Jingang Jiang, J. Sun, Yang Zeng, Yongde Zhang, Jingchao Wang, Shanwei Zhou
Compared to other orthodontic acceleration methods such as drug, electric current, and laser, vibratory loading is less invasive and easier to use. But the optimal duration for vibratory load application has not been determined, nor can the alveolar bone parameters be predicted after vibratory load application. Therefore, this work examined the mechanism of vibration-accelerated alveolar bone reconstruction and established a numerical model for simulating alveolar bone damage caused by vibration loads. That is, the role of vibration load in orthodontic acceleration was analyzed, and a finite element model was established to validate the vibra-tion-accelerated orthodontic mechanism with a simulated numerical model of alveolar bone damage. The optimal duration of application was obtained for the right anterior incisor under vibratory loading of 5 N orthodontic force, 50 Hz in the gingival orientation and 0.2 cm amplitude for 120 to 140 minutes. This work is of guidance and reference significance in promoting the development of orthodontic treatment and shortening the orthodontic treatment cycle.
{"title":"Determination of vibration acceleration mechanism and vibration load application duration from a non-biological perspective: Orthodontic Acceleration","authors":"Jingang Jiang, J. Sun, Yang Zeng, Yongde Zhang, Jingchao Wang, Shanwei Zhou","doi":"10.1590/1679-78257369","DOIUrl":"https://doi.org/10.1590/1679-78257369","url":null,"abstract":"Compared to other orthodontic acceleration methods such as drug, electric current, and laser, vibratory loading is less invasive and easier to use. But the optimal duration for vibratory load application has not been determined, nor can the alveolar bone parameters be predicted after vibratory load application. Therefore, this work examined the mechanism of vibration-accelerated alveolar bone reconstruction and established a numerical model for simulating alveolar bone damage caused by vibration loads. That is, the role of vibration load in orthodontic acceleration was analyzed, and a finite element model was established to validate the vibra-tion-accelerated orthodontic mechanism with a simulated numerical model of alveolar bone damage. The optimal duration of application was obtained for the right anterior incisor under vibratory loading of 5 N orthodontic force, 50 Hz in the gingival orientation and 0.2 cm amplitude for 120 to 140 minutes. This work is of guidance and reference significance in promoting the development of orthodontic treatment and shortening the orthodontic treatment cycle.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67623063","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}
Friction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect.
{"title":"Improved friction model applied to plane sliding connections by a large deformation FEM formulation","authors":"Tiago Morkis Siqueira, H. B. Coda","doi":"10.1590/1679-78257321","DOIUrl":"https://doi.org/10.1590/1679-78257321","url":null,"abstract":"Friction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67621985","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}
Jailson França dos Santos, É. L. Albuquerque, L. Campos
This paper describes an isogeometric analysis of the boundary element method, called IGABEM, applied to anisotropic 2D plane elastic problems. The Lekhnitskii's anisotropic fundamental solution is used and the singular integral terms is regularized. For the weak singularity kernel, the Telles transform is used. On the other hand, in the strong singularity term, the Singularity Subtraction Technique – SST is used. The shape functions used are the Non-Uniform Rational B-Spline - NURBS. Thus, the same mathematical representation of Computer Aided Design - CAD is used in the implemented computational code. This avoids the generation of meshes and provides an exact representation of most complex geometries. As a reflection of this isoparametric concept, errors from geometric interpolation are excluded, improving numerical results. Furthermore, to increase the numerical efficiency of the code, the NURBS are decomposed into Bézier curves. To evaluate the accuracy of the formulation, complex problems using high-order isogeometric boundary elements are analyzed. Their results are compared to analytical solutions showing good agreement.
