Pub Date : 2021-08-18DOI: 10.13052/ejcm1779-7179.3013
Haijing Pan
Due to the lack of more precise and complete data support, the reliability of posture stability evaluation method based on common technology is poor. In the face of such problems, the application of multi-body system coupling dynamic model in the evaluation of sports posture stability is proposed. The coupling dynamic model of human motion posture is established, and the relevant data of human motion posture is collected. The complete data of human motion posture is obtained by solving the dynamic model. Choose the appropriate stability evaluation index, calculate the stability evaluation index, divide the stability level, and realize the evaluation of posture stability. The experimental results show that: the application of multi-body system coupling dynamic model in the stability evaluation method makes the time delay and data error of the evaluation method small, and its overall reliability is improved.
{"title":"Application of Multi Body System Coupling Dynamic Model in Posture Stability Evaluation of Sports","authors":"Haijing Pan","doi":"10.13052/ejcm1779-7179.3013","DOIUrl":"https://doi.org/10.13052/ejcm1779-7179.3013","url":null,"abstract":"Due to the lack of more precise and complete data support, the reliability of posture stability evaluation method based on common technology is poor. In the face of such problems, the application of multi-body system coupling dynamic model in the evaluation of sports posture stability is proposed. The coupling dynamic model of human motion posture is established, and the relevant data of human motion posture is collected. The complete data of human motion posture is obtained by solving the dynamic model. Choose the appropriate stability evaluation index, calculate the stability evaluation index, divide the stability level, and realize the evaluation of posture stability. The experimental results show that: the application of multi-body system coupling dynamic model in the stability evaluation method makes the time delay and data error of the evaluation method small, and its overall reliability is improved.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48496181","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}
Pub Date : 2021-07-19DOI: 10.13052/EJCM1779-7179.3011
A. Khoei, T. Ahmadpour, Y. Navidtehrani
In this paper, an enriched–FEM method is presented based on the X-FEM technique by applying a damage–plasticity model to investigate the effect of FRP strengthening on the concrete arch. In this manner, the damage strain is lumped into the crack interface while the elastic and plastic strains are employed within the bulk volume of element. The damage stress–strain relation is converted to the traction separation law using an acoustic tensor. The interface between the FRP and concrete is modeled using a cohesive fracture model. The X-FEM technique is applied where the FE mesh is not necessary to be conformed to the fracture geometry, so the regular mesh is utilized independent of the position of the fracture. The accuracy of the proposed plastic-damage model is investigated under the monotonic tension, compression, and cyclic tension loading. Furthermore, the accuracy of the cohesive fracture model is investigated using the experimental data reported for the debonding test. In order to verify the accuracy of the proposed computational algorithm, the numerical results are compared with those of experimental data obtained from two tests conducted on reinforced concrete arches strengthened with FRP. Finally, a parametric study is performed by evaluating the effects of high to span ratio, longitudinal reinforcement ratio, and strengthening method.
{"title":"An X–FEM Technique for Modeling the FRP Strengthening of Concrete Arches with a Plastic–Damage Model; Numerical and Experimental Investigations","authors":"A. Khoei, T. Ahmadpour, Y. Navidtehrani","doi":"10.13052/EJCM1779-7179.3011","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.3011","url":null,"abstract":"In this paper, an enriched–FEM method is presented based on the X-FEM technique by applying a damage–plasticity model to investigate the effect of FRP strengthening on the concrete arch. In this manner, the damage strain is lumped into the crack interface while the elastic and plastic strains are employed within the bulk volume of element. The damage stress–strain relation is converted to the traction separation law using an acoustic tensor. The interface between the FRP and concrete is modeled using a cohesive fracture model. The X-FEM technique is applied where the FE mesh is not necessary to be conformed to the fracture geometry, so the regular mesh is utilized independent of the position of the fracture. The accuracy of the proposed plastic-damage model is investigated under the monotonic tension, compression, and cyclic tension loading. Furthermore, the accuracy of the cohesive fracture model is investigated using the experimental data reported for the debonding test. In order to verify the accuracy of the proposed computational algorithm, the numerical results are compared with those of experimental data obtained from two tests conducted on reinforced concrete arches strengthened with FRP. Finally, a parametric study is performed by evaluating the effects of high to span ratio, longitudinal reinforcement ratio, and strengthening method.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42463337","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}
Pub Date : 2021-05-22DOI: 10.13052/EJCM1779-7179.29469
K. Paul, B. Mukhopadhyay
Our current work is related to the study of vibrations induced by laser beams on the behalf of distinct theories of magneto-thermo-elastic diffusion problem in a semi-infinitely long, conducting isotropic elastic solid with cylindrical hole in a uniform magnetic field acting on the surface of the cylindrical hole of the solid in the direction of the axis of the cylindrical hole. The temporal scheme of laser beam is considered as non-Gaussian and is acted on the surface of the cylindrical hole. The problem is solved with the help of Laplace transform domain and finally illustrated graphically. Note: This article will be very useful in material science specially, in powder metallurgy during sintering, hot pressing, wire and rods annealing are examined from a unified physical point of view, in different branches of engineering physics like plasma physics, nuclear physics, geophysics and related topics and also in oil industry (Lyashenko and Hryhorova (2014), Long and Heng-Wei (2018), Fryxell and Aitken (1969), Nowinski (1978), Legros et al. (1998), Galliero et al. (2019) etc.).
