We study the behavior of attractors of the reaction–diffusion equation in a perforated domain as the small parameter characterizing the perforation tends to zero. Résumé. Nous étudions le comportement des attracteurs de l’équation de réaction–diffusion dans le domaine perforé car le petit paramètre caractérisant la perforation tend vers zéro.
(We the behavior of attractors of the study in a反应—传播方程perforated domain as the small参数characterizing the穿孔山野to zero。摘要。我们研究了反应扩散方程吸引子在穿孔区域的行为，因为表征穿孔的小参数趋向于零。
{"title":"Attractors and a “strange term” in homogenized equation","authors":"K. Bekmaganbetov, G. Chechkin, V. Chepyzhov","doi":"10.5802/crmeca.1","DOIUrl":"https://doi.org/10.5802/crmeca.1","url":null,"abstract":"We study the behavior of attractors of the reaction–diffusion equation in a perforated domain as the small parameter characterizing the perforation tends to zero. Résumé. Nous étudions le comportement des attracteurs de l’équation de réaction–diffusion dans le domaine perforé car le petit paramètre caractérisant la perforation tend vers zéro.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"27 1","pages":"351-359"},"PeriodicalIF":0.8,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83320087","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}
A semi-analytical finite element method algorithm was established to plot the dispersion curves of isotropic aluminum and orthotropic plates. The curves obtained are compared with those plotted by the DISPERSE software and with previous experimental work. The results showed that the accuracy of the method depends on the number of elements for meshing. To ensure good precision and speed of the method, the number of elements per plate thickness must be optimized.
{"title":"Quantitative evaluation of semi-analytical finite element method for modeling Lamb waves in orthotropic plates","authors":"Salah Nissabouri, M. Allami, E. Boutyour","doi":"10.5802/crmeca.13","DOIUrl":"https://doi.org/10.5802/crmeca.13","url":null,"abstract":"A semi-analytical finite element method algorithm was established to plot the dispersion curves of isotropic aluminum and orthotropic plates. The curves obtained are compared with those plotted by the DISPERSE software and with previous experimental work. The results showed that the accuracy of the method depends on the number of elements for meshing. To ensure good precision and speed of the method, the number of elements per plate thickness must be optimized.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"500 1","pages":"335-350"},"PeriodicalIF":0.8,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85640142","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}
Daniel Dorostghoal, A. Zare, Ali Alipour Mansourkhani
In the present study, the governing differential equations of motion are developed by using the Hamilton principle for a three-layered curved sandwich beam with symmetric face layers. To develop the dynamic stiffness matrix, the face layers are considered to behave like Euler–Bernoulli beams although only shear deformation occurs in the core. In this research, for computing the natural frequencies of curved sandwich beams, the Wittrick–Williams algorithm is applied. After the procedure is validated by comparison with various published results, to indicate its range of application, natural frequencies of a complex frame are computed. Finally, a parametric study investigated the effect of thickness and curvature for various boundary conditions on the natural frequencies.
{"title":"Exact free vibration of symmetric three-layered curved sandwich beams using dynamic stiffness matrix","authors":"Daniel Dorostghoal, A. Zare, Ali Alipour Mansourkhani","doi":"10.5802/crmeca.45","DOIUrl":"https://doi.org/10.5802/crmeca.45","url":null,"abstract":"In the present study, the governing differential equations of motion are developed by using the Hamilton principle for a three-layered curved sandwich beam with symmetric face layers. To develop the dynamic stiffness matrix, the face layers are considered to behave like Euler–Bernoulli beams although only shear deformation occurs in the core. In this research, for computing the natural frequencies of curved sandwich beams, the Wittrick–Williams algorithm is applied. After the procedure is validated by comparison with various published results, to indicate its range of application, natural frequencies of a complex frame are computed. Finally, a parametric study investigated the effect of thickness and curvature for various boundary conditions on the natural frequencies.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"87 1","pages":"375-392"},"PeriodicalIF":0.8,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78292924","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}
H. Boussetta, A. Laksimi, H. Kebir, M. Beyaoui, L. Walha, M. Haddar
The aim of this paper is to propose a theoretical meso-model describing the nonlinear behaviour of filament wound glass–polyester composite structures based on a progressive damage and failure analysis. This model has been implemented in the finite element modelling software Abaqus through the user material subroutine and then validated by experimental investigations. Numerical results have been compared with experimental data obtained from a set of tests on representative specimens using the strain measurement technique.
