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Effect of quadratically varying electric potential on the multiple cracks in piezoelectric materials 二次变化电势对压电材料多重裂纹的影响
Mathematics and Mechanics of Solids Pub Date : 2024-06-03 DOI: 10.1177/10812865241249439
Irshad Saifi, S. Hasan
{"title":"Effect of quadratically varying electric potential on the multiple cracks in piezoelectric materials","authors":"Irshad Saifi, S. Hasan","doi":"10.1177/10812865241249439","DOIUrl":"https://doi.org/10.1177/10812865241249439","url":null,"abstract":"A basic solution to the problem of three collinear equal cracks in a transversely isotropic piezoelectric material plate is obtained under the influence of electromechanical forces. Stroh formalism and complex variable methods are used to derive the mathematical expressions for SIF (stress intensity factor), COD (crack opening displacement), and COP (crack opening potential). The length of the saturation zones is investigated at each crack tip under the influence of quadratically varying electric displacement. Furthermore, a numerical study is carried out to discuss the effect of quadratically varying electrical potential on the saturation zone, COD, and COP. The results obtained numerically are reported graphically.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"23 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141270537","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
A simple method for mechanical analysis of pressurized functionally graded material thick-walled cylinder 加压功能分级材料厚壁圆柱体力学分析的简单方法
Mathematics and Mechanics of Solids Pub Date : 2024-05-24 DOI: 10.1177/10812865241249750
Yijie Liu, Bensheng Huang, Mingdao Yuan, Yunqian Xu, Wei Wang, Fengjie Yang
{"title":"A simple method for mechanical analysis of pressurized functionally graded material thick-walled cylinder","authors":"Yijie Liu, Bensheng Huang, Mingdao Yuan, Yunqian Xu, Wei Wang, Fengjie Yang","doi":"10.1177/10812865241249750","DOIUrl":"https://doi.org/10.1177/10812865241249750","url":null,"abstract":"The complex function method is employed to establish a mechanical model for pressurized thick-wall cylinders made of functionally graded materials (FGM). This model is applicable to all radial varying modes of material properties, including both continuous and discontinuous variations in Young’s modulus and Poisson’s ratio. The main concept behind this mechanical model involves dividing the thick-walled cylinder into concentric thin cylinders, each equipped with a pair of analytical functions representing stress functions. By imposing continuity conditions between adjacent thin cylinders and considering the stress boundary conditions of the entire structure, all unknown forms of analytical functions can be determined. Subsequently, by establishing the correspondence relationship between these analytical functions and stress or displacement, it becomes possible to solve for the stress or displacement at any radial position within the thick-walled cylinder. Through comparison and verification against the numerical simulation results, it can demonstrate that as long as the differential scale is sufficiently small, high accuracy can be achieved in the final result. In other words, solutions obtained for multi-layered hollow cylinder converge toward those obtained for continuously graded thick-walled cylinder. Notably, by starting from the level of stress function and avoiding complex differential and integral equations, a linear equation system can provide information on stress and displacement distributions along the radial direction. Therefore, compared to other solving methods available, this proposed approach offers simplicity and applicability.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"2 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141100123","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
A two-dimensional elastic contact problem with unilateral constraints 具有单边约束条件的二维弹性接触问题
Mathematics and Mechanics of Solids Pub Date : 2024-05-17 DOI: 10.1177/10812865241247807
M. Sofonea, Á. Arós
{"title":"A two-dimensional elastic contact problem with unilateral constraints","authors":"M. Sofonea, Á. Arós","doi":"10.1177/10812865241247807","DOIUrl":"https://doi.org/10.1177/10812865241247807","url":null,"abstract":"We consider a mathematical model which describes the equilibrium of two elastic membranes fixed on their boundary and attached to an adhesive body, say a glue. The variational formulation of the model is in a form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the model, and then we state and prove a convergence result, for which we provide the corresponding mechanical interpretation. Next, we consider two associated optimization problems for which we provide existence results. Finally, we the present numerical simulation which validates our convergence result. We end this paper with some concluding remarks and an Appendix, in which we present the preliminary material needed in this paper.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140965942","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