{"title":"Transient Dynamic Response of a Semi-infinite Elastic Permeable Solid with Cylindrical Hole Subject to Laser Pulse Heating Under Different Theories of Generalized Thermoelasticity","authors":"K. Paul, B. Mukhopadhyay","doi":"10.13052/EJCM1779-7179.29469","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.29469","url":null,"abstract":"Our current work is related to the study of vibrations induced by laser beams on the behalf of distinct theories of magneto-thermo-elastic diffusion problem in a semi-infinitely long, conducting isotropic elastic solid with cylindrical hole in a uniform magnetic field acting on the surface of the cylindrical hole of the solid in the direction of the axis of the cylindrical hole. The temporal scheme of laser beam is considered as non-Gaussian and is acted on the surface of the cylindrical hole. The problem is solved with the help of Laplace transform domain and finally illustrated graphically. \u0000Note: This article will be very useful in material science specially, in powder metallurgy during sintering, hot pressing, wire and rods annealing are examined from a unified physical point of view, in different branches of engineering physics like plasma physics, nuclear physics, geophysics and related topics and also in oil industry (Lyashenko and Hryhorova (2014), Long and Heng-Wei (2018), Fryxell and Aitken (1969), Nowinski (1978), Legros et al. (1998), Galliero et al. (2019) etc.).","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"517–548-517–548"},"PeriodicalIF":1.2,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41317384","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}
Pub Date : 2021-05-22DOI: 10.13052/EJCM1779-7179.29468
Amir Hossein Nasrollah Barati, A. Jafari, S. Haghighi, A. Maghsoudpour
The present study aims to evaluate the nonlinear vibration of an annular circular plate in contact with the fluid. Analysis of plate is based on first-order Shear Deformation Theory (FSDT) by considering of rotational inertial effects and transverse shear stresses. The governing equation of the oscillatory behavior of the fluid is determined by solving the Laplace equation and satisfying its boundary conditions. The nonlinear differential equations are solved based on the differential quadrature method and obtaining nonlinear natural frequency. In addition, the numerical results are presented for a sample plate, and the effect of some parameters such as aspect ratio, boundary conditions, fluid density, and fluid height are investigated. Finally, the results are compared with those of similar studies in the literature.