{"title":"Plastic-damage-response analysis of glass/polyester filament wound structures: 3D meso-scale numerical modelling, experimental identification and validation","authors":"H. Boussetta, A. Laksimi, H. Kebir, M. Beyaoui, L. Walha, M. Haddar","doi":"10.5802/crmeca.10","DOIUrl":"https://doi.org/10.5802/crmeca.10","url":null,"abstract":"The aim of this paper is to propose a theoretical meso-model describing the nonlinear behaviour of filament wound glass–polyester composite structures based on a progressive damage and failure analysis. This model has been implemented in the finite element modelling software Abaqus through the user material subroutine and then validated by experimental investigations. Numerical results have been compared with experimental data obtained from a set of tests on representative specimens using the strain measurement technique.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"34 1","pages":"315-333"},"PeriodicalIF":0.8,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89840577","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}
In the present study, a novel quadrilateral element, namely SQ4C, combined with the Timoshenko beam element is proposed for the static and buckling analyses of stiffened plate/shell structures. The idea behind these elements is a treatment for shear locking as well as membrane locking arising from the framework of the first-order shear deformation theory and a mesh with curved shell geometry. Formulations with eccentricity are also presented in this paper for the general case. The static and buckling analysis solutions and comparison with other available numerical solutions are presented to illustrate the robustness of the proposed elements to stiffened plate/shell structures. This paper also helps engineers in supplementing their knowledge.
{"title":"Static and buckling analyses of stiffened plate/shell structures using the quadrilateral element SQ4C","authors":"H. Ton-that, H. Nguyen-Van, T. Chau-Dinh","doi":"10.5802/crmeca.7","DOIUrl":"https://doi.org/10.5802/crmeca.7","url":null,"abstract":"In the present study, a novel quadrilateral element, namely SQ4C, combined with the Timoshenko beam element is proposed for the static and buckling analyses of stiffened plate/shell structures. The idea behind these elements is a treatment for shear locking as well as membrane locking arising from the framework of the first-order shear deformation theory and a mesh with curved shell geometry. Formulations with eccentricity are also presented in this paper for the general case. The static and buckling analysis solutions and comparison with other available numerical solutions are presented to illustrate the robustness of the proposed elements to stiffened plate/shell structures. This paper also helps engineers in supplementing their knowledge.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"16 1","pages":"285-305"},"PeriodicalIF":0.8,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74546801","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}
{"title":"Correspondence between de Saint-Venant and Boussinesq 3: de Saint-Venant’s professional career and private life","authors":"W. Hager, K. Hutter, O. Castro-Orgaz","doi":"10.5802/crmeca.40","DOIUrl":"https://doi.org/10.5802/crmeca.40","url":null,"abstract":"","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"169 1","pages":"245-273"},"PeriodicalIF":0.8,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73695266","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}
This paper deals with the lower bound for blow-up solutions to a quasilinear hyperbolic equation with strong damping. An inverse Hölder inequality with a correction constant is employed to overcome the difficulty caused by the failure of the embedding inequality. Moreover, a lower bound for blow-up time is obtained by constructing a new control functional with a small dissipative term and by applying an inverse Hölder inequality as well as energy inequalities. This result gives a positive answer to the open problem presented in [1].
