A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization...A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.展开更多
The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent ...The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.展开更多
The variation of the principal stress of formations with the working and geo-mechanical conditions can trigger wellbore instabilities and adversely affect the well completion.A finite element model,based on the theory...The variation of the principal stress of formations with the working and geo-mechanical conditions can trigger wellbore instabilities and adversely affect the well completion.A finite element model,based on the theory of poro-elasticity and the Mohr-Coulomb rock damage criterion,is used here to analyze such a risk.The changes in wellbore stability before and after reservoir acidification are simulated for different pressure differences.The results indicate that the risk of wellbore instability grows with an increase in the production-pressure difference regardless of whether acidification is completed or not;the same is true for the instability area.After acidizing,the changes in the main geomechanical parameters(i.e.,elastic modulus,Poisson’s ratio,and rock strength)cause the maximum wellbore instability coefficient to increase.展开更多
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their...This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.展开更多
In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avo...In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.展开更多
We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is ...We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.展开更多
The simulation of the electromagnetic wave propagation plays an important role in predicting the performance of wireless transmission and communication systems. This research paper performs a numerical simulation usin...The simulation of the electromagnetic wave propagation plays an important role in predicting the performance of wireless transmission and communication systems. This research paper performs a numerical simulation using the finite element method (FEM) to study electromagnetic propagation through both conductive and dielectric media. The simulations are made using the COMSOL Multiphysics software which notably implements the finite element method. The microwave is produced by a Vivaldi antenna at the respective frequencies of 2.6 and 5 GHz and the propagation equation is formulated from Maxwell’s equations. The results obtained show that in the air, strong electric fields are observed in the slot and the micro-strip line for the two frequencies, they are even greater when the wave propagates in the glass and very weak for the copper. The 3D evolutions of the wave in air and glass present comparable values at equal frequencies, the curves being more regular in air (dielectric). The radiation patterns produced for air and glass are directional, with a large main lobe, which is narrower at 5 GHz. For copper, the wave propagation is quite uniform in space, and the radiation patterns show two main lobes with a much larger size at 2.6 GHz than at 5 GHz. The propagation medium would therefore influence the range of values of the gain of the antenna.展开更多
The connecting rod is one of the most important moving components in an internal combustion engine. The present work determined the possibility of using aluminium alloy 7075 material to design and manufacture a connec...The connecting rod is one of the most important moving components in an internal combustion engine. The present work determined the possibility of using aluminium alloy 7075 material to design and manufacture a connecting rod for weight optimisation without losing the strength of the connecting rod. It considered modal and thermal analyses to investigate the suitability of the material for connecting rod design. The parameters that were considered under the modal analysis were: total deformation, and natural frequency, while the thermal analysis looked at the temperature distribution, total heat flux and directional heat flux of the four connecting rods made with titanium alloy, grey cast iron, structural steel and aluminium 7075 alloy respectively. The connecting rod was modelled using Autodesk inventor2017 software using the calculated parameters. The steady-state thermal analysis was used to determine the induced heat flux and directional heat flux. The study found that Aluminium 7075 alloy deformed more than the remaining three other materials but has superior qualities in terms of vibrational natural frequency, total heat flux and lightweight compared to structural steel, grey cast iron and titanium alloy.展开更多
In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m...In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.展开更多
As key components connecting offshore floating production platforms and subsea imports, offshore flexible pipes play significant roles in oil, natural gas, and water injection. It is found that torsional failure is on...As key components connecting offshore floating production platforms and subsea imports, offshore flexible pipes play significant roles in oil, natural gas, and water injection. It is found that torsional failure is one of the failure modes of flexible pipes during transportation and laying. In this paper, a theoretical model(TM) of a flexible pipe section mechanics is established, in which the carcass layer and the pressure armor layer are equivalent to the orthogonal anisotropic layers due to its complex cross-section structure. The calculation results of the TM are consistent with those of a finite element model(FEM), which can accurately describe the torsional response of the flexible pipe.Subsequently, the TM and FEM are used to discuss the influence of boundary conditions on the torsional response.The structure of the flexible pipe is stable when twisted counterclockwise. However, limiting the top axial displacement can improve the axial and radial instability of the tensile armor layer when twisted clockwise. Finally, it is recommended that the flexible pipe can be kept under top fixation during service or installation to avoid torsional failure.展开更多
