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Post-Buckling Solutions for the Gao Beam 高梁的后屈曲解
4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2023-09-24 DOI: 10.1093/qjmam/hbad007
H Netuka, J Machalová
{"title":"Post-Buckling Solutions for the Gao Beam","authors":"H Netuka, J Machalová","doi":"10.1093/qjmam/hbad007","DOIUrl":"https://doi.org/10.1093/qjmam/hbad007","url":null,"abstract":"Summary This article analyses static buckling of the so-called Gao beam nonlinear model. It considers pure buckling problems in which the vertical loads are omitted. The analysis, using minimisation of energy and the concept of a modified Rayleigh quotient, leads to new results regarding the critical load necessary for buckling, and the existence and number of post-buckling solutions. Computational results are provided for cases with fixed axial loading. Furthermore, the authors explore the impact of the system parameters on the solutions, which are summarised in a table. The new findings in this research are unique and help to better understand the behaviour of the static and dynamic Gao beam.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135924485","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: 0
Harmonic And Neutral Spherical Elastic Inhomogeneities with A Functionally Graded Interphase Layer 具有功能梯度相间层的调和和中性球弹性非均质性
4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2023-09-16 DOI: 10.1093/qjmam/hbad006
Xu Wang, Peter Schiavone
{"title":"Harmonic And Neutral Spherical Elastic Inhomogeneities with A Functionally Graded Interphase Layer","authors":"Xu Wang, Peter Schiavone","doi":"10.1093/qjmam/hbad006","DOIUrl":"https://doi.org/10.1093/qjmam/hbad006","url":null,"abstract":"Summary We study the elastic field in a three-phase composite composed of an internal spherical homogeneous elastic inhomogeneity, an intermediate functionally graded interphase layer and an outer unbounded homogeneous elastic matrix subjected to an arbitrary uniform remote loading. The shear modulus of the interphase layer obeys a power law distribution along the radial direction. We accomplish the design of harmonic and neutral spherical elastic inhomogeneities. Specifically, the shear modulus of the matrix can be judiciously chosen in such a way that the insertion of the harmonic spherical inhomogeneity does not disturb the original constant mean stress in the surrounding matrix. The shear modulus of the matrix and relative thickness of the interphase can also be suitably chosen such that the insertion of the neutral spherical inhomogeneity does not disturb the original uniform deviatoric stresses in the surrounding matrix.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135306039","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: 0
Theory of Perturbation of Electrostatic Field By A Coated Anisotropic Dielectric Sphere 涂覆各向异性介电球对静电场的扰动理论
4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2023-09-10 DOI: 10.1093/qjmam/hbad005
Nikolaos L Tsitsas, Hamad M Alkhoori, Akhlesh Lakhtakia
{"title":"Theory of Perturbation of Electrostatic Field By A Coated Anisotropic Dielectric Sphere","authors":"Nikolaos L Tsitsas, Hamad M Alkhoori, Akhlesh Lakhtakia","doi":"10.1093/qjmam/hbad005","DOIUrl":"https://doi.org/10.1093/qjmam/hbad005","url":null,"abstract":"Summary A boundary-value problem was formulated for perturbation of an electrostatic field by a coated dielectric sphere made of two distinct linear anisotropic dielectric (LAD) materials. Specific affine transformations were employed to represent the electric potential inside the core and the coating in terms of the solutions of the Laplace equation. A transition matrix was found to relate the source potential and the perturbation potential in the exterior region. The formulation can be straightforwardly extended to concentrically multilayered spheres made of several homogeneous LAD materials.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136072128","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: 1
Homogenisation of Nonlinear Heterogeneous Thin Plate When the Plate Thickness and In-Plane Heterogeneities are of the Same Order of Magnitude 当板厚度和平面内非均匀性为同一数量级时非线性非均匀薄板的均匀化
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2023-07-26 DOI: 10.1093/qjmam/hbad004
E. Pruchnicki
{"title":"Homogenisation of Nonlinear Heterogeneous Thin Plate When the Plate Thickness and In-Plane Heterogeneities are of the Same Order of Magnitude","authors":"E. Pruchnicki","doi":"10.1093/qjmam/hbad004","DOIUrl":"https://doi.org/10.1093/qjmam/hbad004","url":null,"abstract":"\u0000 In this work, we propose a new two-scale finite-strain thin plate theory for highly heterogeneous plates described by a repetitive periodic microstructure. For this type of theory, two scales exist, the macroscopic one is linked to the entire plate and the microscopic one is linked to the size of the heterogeneity. We consider the case when the plate thickness is comparable to in-plane heterogeneities. We assume that the nonlinear macroscopic part of the model is of Kirchhoff–Love type. We obtain the nonlinear homogenised model by performing simultaneously both the homogenisation and the reduction of the initial three-dimensional plate problem to a two-dimensional one. Since nonlinear equations are difficult to solve, we linearise this homogenised Kirchhoff–Love plate theory. Finally, we discuss the treatment of edge effects in the vicinity of the lateral boundary of the plate.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48827087","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: 1
Scattering by a Perforated Sandwich Panel: Method of Riemann Surfaces 多孔夹层板的散射:黎曼曲面的方法
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2023-04-03 DOI: 10.1093/qjmam/hbad003
Y. Antipov
{"title":"Scattering by a Perforated Sandwich Panel: Method of Riemann Surfaces","authors":"Y. Antipov","doi":"10.1093/qjmam/hbad003","DOIUrl":"https://doi.org/10.1093/qjmam/hbad003","url":null,"abstract":"\u0000 The model problem of scattering of a sound wave by an infinite plane structure formed by a semi-infinite acoustically hard screen and a semi-infinite sandwich panel perforated from one side and covered by a membrane from the other is exactly solved. The model is governed by two Helmholtz equations for the velocity potentials in the upper and lower half-planes coupled by the Leppington effective boundary condition and the equation of vibration of a membrane in a fluid. Two methods of solution are proposed and discussed. Both methods reduce the problem to an order-2 vector Riemann–Hilbert problem. The matrix coefficients have different entries, have the Chebotarev–Khrapkov structure and share the same order-4 characteristic polynomial. Exact Wiener–Hopf matrix factorization requires solving a scalar Riemann–Hilbert on an elliptic surface and the associated genus-1 Jacobi inversion problem solved in terms of the associated Riemann θ-function. Numerical results for the absolute value of the total velocity potentials are reported and discussed.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42584509","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: 0