{"title":"Effect of Hydrostatic Pressure on Nonlinear Vibrating of Annular Circular Plate Coupled with Bounded Fluid","authors":"Amir Hossein Nasrollah Barati, A. Jafari, S. Haghighi, A. Maghsoudpour","doi":"10.13052/EJCM1779-7179.29468","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.29468","url":null,"abstract":"The present study aims to evaluate the nonlinear vibration of an annular circular plate in contact with the fluid. Analysis of plate is based on first-order Shear Deformation Theory (FSDT) by considering of rotational inertial effects and transverse shear stresses. The governing equation of the oscillatory behavior of the fluid is determined by solving the Laplace equation and satisfying its boundary conditions. The nonlinear differential equations are solved based on the differential quadrature method and obtaining nonlinear natural frequency. In addition, the numerical results are presented for a sample plate, and the effect of some parameters such as aspect ratio, boundary conditions, fluid density, and fluid height are investigated. Finally, the results are compared with those of similar studies in the literature.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"491–516-491–516"},"PeriodicalIF":1.2,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48572723","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}
Pub Date : 2021-05-22DOI: 10.13052/EJCM1779-7179.294610
Saber Rezaey
One of the most important components of fluid transmission systems is a control valve located in the pipelines of oil, gas, etc. The primary purpose of this valve is to control the rate of fluid flow passing through it under pressure changes and the most important issue is to investigate the flow’s characteristics in order to achieve a proper geometry to control the flow rate and pressure as desired. The valves used in pipelines add to the overall head loss of the system. Therefore, valves with proper geometry can reduce these minor losses and finally decrease total energy losses. In this paper, a globe control valve is modeled and then numerically investigated to extract its functional relation, which relates pressure ratio to inlet Reynolds number, and estimate its loss coefficient at the valve’s different opening states which have not been addressed completely before and can be beneficial for the selection and usage of globe valves under certain conditions. According to the results, it is found that pressure ratio and loss coefficient are functions of inlet velocity and the valve’s opening state’s percentage, which are directly related to the valve’s geometry. When the valve opens, the rate of change in pressure ratio and loss coefficient are very sharp. Gradually, this rate decreases and the results tend to the final value at the valve’s fully opened state.
{"title":"Numerical Investigation of a Globe Control Valve and Estimating its Loss Coefficient at Different Opening States","authors":"Saber Rezaey","doi":"10.13052/EJCM1779-7179.294610","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.294610","url":null,"abstract":"One of the most important components of fluid transmission systems is a control valve located in the pipelines of oil, gas, etc. The primary purpose of this valve is to control the rate of fluid flow passing through it under pressure changes and the most important issue is to investigate the flow’s characteristics in order to achieve a proper geometry to control the flow rate and pressure as desired. The valves used in pipelines add to the overall head loss of the system. Therefore, valves with proper geometry can reduce these minor losses and finally decrease total energy losses. In this paper, a globe control valve is modeled and then numerically investigated to extract its functional relation, which relates pressure ratio to inlet Reynolds number, and estimate its loss coefficient at the valve’s different opening states which have not been addressed completely before and can be beneficial for the selection and usage of globe valves under certain conditions. According to the results, it is found that pressure ratio and loss coefficient are functions of inlet velocity and the valve’s opening state’s percentage, which are directly related to the valve’s geometry. When the valve opens, the rate of change in pressure ratio and loss coefficient are very sharp. Gradually, this rate decreases and the results tend to the final value at the valve’s fully opened state.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"549–576-549–576"},"PeriodicalIF":1.2,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49213037","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}
Pub Date : 2021-05-22DOI: 10.13052/EJCM1779-7179.29466
P. K. Karsh, B. Thakkar, R. R. Kumar, Abhijeet Kumar, S. Dey
The delamination is one of the major modes of failure occurring in the laminated composite due to insufficient bonding between the layers. In this paper, the natural frequencies of delaminated S-glass and E-glass epoxy cantilever composite plates are presented by employing the finite element method (FEM) approach. The rotary inertia and transverse shear deformation are considered in the present study. The effect of parameters such as the location of delamination along the length, across the thickness, the percentage of delamination, and ply-orientation angle on first three natural frequencies of the cantilever plates are presented for S-glass and E-glass epoxy composites. The standard eigenvalue problem is solved to obtain the natural frequencies and corresponding mode shapes. First three mode shape of S-Glass and E-Glass epoxy laminated composites are portrayed corresponding to different ply angle of lamina.