{"title":"Anisotropic elastic applications in composite materials using the isogeometric boundary element method","authors":"Jailson França dos Santos, É. L. Albuquerque, L. Campos","doi":"10.1590/1679-78257294","DOIUrl":"https://doi.org/10.1590/1679-78257294","url":null,"abstract":"This paper describes an isogeometric analysis of the boundary element method, called IGABEM, applied to anisotropic 2D plane elastic problems. The Lekhnitskii's anisotropic fundamental solution is used and the singular integral terms is regularized. For the weak singularity kernel, the Telles transform is used. On the other hand, in the strong singularity term, the Singularity Subtraction Technique – SST is used. The shape functions used are the Non-Uniform Rational B-Spline - NURBS. Thus, the same mathematical representation of Computer Aided Design - CAD is used in the implemented computational code. This avoids the generation of meshes and provides an exact representation of most complex geometries. As a reflection of this isoparametric concept, errors from geometric interpolation are excluded, improving numerical results. Furthermore, to increase the numerical efficiency of the code, the NURBS are decomposed into Bézier curves. To evaluate the accuracy of the formulation, complex problems using high-order isogeometric boundary elements are analyzed. Their results are compared to analytical solutions showing good agreement.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67621872","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}
Emerson Bastos, É. L. Albuquerque, L. Campos, L. Wrobel
This work presents two fast isogeometric formulations of the Boundary Element Method (BEM) applied to heat conduction problems, one accelerated by Fast Multipole Method (FMM) and other by Hierarchical Matrices. The Fast Multipole Method uses complex variables and expansion of fundamental solutions into Laurant series, while the Hierarchical Matrices are created by low rank CUR approximations from the k−Means clustering technique for geometric sampling. Both use Non-Uniform Rational B-Splines (NURBS) as shape functions. To reduce computational cost and facilitate implementation, NURBS are decomposed into Bézier curves, making the isogeometric formulation very similar to the conventional BEM. A description of the hierarchical structure of the data and the implemented algorithms are presented. Validation is performed by comparing the results of the proposed formulations with those of the conventional BEM formulation. The computational cost of both formulations is analyzed showing the advantages of the proposed formulations for large scale problems.
{"title":"Two accelerated isogeometric boundary element method formulations: fast multipole method and hierarchical matrices method","authors":"Emerson Bastos, É. L. Albuquerque, L. Campos, L. Wrobel","doi":"10.1590/1679-78257244","DOIUrl":"https://doi.org/10.1590/1679-78257244","url":null,"abstract":"This work presents two fast isogeometric formulations of the Boundary Element Method (BEM) applied to heat conduction problems, one accelerated by Fast Multipole Method (FMM) and other by Hierarchical Matrices. The Fast Multipole Method uses complex variables and expansion of fundamental solutions into Laurant series, while the Hierarchical Matrices are created by low rank CUR approximations from the k−Means clustering technique for geometric sampling. Both use Non-Uniform Rational B-Splines (NURBS) as shape functions. To reduce computational cost and facilitate implementation, NURBS are decomposed into Bézier curves, making the isogeometric formulation very similar to the conventional BEM. A description of the hierarchical structure of the data and the implemented algorithms are presented. Validation is performed by comparing the results of the proposed formulations with those of the conventional BEM formulation. The computational cost of both formulations is analyzed showing the advantages of the proposed formulations for large scale problems.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67621638","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}
Renato Takeo Kishino, Vitor Hiroshi Kishino, R. Sanches, H. B. Coda
The fundamental difference in the solution of solids and fluids relies on the respective constitutive laws. Based on the Rivlin-Saunders-Düster-Hartmann hyperelastic model and using the Flory’s strain decomposition, we present a new total Lagrangian viscoelastic constitutive model for both Kelvin-Voigt viscoelastic solids and free-surface compressive viscous isothermal fluids. A dissipative viscous virtual work is written as a function of the time rate of isochoric invariants and its relation with the viscous stress is derived. Local time derivatives are solved by backward finite difference, allowing a consistent tangent viscoelastic constitutive tensor. The virtual work principle is used to write the weak equilibrium equation and its position-based finite element counterpart. Dynamic time integration is carried out by the Newmark β method and the Newton-Raphson procedure is used to solve time steps. The formulation is validated against experimental and numerical literature results revealing good precision. Additional examples are shown in order to demonstrate the applicability and future possibilities of the technique.