Solitary waves on flows with an exponentially sheared current and stagnation points 具有指数剪切流和滞止点的流上的孤波
4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2023-01-09 DOI: 10.1093/qjmam/hbac021
Marcelo V Flamarion, Roberto-J R Ribeiro
{"title":"Solitary waves on flows with an exponentially sheared current and stagnation points","authors":"Marcelo V Flamarion, Roberto-J R Ribeiro","doi":"10.1093/qjmam/hbac021","DOIUrl":"https://doi.org/10.1093/qjmam/hbac021","url":null,"abstract":"Summary While several articles have been written on water waves on flows with constant vorticity, little is known about the extent to which a non-constant vorticity affects the flow structure, such as the appearance of stagnation points. In order to shed light on this topic, we investigate in detail the flow beneath solitary waves propagating on an exponentially decaying sheared current. Our focus is to analyse numerically the emergence of stagnation points. For this purpose, we approximate the velocity field within the fluid bulk through the classical Korteweg-de Vries asymptotic expansion and use the Matlab language to evaluate the resulting stream function. Our findings suggest that the flow beneath the waves can have 0, 1 or 2 stagnation points in the fluid body. We also study the bifurcation between these flows. Our simulations indicate that the stagnation points emerge from a streamline with a sharp corner.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136377346","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: 2
A new solution for the deformations of an initially elliptical elastic-walled tube 初始椭圆弹性壁管变形的新解
4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2023-01-09 DOI: 10.1093/qjmam/hbac018
D J Netherwood, R J Whittaker
{"title":"A new solution for the deformations of an initially elliptical elastic-walled tube","authors":"D J Netherwood, R J Whittaker","doi":"10.1093/qjmam/hbac018","DOIUrl":"https://doi.org/10.1093/qjmam/hbac018","url":null,"abstract":"Summary We investigate the small-amplitude deformations of a long thin-walled elastic tube having an initially axially uniform elliptical cross-section. The tube is deformed by a (possibly non-uniform) transmural pressure. At leading order, its deformations are shown to be governed by a single partial differential equation (PDE) for the azimuthal displacement as a function of the axial and azimuthal co-ordinates and time. Previous authors have obtained solutions to this PDE by making ad hoc approximations based on truncating an approximate Fourier representation. In this article, we instead write the azimuthal displacement as a sum over the azimuthal eigenfunctions of a generalised eigenvalue problem and show that we are able to derive an uncoupled system of linear PDEs with constant coefficients for the amplitude of the azimuthal modes as a function of the axial co-ordinate and time. This results in a formal solution of the whole system being found as a sum over the azimuthal modes. We show that the $n$th mode’s contribution to the tube’s relative area change is governed by a simplified second-order PDE and examine the case in which the tube’s deformations are driven by a uniform transmural pressure. The relative errors induced by truncating the series solution after the first and second terms are then evaluated as a function of both the ellipticity and pre-stress of the tube. After comparing our results with Whittaker et al. (A rational derivation of a tube law from shell theory, Q. J. Mech. Appl. Math. 63 (2010) 465–496), we find that this new method leads to a significant simplification when calculating contributions from the higher-order azimuthal modes, which in turn makes a more accurate solution easier to obtain.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135013259","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: 0
Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions 直角无对比可穿透楔的衍射:谱函数的解析延拓
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2022-11-23 DOI: 10.1093/qjmam/hbad002
Valentin D. Kunz, R. Assier
{"title":"Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions","authors":"Valentin D. Kunz, R. Assier","doi":"10.1093/qjmam/hbad002","DOIUrl":"https://doi.org/10.1093/qjmam/hbad002","url":null,"abstract":"\u0000 We study the problem of diffraction by a right-angled no-contrast penetrable wedge by means of a two-complex-variable Wiener–Hopf approach. Specifically, the analyticity properties of the unknown (spectral) functions of the two-complex-variable Wiener–Hopf equation are studied. We show that these spectral functions can be analytically continued onto a two-complex dimensional manifold, and unveil their singularities in C2. To do so, integral representation formulae for the spectral functions are given and thoroughly used. It is shown that the novel concept of additive crossing holds for the penetrable wedge diffraction problem, and that we can reformulate the physical diffraction problem as a functional problem using this concept.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45248831","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: 2
OUP accepted manuscript OUP接受稿件
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.1093/qjmam/hbac004
{"title":"OUP accepted manuscript","authors":"","doi":"10.1093/qjmam/hbac004","DOIUrl":"https://doi.org/10.1093/qjmam/hbac004","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61233389","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: 3
OUP accepted manuscript OUP接受稿件
IF 0.9 4区 工程技术
Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.1093/qjmam/hbac003
{"title":"OUP accepted manuscript","authors":"","doi":"10.1093/qjmam/hbac003","DOIUrl":"https://doi.org/10.1093/qjmam/hbac003","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61233841","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: 0
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