{"title":"Effect of Delamination on Natural Frequencies of E-glass and S-glass Epoxy Composite Plates","authors":"P. K. Karsh, B. Thakkar, R. R. Kumar, Abhijeet Kumar, S. Dey","doi":"10.13052/EJCM1779-7179.29466","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.29466","url":null,"abstract":"The delamination is one of the major modes of failure occurring in the laminated composite due to insufficient bonding between the layers. In this paper, the natural frequencies of delaminated S-glass and E-glass epoxy cantilever composite plates are presented by employing the finite element method (FEM) approach. The rotary inertia and transverse shear deformation are considered in the present study. The effect of parameters such as the location of delamination along the length, across the thickness, the percentage of delamination, and ply-orientation angle on first three natural frequencies of the cantilever plates are presented for S-glass and E-glass epoxy composites. The standard eigenvalue problem is solved to obtain the natural frequencies and corresponding mode shapes. First three mode shape of S-Glass and E-Glass epoxy laminated composites are portrayed corresponding to different ply angle of lamina.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"437–458-437–458"},"PeriodicalIF":1.2,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49492532","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}
Pub Date : 2021-05-22DOI: 10.13052/EJCM1779-7179.29467
A. Khalaf, Asaad A. Abdullah
This work explores the possibility of using Newtonian turbulence k−ϵ and k−ω models for modelling crude oil flow in pipelines with drag reduction agents. These models have been applied to predict the friction factor, pressure drop and the drag reduction percentage. The simulation results of both models were compared with six published experimental data for crude oil flow in pipes with different types of drag reduction agents. The velocity near the wall was determined using the log law line of Newtonian fluid equation and by changing the parameter ΔB to achieve an excellent agreement with experimental data. Simulated data for k−ϵ model shows better agreement with most experimental data than the k−ω turbulence model.
{"title":"Simulation of Crude Oil Transportation with Drag Reduction Agents Using k-ϵ and k-ω Models","authors":"A. Khalaf, Asaad A. Abdullah","doi":"10.13052/EJCM1779-7179.29467","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.29467","url":null,"abstract":"This work explores the possibility of using Newtonian turbulence k−ϵ and k−ω models for modelling crude oil flow in pipelines with drag reduction agents. These models have been applied to predict the friction factor, pressure drop and the drag reduction percentage. The simulation results of both models were compared with six published experimental data for crude oil flow in pipes with different types of drag reduction agents. The velocity near the wall was determined using the log law line of Newtonian fluid equation and by changing the parameter ΔB to achieve an excellent agreement with experimental data. Simulated data for k−ϵ model shows better agreement with most experimental data than the k−ω turbulence model.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"459–490-459–490"},"PeriodicalIF":1.2,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46297987","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}
Pub Date : 2021-05-13DOI: 10.13052/EJCM1779-7179.29462
Sangamesh Gondegaon, Hari K. Voruganti
Isogeometric analysis (IGA) is a mesh free technique which make use of B-spline basis functions for geometry and field variable representation. Parameterization of B-spline for IGA is the counterpart of meshing as in finite element method (FEM). The objective of parameterization is to find the optimum set of control points for B-spline modelling. The position of control points of a B-spline model has huge effect on IGA results. In this work, the effect of B-spline parameterization on IGA result is presented. One dimensional case of bar with self-weight is solved and compared with exact analytical solution. First fundamental matrix is used as evaluation metric to check the quality of parameterization for 2-D domains. A heat conduction problem of a square domain is presented to study the parameterization effect for 2-D case.
{"title":"Sensitivity Analysis of Quality of B-spline Parameterization on Isogeometric Analysis","authors":"Sangamesh Gondegaon, Hari K. Voruganti","doi":"10.13052/EJCM1779-7179.29462","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.29462","url":null,"abstract":"Isogeometric analysis (IGA) is a mesh free technique which make use of B-spline basis functions for geometry and field variable representation. Parameterization of B-spline for IGA is the counterpart of meshing as in finite element method (FEM). The objective of parameterization is to find the optimum set of control points for B-spline modelling. The position of control points of a B-spline model has huge effect on IGA results. In this work, the effect of B-spline parameterization on IGA result is presented. One dimensional case of bar with self-weight is solved and compared with exact analytical solution. First fundamental matrix is used as evaluation metric to check the quality of parameterization for 2-D domains. A heat conduction problem of a square domain is presented to study the parameterization effect for 2-D case.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"345–362-345–362"},"PeriodicalIF":1.2,"publicationDate":"2021-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48301222","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}
Pub Date : 2021-05-13DOI: 10.13052/EJCM1779-7179.29465
T. Saju, M. Velu
This paper presents results of simulation of friction stir dissimilar welding of 5 mm thick, Nickel-based super-alloys, Inconel 718, and Nimonic 80A using Abaqus software. Four different trials were done to understand the influence of tool rotation speed on temperature distribution in weld zone while travel speed remains constant. The temperature in the weld zone was found to increase with the increase in tool rotation speed and travel speed. The temperature on the advancing side of the tool was higher than that of the retreating side. The tensile strength of weldment was found, by simulation, to be 25% more than that of base metal, Inconel 718. This may be due to grain refinement and dynamic recrystallization during FSW. The simulated bend test revealed an adequate level of ductility of weldments.