A modified couple stress model to analyze the effect of size-dependent on thermal interactions in rotating nanobeams whose properties change with temperature 用修正的耦合应力模型分析旋转纳米梁中随温度变化而变化的热相互作用的尺寸效应
Mathematics and Mechanics of Solids Pub Date : 2024-02-14 DOI: 10.1177/10812865241228301
A. Abouelregal, Mohammed NA Rabih, Hind A Alharbi, Sami F. Megahid
{"title":"A modified couple stress model to analyze the effect of size-dependent on thermal interactions in rotating nanobeams whose properties change with temperature","authors":"A. Abouelregal, Mohammed NA Rabih, Hind A Alharbi, Sami F. Megahid","doi":"10.1177/10812865241228301","DOIUrl":"https://doi.org/10.1177/10812865241228301","url":null,"abstract":"Understanding the behavior of rotating materials and structures on small scales is crucial for many scientific and engineering fields, and such studies play an important role in this regard. This paper aims to propose a novel paradigm for analyzing the vibrational characteristics of thermoelastic nanobeams with diverse physical attributes. The incorporation of size effects in the structural and thermal constitutive relationships involves the consideration of nonlocal elasticity theory (NET) and the modified couple stress (MCS) model, together with the utilization of the Euler–Bernoulli assumptions for thin beams. The work also involves the development of a new non-Fourier thermoelasticity model that incorporates the Moore–Gibson–Thompson (MGT) equation. Furthermore, it was taken into account that the thermal conductivity of the flexible materials is not consistent but rather changes with temperature. Periodic pulse heating was applied to rotating nanobeams, and the behavior of the nanobeams was investigated with respect to thermal, rotational, and length-scale effects. To demonstrate the impact of the distinctive characteristics of the MCS and MGT thermoelastic models on the physical fields, a range of numerical data are presented. The study also investigated the propagation characteristics of thermo-mechanical waves, taking into account aspects such as thermal relaxation time and the influence of temperature change on physical properties. Based on the observed results, including the size impact in the structural and thermal equations can lead to significant disparities when compared to conventional models. The inclusion of the length-scale component in the MCS theory, which increases the rigidity and hardiness of the nanobeam structure, may help to explain the observed effect.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"56 46","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139777883","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
A modified couple stress model to analyze the effect of size-dependent on thermal interactions in rotating nanobeams whose properties change with temperature 用修正的耦合应力模型分析旋转纳米梁中随温度变化而变化的热相互作用的尺寸效应
Mathematics and Mechanics of Solids Pub Date : 2024-02-14 DOI: 10.1177/10812865241228301
A. Abouelregal, Mohammed NA Rabih, Hind A Alharbi, Sami F. Megahid
{"title":"A modified couple stress model to analyze the effect of size-dependent on thermal interactions in rotating nanobeams whose properties change with temperature","authors":"A. Abouelregal, Mohammed NA Rabih, Hind A Alharbi, Sami F. Megahid","doi":"10.1177/10812865241228301","DOIUrl":"https://doi.org/10.1177/10812865241228301","url":null,"abstract":"Understanding the behavior of rotating materials and structures on small scales is crucial for many scientific and engineering fields, and such studies play an important role in this regard. This paper aims to propose a novel paradigm for analyzing the vibrational characteristics of thermoelastic nanobeams with diverse physical attributes. The incorporation of size effects in the structural and thermal constitutive relationships involves the consideration of nonlocal elasticity theory (NET) and the modified couple stress (MCS) model, together with the utilization of the Euler–Bernoulli assumptions for thin beams. The work also involves the development of a new non-Fourier thermoelasticity model that incorporates the Moore–Gibson–Thompson (MGT) equation. Furthermore, it was taken into account that the thermal conductivity of the flexible materials is not consistent but rather changes with temperature. Periodic pulse heating was applied to rotating nanobeams, and