The key component of finite element analysis of structures with fuzzy parameters,which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing...The key component of finite element analysis of structures with fuzzy parameters,which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic.According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers.It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.展开更多
The element energy projection(EEP) method for computation of superconvergent resulting in a one-dimensional finite element method(FEM) is successfully used to self-adaptive FEM analysis of various linear problems, bas...The element energy projection(EEP) method for computation of superconvergent resulting in a one-dimensional finite element method(FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems.The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a result, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed.The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation(ODE) of second-order as the model problem, this paper describes the related fundamental idea, the implementation strategy, and the computational algorithm. Representative numerical examples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.展开更多
A highly efficient H1-Galerkin mixed finite element method(MFEM) is presented with linear triangular element for the parabolic integro-differential equation.Firstly, some new results about the integral estimation and ...A highly efficient H1-Galerkin mixed finite element method(MFEM) is presented with linear triangular element for the parabolic integro-differential equation.Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(π) norm and the flux p =u in H(div,π) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.展开更多
A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and vi...A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.展开更多
n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwat...n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.展开更多
The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-sc...The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate es- timates and numerical examples which show the effectiveness of the method are presented.展开更多
The finite cell method(FCM) combines the high-order finite element method(FEM) with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow the...The finite cell method(FCM) combines the high-order finite element method(FEM) with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method(h-FEM). The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.展开更多
In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element...In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.展开更多
Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,compara...Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats.展开更多
基金supported by a Major Research Project in Higher Education Institutions in Henan Province,with Project Number 23A560015.
文摘A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.
文摘The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.
基金This work is financially sponsored by Tarim Oilfield“Study on Adaptability Evaluation and Parameter Optimization of Completion Technology in Bozi Block,Tarim Oilfield”(Item Number:201021113436).
文摘The variation of the principal stress of formations with the working and geo-mechanical conditions can trigger wellbore instabilities and adversely affect the well completion.A finite element model,based on the theory of poro-elasticity and the Mohr-Coulomb rock damage criterion,is used here to analyze such a risk.The changes in wellbore stability before and after reservoir acidification are simulated for different pressure differences.The results indicate that the risk of wellbore instability grows with an increase in the production-pressure difference regardless of whether acidification is completed or not;the same is true for the instability area.After acidizing,the changes in the main geomechanical parameters(i.e.,elastic modulus,Poisson’s ratio,and rock strength)cause the maximum wellbore instability coefficient to increase.
文摘This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.
基金the National Natural Science Foundation of China(Grant No.41807223)the Fundamental Research Funds for the Central Universities(Grant No.B210202096)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA 23090202).
文摘In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.
基金supported by the National Natural Science Foundation of China(Nos.12132001 and 52192632)。
文摘We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.
文摘The simulation of the electromagnetic wave propagation plays an important role in predicting the performance of wireless transmission and communication systems. This research paper performs a numerical simulation using the finite element method (FEM) to study electromagnetic propagation through both conductive and dielectric media. The simulations are made using the COMSOL Multiphysics software which notably implements the finite element method. The microwave is produced by a Vivaldi antenna at the respective frequencies of 2.6 and 5 GHz and the propagation equation is formulated from Maxwell’s equations. The results obtained show that in the air, strong electric fields are observed in the slot and the micro-strip line for the two frequencies, they are even greater when the wave propagates in the glass and very weak for the copper. The 3D evolutions of the wave in air and glass present comparable values at equal frequencies, the curves being more regular in air (dielectric). The radiation patterns produced for air and glass are directional, with a large main lobe, which is narrower at 5 GHz. For copper, the wave propagation is quite uniform in space, and the radiation patterns show two main lobes with a much larger size at 2.6 GHz than at 5 GHz. The propagation medium would therefore influence the range of values of the gain of the antenna.
