Mathematics and Mechanics of Solids最新文献_第4页

An analytical solution for the orthotropic semi-infinite plane with an arbitrary-shaped hole 带任意形状孔的正交半无限平面的解析解

Mathematics and Mechanics of Solids Pub Date : 2024-02-06 DOI: 10.1177/10812865231225131

Yulin Zhou, A. Lu, Ning Zhang

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引用次数: 0

A study on the effect of defects on the buckling of double-walled carbon nanotubes under compression based on a new atomic-continuum coupling method 基于原子-真空耦合新方法的缺陷对双壁碳纳米管压缩屈曲影响的研究

Mathematics and Mechanics of Solids Pub Date : 2024-02-06 DOI: 10.1177/10812865231217705

Xiangyang Wang, H. Qi, Jiqiang Li, Junying Bi, Renpeng Qiao, Jingrui Zhang

引用次数: 0

A two-dimensional four-node quadrilateral inverse element for shape sensing and structural health monitoring 用于形状传感和结构健康监测的二维四节点四边形反演元件

Mathematics and Mechanics of Solids Pub Date : 2024-02-06 DOI: 10.1177/10812865231224384

Mingyang Li, Erkan Oterkus, S. Oterkus

引用次数: 0

Debonding of an elastic layer with a cavity from a rigid substrate caused by rotation of a bonded rigid cylinder 粘合刚性圆柱体旋转导致带有空腔的弹性层与刚性基体脱粘

Mathematics and Mechanics of Solids Pub Date : 2024-02-05 DOI: 10.1177/10812865231214197

P. Malits

{"title":"Debonding of an elastic layer with a cavity from a rigid substrate caused by rotation of a bonded rigid cylinder","authors":"P. Malits","doi":"10.1177/10812865231214197","DOIUrl":"https://doi.org/10.1177/10812865231214197","url":null,"abstract":"Debonding of an elastic layer with a circular cylindrical cavity [Formula: see text], [Formula: see text], from a rigid substrate under action of a rigid cylinder is the object of this study. The annular debonding zone [Formula: see text] is caused by rotation of a cylinder bonded to the cavity surface. The problem is reformulated as dual integral equations with Weber integral transforms kernels. A Volterra operator transforming a Weber transforms kernel into a Bessel function of the first kind and Hankel integral transforms allow us to reduce dual equations to a Fredholm integral equation of the second kind and then, by some transformation, to another Fredholm integral equation which is more suitable for approximate methods. As [Formula: see text] and [Formula: see text], a highly accurate analytic approximate solution of the problem is suggested. The asymptotic solution of the problem is obtained as the width of debonding zone is very small while the thickness is not small. When the thickness is small, the Fredholm integral equations are computationally inefficient. A new method based on an operator transforming a Bessel function of the first kind into the kernel of Mehler–Fock integral transforms enabled us to convert one of the above-mentioned Fredholm equations into an equivalent Fredholm integral equation of the second kind that is effective for a small thickness. The asymptotic solution of the problem is obtained when both the layer thickness and the debonding zone width are small. Accurate mathematical methods, in particular investigations, and transformations of equations, developed in this study can be interesting to researchers employing dual integral equations technique in problems of mechanics and mathematical physics with mixed boundary conditions.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"73 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139863216","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: 0

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials 用 Wiener-Hopf 方法求解正交各向同性复合材料中移动半无限裂缝的反平面问题

Mathematics and Mechanics of Solids Pub Date : 2024-02-05 DOI: 10.1177/10812865231224348

Shiv Shankar Das, A. Tanwar, Subir Das, E. Crăciun

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引用次数: 0

Debonding of an elastic layer with a cavity from a rigid substrate caused by rotation of a bonded rigid cylinder 粘合刚性圆柱体旋转导致带有空腔的弹性层与刚性基体脱粘

Mathematics and Mechanics of Solids Pub Date : 2024-02-05 DOI: 10.1177/10812865231214197

P. Malits

{"title":"Debonding of an elastic layer with a cavity from a rigid substrate caused by rotation of a bonded rigid cylinder","authors":"P. Malits","doi":"10.1177/10812865231214197","DOIUrl":"https://doi.org/10.1177/10812865231214197","url":null,"abstract":"Debonding of an elastic layer with a circular cylindrical cavity [Formula: see text], [Formula: see text], from a rigid substrate under action of a rigid cylinder is the object of this study. The annular debonding zone [Formula: see text] is caused by rotation of a cylinder bonded to the cavity surface. The problem is reformulated as dual integral equations with Weber integral transforms kernels. A Volterra operator transforming a Weber transforms kernel into a Bessel function of the first kind and Hankel integral transforms allow us to reduce dual equations to a Fredholm integral equation of the second kind and then, by some transformation, to another Fredholm integral equation which is more suitable for approximate methods. As [Formula: see text] and [Formula: see text], a highly accurate analytic approximate solution of the problem is suggested. The asymptotic solution of the problem is obtained as the width of debonding zone is very small while the thickness is not small. When the thickness is small, the Fredholm integral equations are computationally inefficient. A new method based on an operator transforming a Bessel function of the first kind into the kernel of Mehler–Fock integral transforms enabled us to convert one of the above-mentioned Fredholm equations into an equivalent Fredholm integral equation of the second kind that is effective for a small thickness. The asymptotic solution of the problem is obtained when both the layer thickness and the debonding zone width are small. Accurate mathematical methods, in particular investigations, and transformations of equations, developed in this study can be interesting to researchers employing dual integral equations technique in problems of mechanics and mathematical physics with mixed boundary conditions.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"5 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139803222","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: 0

Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures 针对可压缩夹层结构的带剪应力连续性的增强梁和板有限元

Mathematics and Mechanics of Solids Pub Date : 2024-02-05 DOI: 10.1177/10812865231221992

Bence Hauck, A. Szekrényes

{"title":"Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures","authors":"Bence Hauck, A. Szekrényes","doi":"10.1177/10812865231221992","DOIUrl":"https://doi.org/10.1177/10812865231221992","url":null,"abstract":"This paper concerns and presents new improved beam and plate finite elements for analysing sandwich structures from the structural and modal points of view. In this study, the material behaviour is supposed to be linear elastic and orthotropic, but the method could be extended for nonlinear problems as well. The current models are able to treat the compressibility of the soft core materials, besides the interlaminar continuity conditions and the zero shear stresses on the shear-free surfaces are granted by the Lagrange multiplier method. In order to provide stress continuity along the element boundaries, the Hermite interpolation is employed for the elementary formulations that yields subparametric finite elements. On the contrary, the semi-analytical solutions of these enhanced beam and plate models are also discussed here for particular boundary conditions. The verification of the new finite elements is carried out by two case studies. The test examples are modelled and solved in commercial finite element software (ANSYS) with general shell and solid elements, too. The results derived from different models are subjected to a comprehensive comparison. Also, the structural and modal analyses of the test examples are presented during the case studies. The structural analysis of an overconstrained sandwich panel is also discussed to point out the significance of the proper shear stress distributions. Finally, the advantages and disadvantages of the newly developed elements and semi-analytical solutions are revealed in detail.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"13 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139805870","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: 0

Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures 针对可压缩夹层结构的带剪应力连续性的增强梁和板有限元

Mathematics and Mechanics of Solids Pub Date : 2024-02-05 DOI: 10.1177/10812865231221992

Bence Hauck, A. Szekrényes

{"title":"Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures","authors":"Bence Hauck, A. Szekrényes","doi":"10.1177/10812865231221992","DOIUrl":"https://doi.org/10.1177/10812865231221992","url":null,"abstract":"This paper concerns and presents new improved beam and plate finite elements for analysing sandwich structures from the structural and modal points of view. In this study, the material behaviour is supposed to be linear elastic and orthotropic, but the method could be extended for nonlinear problems as well. The current models are able to treat the compressibility of the soft core materials, besides the interlaminar continuity conditions and the zero shear stresses on the shear-free surfaces are granted by the Lagrange multiplier method. In order to provide stress continuity along the element boundaries, the Hermite interpolation is employed for the elementary formulations that yields subparametric finite elements. On the contrary, the semi-analytical solutions of these enhanced beam and plate models are also discussed here for particular boundary conditions. The verification of the new finite elements is carried out by two case studies. The test examples are modelled and solved in commercial finite element software (ANSYS) with general shell and solid elements, too. The results derived from different models are subjected to a comprehensive comparison. Also, the structural and modal analyses of the test examples are presented during the case studies. The structural analysis of an overconstrained sandwich panel is also discussed to point out the significance of the proper shear stress distributions. Finally, the advantages and disadvantages of the newly developed elements and semi-analytical solutions are revealed in detail.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"12 4-5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139865894","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: 0

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials 用 Wiener-Hopf 方法求解正交各向同性复合材料中移动半无限裂缝的反平面问题

Mathematics and Mechanics of Solids Pub Date : 2024-02-05 DOI: 10.1177/10812865231224348

Shiv Shankar Das, A. Tanwar, Subir Das, E. Crăciun

{"title":"Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials","authors":"Shiv Shankar Das, A. Tanwar, Subir Das, E. Crăciun","doi":"10.1177/10812865231224348","DOIUrl":"https://doi.org/10.1177/10812865231224348","url":null,"abstract":"This paper contains the solution to the problem of a semi-infinite moving crack situated in an orthotropic strip bonded between two identical strips. The crack moves with a constant velocity, and the surface is under shear wave disturbance. We first examine the equations of elasticity, which include equilibrium equations and stress and displacement constitutive relations with the model-specific continuity and boundary conditions. Using the Fourier integral transform, the standard form for the Wiener–Hopf (W-H) equation is obtained, which is solved using the W-H method. The analytical expressions for the considered crack problem have been obtained for stress intensity factor (SIF), normalized stress intensity factor (NSIF), and stress magnification factor (SMF). The behavior of NSIF has been graphically presented for particular cases of composite materials for different crack propagation velocities and various depth ratios of the strips. The novelty of this paper lies in the analytic solutions using the W-H method for the semi-infinite moving crack problem under the influence of anti-plane shear waves. The pictorial presentations of normalized SIF clearly show their dependency on strip depths, crack propagation velocities and elastic constants.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"105 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139804523","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: 0

Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics 进化微分变分-半变量不等式的良好拟合及其在摩擦接触力学中的应用

Mathematics and Mechanics of Solids Pub Date : 2024-02-03 DOI: 10.1177/10812865231209256

N. S. Taki, Kundan Kumar

引用次数: 0