{"title":"Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids","authors":"Renato Takeo Kishino, Vitor Hiroshi Kishino, R. Sanches, H. B. Coda","doi":"10.1590/1679-78257010","DOIUrl":"https://doi.org/10.1590/1679-78257010","url":null,"abstract":"The fundamental difference in the solution of solids and fluids relies on the respective constitutive laws. Based on the Rivlin-Saunders-Düster-Hartmann hyperelastic model and using the Flory’s strain decomposition, we present a new total Lagrangian viscoelastic constitutive model for both Kelvin-Voigt viscoelastic solids and free-surface compressive viscous isothermal fluids. A dissipative viscous virtual work is written as a function of the time rate of isochoric invariants and its relation with the viscous stress is derived. Local time derivatives are solved by backward finite difference, allowing a consistent tangent viscoelastic constitutive tensor. The virtual work principle is used to write the weak equilibrium equation and its position-based finite element counterpart. Dynamic time integration is carried out by the Newmark β method and the Newton-Raphson procedure is used to solve time steps. The formulation is validated against experimental and numerical literature results revealing good precision. Additional examples are shown in order to demonstrate the applicability and future possibilities of the technique.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67619794","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}
L. F. Nicolini, J. Greven, P. Kobbe, F. Hildebrand, M. Stoffel, B. Markert, Borja Martinez Yllera, Marcelo Simoni Simões, C. Roesler, E. Fancello
This study investigates the biomechanics of the spine after insertion of vertebral body tethering (VBT) with different cord pretensions. For that purpose, a Finite Element model of the average thoracolumbar spine was stepwise calibrated and validated. The VBT instrumentation was inserted in the left side of the L1-L2 segment with different cord pretensions. As a second test, the L1-L2 segment was submitted to an external pure moment of 6 Nm in left and right lateral bending. The range of motion (ROM) for the spine with VBT was determined with respect to its initial post VBT position. Pretension forces of 100 N and 300 N resulted in a change of scoliotic angle of 2.7° and 5.3° to the left side of the spine, respectively. The ROM of the native spine was 4.5° in right lateral bending and reduced to 1.8° and 1.4° for the cases of the spine with a cord pretension of 100 N and 300 N, respectively. In left lateral bending, the absolute ROM of the native spine was 4.6°. For the cases of a cord pretension of 100 N and 300 N, the spine bent 1.9° and 0.8° to the left side from its initial post VBT position, respectively.
{"title":"The effects of tether pretension within vertebral body tethering on the biomechanics of the spine: a Finite Element analysis","authors":"L. F. Nicolini, J. Greven, P. Kobbe, F. Hildebrand, M. Stoffel, B. Markert, Borja Martinez Yllera, Marcelo Simoni Simões, C. Roesler, E. Fancello","doi":"10.1590/1679-78256932","DOIUrl":"https://doi.org/10.1590/1679-78256932","url":null,"abstract":"This study investigates the biomechanics of the spine after insertion of vertebral body tethering (VBT) with different cord pretensions. For that purpose, a Finite Element model of the average thoracolumbar spine was stepwise calibrated and validated. The VBT instrumentation was inserted in the left side of the L1-L2 segment with different cord pretensions. As a second test, the L1-L2 segment was submitted to an external pure moment of 6 Nm in left and right lateral bending. The range of motion (ROM) for the spine with VBT was determined with respect to its initial post VBT position. Pretension forces of 100 N and 300 N resulted in a change of scoliotic angle of 2.7° and 5.3° to the left side of the spine, respectively. The ROM of the native spine was 4.5° in right lateral bending and reduced to 1.8° and 1.4° for the cases of the spine with a cord pretension of 100 N and 300 N, respectively. In left lateral bending, the absolute ROM of the native spine was 4.6°. For the cases of a cord pretension of 100 N and 300 N, the spine bent 1.9° and 0.8° to the left side from its initial post VBT position, respectively.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67620099","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":"Numerical and experimental investigation of the ballistic performance of the armor structure with in-layer deflector against bullets","authors":"M. Çalışkan, Erdal Camcı, F. Findik","doi":"10.1590/1679-78257269","DOIUrl":"https://doi.org/10.1590/1679-78257269","url":null,"abstract":"","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67621186","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}
