J. Keller

引用次数: 0

The stress-driven redistribution of point defects in the vicinity of crack-like singularities 裂纹奇异点附近点缺陷的应力驱动重分布

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0001

H. Rauh, R. Bullough

引用次数: 3

Singular global bifurcation problems for the buckling of anisotropic plates 各向异性板屈曲的奇异全局分岔问题

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0005

P. V. Negrón-Marrero, S. Antman

{"title":"Singular global bifurcation problems for the buckling of anisotropic plates","authors":"P. V. Negrón-Marrero, S. Antman","doi":"10.1098/rspa.1990.0005","DOIUrl":"https://doi.org/10.1098/rspa.1990.0005","url":null,"abstract":"This paper treats a variety of unexpected pathologies that arise in the global bifurcation analysis of axisymmetrie buckled states of anisotropic plates. The geometrically exact plate theory used accounts for flexure, extension and shear. The nonlinear constitutive functions have very general form. As a consequence of the anisotropy the trivial solution may depend discontinuously on the load parameter. Accordingly, the equations for the bifurcation problem have the same character, so that bifurcating branches of solutions become disconnected as the load parameter crosses values at which discontinuities occur. The anisotropy furthermore implies that the governing equations have a singular behaviour much worse than that for isotropic plates. Consequently, a variety of novel constructions are required to demonstrate the validity of the essential results upon which global bifurcation theory stands. (These results include the compactness of certain operators and the uniqueness of solutions of initial value problems for singular ordinary differential equations.) It is shown that in regions of solution-parameter space in which the equations depend continuously on the load parameter there exist connected global branches of solution pairs that have detailed nodal properties inherited from eigenfunctions of the linearized problem. Moreover, these nodal properties are preserved across gaps occurring where discontinuities occur. The methodology used to show this result actually supports constructive methods for finding disconnected branches.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"22 1","pages":"137 - 95"},"PeriodicalIF":0.0,"publicationDate":"1990-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73162221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13