文摘The connecting rod is one of the most important moving components in an internal combustion engine. The present work determined the possibility of using aluminium alloy 7075 material to design and manufacture a connecting rod for weight optimisation without losing the strength of the connecting rod. It considered modal and thermal analyses to investigate the suitability of the material for connecting rod design. The parameters that were considered under the modal analysis were: total deformation, and natural frequency, while the thermal analysis looked at the temperature distribution, total heat flux and directional heat flux of the four connecting rods made with titanium alloy, grey cast iron, structural steel and aluminium 7075 alloy respectively. The connecting rod was modelled using Autodesk inventor2017 software using the calculated parameters. The steady-state thermal analysis was used to determine the induced heat flux and directional heat flux. The study found that Aluminium 7075 alloy deformed more than the remaining three other materials but has superior qualities in terms of vibrational natural frequency, total heat flux and lightweight compared to structural steel, grey cast iron and titanium alloy.
文摘In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.
基金financially supported by the Natural Science Starting Project of SWPU (Grant No. 2022QHZ002)Sichuan Natural Science Foundation Youth Fund Project (Grant No. 2023NSFC0918)。
文摘As key components connecting offshore floating production platforms and subsea imports, offshore flexible pipes play significant roles in oil, natural gas, and water injection. It is found that torsional failure is one of the failure modes of flexible pipes during transportation and laying. In this paper, a theoretical model(TM) of a flexible pipe section mechanics is established, in which the carcass layer and the pressure armor layer are equivalent to the orthogonal anisotropic layers due to its complex cross-section structure. The calculation results of the TM are consistent with those of a finite element model(FEM), which can accurately describe the torsional response of the flexible pipe.Subsequently, the TM and FEM are used to discuss the influence of boundary conditions on the torsional response.The structure of the flexible pipe is stable when twisted counterclockwise. However, limiting the top axial displacement can improve the axial and radial instability of the tensile armor layer when twisted clockwise. Finally, it is recommended that the flexible pipe can be kept under top fixation during service or installation to avoid torsional failure.
基金Foundation items:the National Natural Science Foundation of China(59575040,59575032)the Areonautics Science Foundation of China(00B53010)
文摘The key component of finite element analysis of structures with fuzzy parameters,which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic.According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers.It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.
基金supported by the National Natural Science Foundation of China(Nos.51378293,51078199,50678093,and 50278046)the Program for Changjiang Scholars and the Innovative Research Team in University of China(No.IRT00736)
文摘The element energy projection(EEP) method for computation of superconvergent resulting in a one-dimensional finite element method(FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems.The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a result, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed.The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation(ODE) of second-order as the model problem, this paper describes the related fundamental idea, the implementation strategy, and the computational algorithm. Representative numerical examples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.
基金Project supported by the National Natural Science Foundation of China(Nos.10971203,11271340,and 11101381)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘A highly efficient H1-Galerkin mixed finite element method(MFEM) is presented with linear triangular element for the parabolic integro-differential equation.Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(π) norm and the flux p =u in H(div,π) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.
基金This work was supported by the National Natural Science Foundation of China(Nos.51405370&51421004)the National Key Basic Research Program of China(No.2015CB057400)+2 种基金the project supported by Natural Science Basic Plan in Shaanxi Province of China(No.2015JQ5184)the Fundamental Research Funds for the Central Universities(xjj2014014)Shaanxi Province Postdoctoral Research Project.
文摘A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.
基金The authors would like to acknowledge the support of the National Natural Science Foundation of China(Grant 11672081)the Industrial Technology Development Program(Grants JCKY2018604C010 and JCKY2017604C002).Finally,Thanks for the help of Zu-Hui Li during writing the paper.
文摘n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.
基金supported by the National Natural Science Foundation of China(Nos.10801042 and 11171257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20104410120001)
文摘The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate es- timates and numerical examples which show the effectiveness of the method are presented.
基金supported by the Alexander von Humboldt Foundation
文摘The finite cell method(FCM) combines the high-order finite element method(FEM) with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method(h-FEM). The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.
文摘In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.
基金National Natural Science Foundation of China(No.51674280,51774308,51704033,51722406,51950410591)Shandong Provincial Natural Science Foundation(ZR2019JQ21,JQ201808)+3 种基金the Fundamental Research Funds for the Central Universities(No.20CX02113A)National Science and Technology Major Project(2016ZX05014-000407)Program for Changjiang Scholars and Innovative Research Team in University(IRT_16R69)PetroChina Innovation Foundation(No.2018D-5007-0210)。
文摘Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats.