{"title":"Finite Element Simulation of Friction Stir Welding of Inconel 718 to Nimonic 80A","authors":"T. Saju, M. Velu","doi":"10.13052/EJCM1779-7179.29465","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.29465","url":null,"abstract":"This paper presents results of simulation of friction stir dissimilar welding of 5 mm thick, Nickel-based super-alloys, Inconel 718, and Nimonic 80A using Abaqus software. Four different trials were done to understand the influence of tool rotation speed on temperature distribution in weld zone while travel speed remains constant. The temperature in the weld zone was found to increase with the increase in tool rotation speed and travel speed. The temperature on the advancing side of the tool was higher than that of the retreating side. The tensile strength of weldment was found, by simulation, to be 25% more than that of base metal, Inconel 718. This may be due to grain refinement and dynamic recrystallization during FSW. The simulated bend test revealed an adequate level of ductility of weldments.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"417–436-417–436"},"PeriodicalIF":1.2,"publicationDate":"2021-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47275612","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}
Pub Date : 2021-05-13DOI: 10.13052/EJCM1779-7179.29461
Saim Ahmed, H. Abdelhamid, Bensaid Ismail, F. Ahmed
In this paper the dynamic analysis of a shaft rotor whose support is mobile is studied. For the calculation of kinetic energy and stiffness energy, the beam theory of Euler Bernoulli was used, and the matrices of elements and systems are developed using two methods derived from the differential quadrature method (DQM). The first method is the Differential Quadrature Finite Element Method (DQFEM) systematically, as a combination of the Differential Quadrature Method (DQM) and the Standard Finite Element Method (FEM), which has a reduced computational cost for problems in dynamics. The second method is the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) which is used by expressing the matrices of the hierarchical finite element method in a similar form to that of the Differential Quadrature Finite Element Method and introducing an interpolation basis on the element boundary of the hierarchical finite element method. The discretization element used for both methods is a three-dimensional beam element. In the differential quadrature finite element method (DQFEM), the mass, gyroscopic and stiffness matrices are simply calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The sampling points are determined by the Gauss-Lobatto node method. In the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) the same approaches were used, and the cubic Hermite shape functions and the special Legendre polynomial Rodrigues shape polynomial were added. The assembly of the matrices for both methods (DQFEM and DQHFEM) is similar to that of the classical finite element method. The results of the calculation are validated with the h- and hp finite element methods and also with the literature.
{"title":"An Differential Quadrature Finite Element and the Differential Quadrature Hierarchical Finite Element Methods for the Dynamics Analysis of on Board Shaft","authors":"Saim Ahmed, H. Abdelhamid, Bensaid Ismail, F. Ahmed","doi":"10.13052/EJCM1779-7179.29461","DOIUrl":"https://doi.org/10.13052/EJCM1779-7179.29461","url":null,"abstract":"In this paper the dynamic analysis of a shaft rotor whose support is mobile is studied. For the calculation of kinetic energy and stiffness energy, the beam theory of Euler Bernoulli was used, and the matrices of elements and systems are developed using two methods derived from the differential quadrature method (DQM). The first method is the Differential Quadrature Finite Element Method (DQFEM) systematically, as a combination of the Differential Quadrature Method (DQM) and the Standard Finite Element Method (FEM), which has a reduced computational cost for problems in dynamics. The second method is the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) which is used by expressing the matrices of the hierarchical finite element method in a similar form to that of the Differential Quadrature Finite Element Method and introducing an interpolation basis on the element boundary of the hierarchical finite element method. The discretization element used for both methods is a three-dimensional beam element. In the differential quadrature finite element method (DQFEM), the mass, gyroscopic and stiffness matrices are simply calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The sampling points are determined by the Gauss-Lobatto node method. In the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) the same approaches were used, and the cubic Hermite shape functions and the special Legendre polynomial Rodrigues shape polynomial were added. The assembly of the matrices for both methods (DQFEM and DQHFEM) is similar to that of the classical finite element method. The results of the calculation are validated with the h- and hp finite element methods and also with the literature.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"303–344-303–344"},"PeriodicalIF":1.2,"publicationDate":"2021-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45065538","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}
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