Tiago Sartor, Jorge Alberto Valle da Silva, Z.-G. Guan, R. Santiago
This paper aims to investigate the influence of stress triaxiality on the fracture behaviour of Ti6Al4V fabricated by Electron Beam Melting (EBM). Here, specimens with seven configurations were manufactured and tested to obtain a wide range of stress triaxialities. A combined approach using Digital Image Correlation (DIC) and finite element (FE) modelling was used to evaluate the current stress triaxiality levels of the various specimens. The material fracture envelope was defined with the triaxiality in a range from -0.28 to 0.71, noting that the fracture was strongly dependent on the stress triaxiality. The characterisations were then carried out by testing an ad-hoc specimen to evaluate failure criteria at low and high stress triaxialities. It was shown that the FE model using the failure criterion based on triaxiality offers more accurate predictions of the material's failure response than that based on the effective plastic strain. The modelling approach based on anisotropic elasto-plasticity contributes to better predictions of the alloy's response. Thus, the failure models based on the stress triaxiality are highly recommended for producing accurate numerical predictions of the fracture response of Ti6Al4V-EBM.
{"title":"Influence of stress triaxiality on the fracture behaviour of Ti6Al4V alloy manufactured by electron beam melting","authors":"Tiago Sartor, Jorge Alberto Valle da Silva, Z.-G. Guan, R. Santiago","doi":"10.1590/1679-78257293","DOIUrl":"https://doi.org/10.1590/1679-78257293","url":null,"abstract":"This paper aims to investigate the influence of stress triaxiality on the fracture behaviour of Ti6Al4V fabricated by Electron Beam Melting (EBM). Here, specimens with seven configurations were manufactured and tested to obtain a wide range of stress triaxialities. A combined approach using Digital Image Correlation (DIC) and finite element (FE) modelling was used to evaluate the current stress triaxiality levels of the various specimens. The material fracture envelope was defined with the triaxiality in a range from -0.28 to 0.71, noting that the fracture was strongly dependent on the stress triaxiality. The characterisations were then carried out by testing an ad-hoc specimen to evaluate failure criteria at low and high stress triaxialities. It was shown that the FE model using the failure criterion based on triaxiality offers more accurate predictions of the material's failure response than that based on the effective plastic strain. The modelling approach based on anisotropic elasto-plasticity contributes to better predictions of the alloy's response. Thus, the failure models based on the stress triaxiality are highly recommended for producing accurate numerical predictions of the fracture response of Ti6Al4V-EBM.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67621810","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 study, the microstructural-based finite element modeling of dual-phase steels was investigated to visualize the crack initiation and its propagation through the phases that exist in the material. The parameters of various failure models, including Gurson, Gurson-Johnson-Cook, and Johnson-Cook (JC), were calibrated for different microstructure levels of DP600, DP800, and DP1000 steels. The onset of cracking, nucleation, void growth, and coalescence was determined using the models. As a result of the optimization studies, there is not much difference between the flow curves of the materials and the tensile values calculated from the tensile tests for DP600 and DP800, while it is slightly higher for DP1000. However, considering the fracture, martensite phases were found to be the main determinant of this situation. Cracks that start in the martensite phases then propagate through the ferrite phase and eventually cause the material to break. According to the results of the simulations, the difference between the experiments and the simulation results of the Gurson is 3.33%, the Gurson-JC is 1.82%, and the JC model is 2.39%.