the behavior of the nanobeams was investigated with respect to thermal, rotational, and length-scale effects. To demonstrate the impact of the distinctive characteristics of the MCS and MGT thermoelastic models on the physical fields, a range of numerical data are presented. The study also investigated the propagation characteristics of thermo-mechanical waves, taking into account aspects such as thermal relaxation time and the influence of temperature change on physical properties. Based on the observed results, including the size impact in the structural and thermal equations can lead to significant disparities when compared to conventional models. The inclusion of the length-scale component in the MCS theory, which increases the rigidity and hardiness of the nanobeam structure, may help to explain the observed effect.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"91 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139837639","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
Continuous distributions of certain defects in smectic mixtures 胶凝混合物中某些缺陷的连续分布
Mathematics and Mechanics of Solids Pub Date : 2024-02-14 DOI: 10.1177/10812865241227417
Marcelo Epstein
{"title":"Continuous distributions of certain defects in smectic mixtures","authors":"Marcelo Epstein","doi":"10.1177/10812865241227417","DOIUrl":"https://doi.org/10.1177/10812865241227417","url":null,"abstract":"A certain type of defectivity applicable to binary mixtures of uniform solids and liquid crystals is identified as arising from the possible lack of uniformity of the composite as a result of a misalignment between the structures of the underlying constituents. Various local measures of misalignment are derived for the case of a smectic-A combined with solids with discrete or continuous symmetry groups.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"65 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139778843","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
Continuous distributions of certain defects in smectic mixtures 胶凝混合物中某些缺陷的连续分布
Mathematics and Mechanics of Solids Pub Date : 2024-02-14 DOI: 10.1177/10812865241227417
Marcelo Epstein
{"title":"Continuous distributions of certain defects in smectic mixtures","authors":"Marcelo Epstein","doi":"10.1177/10812865241227417","DOIUrl":"https://doi.org/10.1177/10812865241227417","url":null,"abstract":"A certain type of defectivity applicable to binary mixtures of uniform solids and liquid crystals is identified as arising from the possible lack of uniformity of the composite as a result of a misalignment between the structures of the underlying constituents. Various local measures of misalignment are derived for the case of a smectic-A combined with solids with discrete or continuous symmetry groups.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"50 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139838450","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
Response to David Steigmann’s discussion of our paper 回应 David Steigmann 对我们论文的讨论
Mathematics and Mechanics of Solids Pub Date : 2024-02-12 DOI: 10.1177/10812865231224106
T. X. Duong, Mikhail Itskov, R. Sauer
{"title":"Response to David Steigmann’s discussion of our paper","authors":"T. X. Duong, Mikhail Itskov, R. Sauer","doi":"10.1177/10812865231224106","DOIUrl":"https://doi.org/10.1177/10812865231224106","url":null,"abstract":"","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"9 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139783229","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
Response to David Steigmann’s discussion of our paper 回应 David Steigmann 对我们论文的讨论
Mathematics and Mechanics of Solids Pub Date : 2024-02-12 DOI: 10.1177/10812865231224106
T. X. Duong, Mikhail Itskov, R. Sauer
{"title":"Response to David Steigmann’s discussion of our paper","authors":"T. X. Duong, Mikhail Itskov, R. Sauer","doi":"10.1177/10812865231224106","DOIUrl":"https://doi.org/10.1177/10812865231224106","url":null,"abstract":"","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"121 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139842887","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
Response to the reply by Duong et al. 对 Duong 等人答复的回应
Mathematics and Mechanics of Solids Pub Date : 2024-02-12 DOI: 10.1177/10812865231223612
D. Steigmann
{"title":"Response to the reply by Duong et al.","authors":"D. Steigmann","doi":"10.1177/10812865231223612","DOIUrl":"https://doi.org/10.1177/10812865231223612","url":null,"abstract":"","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"213 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139842117","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
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