{"title":"Lower bound estimates of blow-up time for a quasilinear hyperbolic equation with superlinear sources","authors":"G. Zu, Fang-lan Li","doi":"10.5802/crmeca.9","DOIUrl":"https://doi.org/10.5802/crmeca.9","url":null,"abstract":"This paper deals with the lower bound for blow-up solutions to a quasilinear hyperbolic equation with strong damping. An inverse Hölder inequality with a correction constant is employed to overcome the difficulty caused by the failure of the embedding inequality. Moreover, a lower bound for blow-up time is obtained by constructing a new control functional with a small dissipative term and by applying an inverse Hölder inequality as well as energy inequalities. This result gives a positive answer to the open problem presented in [1].","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"51 1","pages":"307-313"},"PeriodicalIF":0.8,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84217139","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}
In this paper, the orthogonal cutting process is studied using Smooth Particle Hydrodynamic (SPH) method by a kinematic rigid cutting tool and two work-piece material models: perfectly elastic-plastic (EPP) model and Johnson–Cook (JC) model. The kinematic tool means that if the cutting tool is assumed a rigid body then the horizontal component speed of work-piece particles at cutting tool region are modified to the cutting speed. The chip shapes of orthogonal cutting process using SPH method with kinematic and kinetic tool models are compared with the experimental results. The chip obtained by the simulation with kinematic tool is more similar to the experimental results. Von-Mises stress distribution at different states of the orthogonal cutting process is investigated. The maximum stress occurs at the shear plane and causes the formation of chip teeth. Comparisons between chips of work-pieces with two material models are investigated including different rake angles of 5, 10 and 17.5◦ with feed rates of 0.3 and 0.4 mm/rev and the cutting forces of the process are obtained. The cutting force of process with 17.5◦ rake angle, 0.4 mm/rev feed rate and 800 m/min cutting speed is validated using experimental result.
{"title":"Analyzing orthogonal cutting process using SPH method by kinematic cutting tool","authors":"M. Dehghani, A. Shafiei, M. M. Abootorabi","doi":"10.5802/crmeca.6","DOIUrl":"https://doi.org/10.5802/crmeca.6","url":null,"abstract":"In this paper, the orthogonal cutting process is studied using Smooth Particle Hydrodynamic (SPH) method by a kinematic rigid cutting tool and two work-piece material models: perfectly elastic-plastic (EPP) model and Johnson–Cook (JC) model. The kinematic tool means that if the cutting tool is assumed a rigid body then the horizontal component speed of work-piece particles at cutting tool region are modified to the cutting speed. The chip shapes of orthogonal cutting process using SPH method with kinematic and kinetic tool models are compared with the experimental results. The chip obtained by the simulation with kinematic tool is more similar to the experimental results. Von-Mises stress distribution at different states of the orthogonal cutting process is investigated. The maximum stress occurs at the shear plane and causes the formation of chip teeth. Comparisons between chips of work-pieces with two material models are investigated including different rake angles of 5, 10 and 17.5◦ with feed rates of 0.3 and 0.4 mm/rev and the cutting forces of the process are obtained. The cutting force of process with 17.5◦ rake angle, 0.4 mm/rev feed rate and 800 m/min cutting speed is validated using experimental result.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"3 1","pages":"149-174"},"PeriodicalIF":0.8,"publicationDate":"2020-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83701649","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}
{"title":"Correspondence between de Saint-Venant and Boussinesq 2: Boussinesq’s professional and private life up to 1886","authors":"W. Hager, K. Hutter, O. Castro-Orgaz","doi":"10.5802/crmeca.8","DOIUrl":"https://doi.org/10.5802/crmeca.8","url":null,"abstract":"","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"43 1","pages":"77-111"},"PeriodicalIF":0.8,"publicationDate":"2020-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75336763","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}
The present investigation presents an efficient meshless method based on the weak form of an element-free-Galerkin method. The formulation of the numerical solution was conducted using an artificial neural network (ANN) approach to compute the optimal number of nodes in the influence domain for each point of interest. The numerical results using the ANN model were tested and compared with different approaches in the literature. Results show a reduction in the computational cost and an enhancement in an error criterion of up to 11%.
{"title":"Optimal influence cover for an element free Galerkin MFree method based on artificial neural network","authors":"Imane Hajjout, Manal Haddouch, El Mostapha Boudi","doi":"10.5802/crmeca.5","DOIUrl":"https://doi.org/10.5802/crmeca.5","url":null,"abstract":"The present investigation presents an efficient meshless method based on the weak form of an element-free-Galerkin method. The formulation of the numerical solution was conducted using an artificial neural network (ANN) approach to compute the optimal number of nodes in the influence domain for each point of interest. The numerical results using the ANN model were tested and compared with different approaches in the literature. Results show a reduction in the computational cost and an enhancement in an error criterion of up to 11%.","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"16 1","pages":"63-76"},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74632402","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}
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