{"title":"Stress-strain distribution and failure mechanisms in dual-phase steels investigated with microstructure-based modeling","authors":"Labinot Topilla, S. Toros","doi":"10.1590/1679-78257157","DOIUrl":"https://doi.org/10.1590/1679-78257157","url":null,"abstract":"In this study, the microstructural-based finite element modeling of dual-phase steels was investigated to visualize the crack initiation and its propagation through the phases that exist in the material. The parameters of various failure models, including Gurson, Gurson-Johnson-Cook, and Johnson-Cook (JC), were calibrated for different microstructure levels of DP600, DP800, and DP1000 steels. The onset of cracking, nucleation, void growth, and coalescence was determined using the models. As a result of the optimization studies, there is not much difference between the flow curves of the materials and the tensile values calculated from the tensile tests for DP600 and DP800, while it is slightly higher for DP1000. However, considering the fracture, martensite phases were found to be the main determinant of this situation. Cracks that start in the martensite phases then propagate through the ferrite phase and eventually cause the material to break. According to the results of the simulations, the difference between the experiments and the simulation results of the Gurson is 3.33%, the Gurson-JC is 1.82%, and the JC model is 2.39%.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67620691","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 study analyzes the bending of a simple electro-elastic cylindrical shell by the compound matrix method. The cross-section of the circular cylindrical shell is a non-circular curved shape, with 𝜇𝜇 1 a function of 𝐴𝐴 𝐵𝐵� and the mode number, where 𝐴𝐴 and 𝐵𝐵 are the pre-deformation inner and outer radii of the cylindrical shell, and 𝜇𝜇 1 is the ratio of the deformed inner radius to 𝐴𝐴 . In the first step, a numerical model of the problem is developed to obtain specific differential equations. The modeling yields a system of two Ordinary Differential Equations with three boundary conditions of the same type. Next, it is shown that the dependence of 𝜇𝜇 1 to 𝐴𝐴 𝐵𝐵� has a boundary layer structure. Simple numerical observations were made for bifurcation conditions. The analysis is, in fact, based on the variations of the inner and outer radii 𝐴𝐴 and 𝐵𝐵 , assuming 𝑎𝑎 = 𝜇𝜇 1 𝐴𝐴 and 𝑏𝑏 = 𝜇𝜇 2 𝐵𝐵 , and based on the bifurcation of 𝜇𝜇 1 and 𝜇𝜇 2 ratios with respect to radius. For this purpose, the compound matrix method is used to show the validity of the arguments.
{"title":"Analysis of the bending of a neo-Hookean electro-elastic shell of arbitrary thickness under an externally-applied hydrostatic pressure","authors":"Omid Teymoori, A. Hatami","doi":"10.1590/1679-78256692","DOIUrl":"https://doi.org/10.1590/1679-78256692","url":null,"abstract":"The present study analyzes the bending of a simple electro-elastic cylindrical shell by the compound matrix method. The cross-section of the circular cylindrical shell is a non-circular curved shape, with 𝜇𝜇 1 a function of 𝐴𝐴 𝐵𝐵� and the mode number, where 𝐴𝐴 and 𝐵𝐵 are the pre-deformation inner and outer radii of the cylindrical shell, and 𝜇𝜇 1 is the ratio of the deformed inner radius to 𝐴𝐴 . In the first step, a numerical model of the problem is developed to obtain specific differential equations. The modeling yields a system of two Ordinary Differential Equations with three boundary conditions of the same type. Next, it is shown that the dependence of 𝜇𝜇 1 to 𝐴𝐴 𝐵𝐵� has a boundary layer structure. Simple numerical observations were made for bifurcation conditions. The analysis is, in fact, based on the variations of the inner and outer radii 𝐴𝐴 and 𝐵𝐵 , assuming 𝑎𝑎 = 𝜇𝜇 1 𝐴𝐴 and 𝑏𝑏 = 𝜇𝜇 2 𝐵𝐵 , and based on the bifurcation of 𝜇𝜇 1 and 𝜇𝜇 2 ratios with respect to radius. For this purpose, the compound matrix method is used to show the validity of the arguments.","PeriodicalId":18192,"journal":{"name":"Latin American Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67618844","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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