This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that ...This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that are governed by Stokes equations system.This technique is constructed by a local pressure projection which is extremely simple,yet effective,to eliminate the poor or even non-convergence as well as the instability of equal-order mixed polygonal technique.In this research,some numerical examples of incompressible Stokes fluid flow that is coded and programmed by MATLAB will be presented to examine the effectiveness of the proposed stabilised method.展开更多
The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basi...The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.展开更多
In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relat...In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.展开更多
The safety of aircraft landing on wet runways is of great importance in runway risk man agement.In order to ensure landing safety on wet runways,real-time risk warning is required.This paper proposes a method to asses...The safety of aircraft landing on wet runways is of great importance in runway risk man agement.In order to ensure landing safety on wet runways,real-time risk warning is required.This paper proposes a method to assess aircraft landing risk in real-time based on finite element-virtual prototype-machine learning co-simulation.Firstly,a tire-water f ilm-runway finite element model was constructed,a virtual prototype model was built based on the Airbus A320 model,and the results of the tire-water film-runway local finite element dynamic analysis were transferred to the system simulation of the virtual proto type for co-simulation.Secondly,considering the influence of wet state parameters on the runway,a database of aircraft anti-skid failure risk was constructed,and three machine learning models were trained to predict aircraft landing risk.The results show that the Support Vector Machine(SVM)model has better generalization capability and should be used to predict the risk level of aircraft landing.The efficacy of the comprehensive taxiing model was validated using an empirical formula for determining the aircraft’s landing dis tance on a wet runway.When an aircraft lands on a runway with an average water film thickness of 8 mm,the braking time is approximately 1.6 times longer than on a dry run way,and the braking distance is roughly 5.3 times greater than on a dry runway.Finally,a risk assessment example was provided:the entire process from landing information input to risk level output for the aircraft model took only 80 ms,which could provide an efficient and real-time aircraft landing risk assessment.展开更多
A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid m...A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.展开更多
This paper investigates a polygonal finite element(PFE)to solve a two-dimensional(2D)incompressible steady fluid problem in a cavity square.It is a well-known standard benchmark(i.e.,lid-driven cavity flow)-to evaluat...This paper investigates a polygonal finite element(PFE)to solve a two-dimensional(2D)incompressible steady fluid problem in a cavity square.It is a well-known standard benchmark(i.e.,lid-driven cavity flow)-to evaluate the numerical methods in solving fluid problems controlled by the Navier-Stokes(N-S)equation system.The approximation solutions provided in this research are based on our developed equal-order mixed PFE,called Pe1Pe1.It is an exciting development based on constructing the mixed scheme method of two equal-order discretisation spaces for both fluid pressure and velocity fields of flows and our proposed stabilisation technique.In this research,to handle the nonlinear problem of N-S,the Picard iteration scheme is applied.Our proposed method’s performance and convergence are validated by several simulations coded by commercial software,i.e.,MATLAB.For this research,the benchmark is executed with variousReynolds numbers up to the maximum Re=1000.All results then numerously compared to available sources in the literature.展开更多
The virtual element method(VEM)can be seen as an extension of the classical finite element method(FEM)based on Galerkin projection.It allows meshes with highly irregular shaped elements,including concave shapes.So far...The virtual element method(VEM)can be seen as an extension of the classical finite element method(FEM)based on Galerkin projection.It allows meshes with highly irregular shaped elements,including concave shapes.So far the virtual element method has been applied to various engineering problems such as elasto-plasticity,multiphysics,damage and fracture mechanics.This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations.Within this framework,we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape.The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior.Generally the construction of a virtual element is based on a projection part and a stabilization part.While the stiffness matrix needs a suitable stabilization,the mass matrix can be calculated using only the projection part.For the implicit time integration scheme,Newmark-Method is used.To show the performance of the method,various two-and three-dimensional numerical examples in are presented.展开更多
Avirtual wall thicknessmethod is developed to simulate the temperature field of turbine bladeswith thermal barrier coatings(TBCs),to simplify the modeling process and improve the calculation efficiency.The results sho...Avirtual wall thicknessmethod is developed to simulate the temperature field of turbine bladeswith thermal barrier coatings(TBCs),to simplify the modeling process and improve the calculation efficiency.The results show that the virtualwall thickness method can improve themesh quality by 20%,reduce the number ofmeshes by 76.7%and save the calculation time by 35.5%,compared with the traditional real wall thickness method.The average calculation error of the two methods is between 0.21%and 0.93%.Furthermore,the temperature at the blade leading edge is the highest and the average temperature of the blade pressure surface is higher than that of the suction surface under a certain service condition.The blade surface temperature presents a high temperature at both ends and a low temperature in themiddle height when the temperature of incoming gas is uniformand constant.The thermal insulation effect of TBCs is the worst near the air film hole,and the best at the blade leading edge.According to the calculated temperature field of the substrate-coating system,the highest thermal insulation temperature of the TC layer is 172.01 K,and the thermal insulation proportions of TC,TGO and BC are 93.55%,1.54%and 4.91%,respectively.展开更多
Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadrati...Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadratic serendipity element shape function is introduced from the linear generalized barycentric coordinates,and the quadratic serendipity element function space based on Wachspress coordinate is selected as the trial function space.Moreover,we construct a family of unified dual partitions for arbitrary convex polygonal meshes,which is crucial to finite volume element scheme,and propose a quadratic serendipity polygonal finite volume element method with fewer degrees of freedom.Finally,under certain geometric assumption conditions,the optimal H1 error estimate for the quadratic serendipity polygonal finite volume element scheme is obtained,and verified by numerical experiments.展开更多
Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes.This enables simple and efficient implementation,but in...Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes.This enables simple and efficient implementation,but in turn,restricts the representation capability of the deformation,often leading to unsatisfactory warping results.We present a novel,flexible polygonal finite element(poly-FEM)method for content-aware image warping.Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image.This allows highly adaptive meshes and smoother warping with fewer degrees of freedom,thus significantly extending the flexibility and capability of the warping representation.Benefiting from the continuous formulation of image deformation,our polyFEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations.We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-ofthe-art methods.展开更多
In this study, Virtual Reality (VR)-based plastic injection molding training system (VPIMTS), which can be modeled as an integrated system with a task planning module, an intelligent instruction module, a simulation m...In this study, Virtual Reality (VR)-based plastic injection molding training system (VPIMTS), which can be modeled as an integrated system with a task planning module, an intelligent instruction module, a simulation module, and virtual envi-ronment (VE) module, was developed. Presented in this paper are an architecture of VPIMTS, a practical knowledge modelling approach for modelling the training scenarios of the system by using Petri nets formalism and key techniques (FEM, injection molding procedure modelling) which have been developed independently. The utilization of the Petri net model realized the environment where the trainee can behave freely, and also made it possible to equip the system with the function of showing the next action of the trainee whenever he wants. The overall system is a powerful approach for highly improving the trainee’s comprehension and injection molding study-efficiency by building digital, intelligent, knowledgeable, and visual aids.展开更多
应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝...应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。展开更多
基金The authors would like to present our gratitude to the Flemish Government financially supporting for the VLIR-OUS TEAM Project,VN2017TEA454A103‘An innovative solution to protect Vietnamese coastal riverbanks from floods and erosion’.
文摘This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that are governed by Stokes equations system.This technique is constructed by a local pressure projection which is extremely simple,yet effective,to eliminate the poor or even non-convergence as well as the instability of equal-order mixed polygonal technique.In this research,some numerical examples of incompressible Stokes fluid flow that is coded and programmed by MATLAB will be presented to examine the effectiveness of the proposed stabilised method.
基金support by Basic Science Research Program through the National Research Foundation(NRF)funded by Korea Ministry of Education(No.2016R1A6A1A0312812).
文摘The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.
文摘In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.
基金The work described in this paper is supported by the National Natural Science Foundation of China(No.52278455)the Shuguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission(21SG24)+1 种基金the International Cooperation Project of Science and Technology Commission of Shanghai Municipality(No.22210710700)the Fundamental Research Funds for the Central Universities.
文摘The safety of aircraft landing on wet runways is of great importance in runway risk man agement.In order to ensure landing safety on wet runways,real-time risk warning is required.This paper proposes a method to assess aircraft landing risk in real-time based on finite element-virtual prototype-machine learning co-simulation.Firstly,a tire-water f ilm-runway finite element model was constructed,a virtual prototype model was built based on the Airbus A320 model,and the results of the tire-water film-runway local finite element dynamic analysis were transferred to the system simulation of the virtual proto type for co-simulation.Secondly,considering the influence of wet state parameters on the runway,a database of aircraft anti-skid failure risk was constructed,and three machine learning models were trained to predict aircraft landing risk.The results show that the Support Vector Machine(SVM)model has better generalization capability and should be used to predict the risk level of aircraft landing.The efficacy of the comprehensive taxiing model was validated using an empirical formula for determining the aircraft’s landing dis tance on a wet runway.When an aircraft lands on a runway with an average water film thickness of 8 mm,the braking time is approximately 1.6 times longer than on a dry run way,and the braking distance is roughly 5.3 times greater than on a dry runway.Finally,a risk assessment example was provided:the entire process from landing information input to risk level output for the aircraft model took only 80 ms,which could provide an efficient and real-time aircraft landing risk assessment.
文摘A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.
基金This work was supported by the VLIR-UOS TEAM Project,VN2017TEA454A 103,‘An innovative solution to protect Vietnamese coastal riverbanks from floods and erosion’funded by the Flemish Government.
文摘This paper investigates a polygonal finite element(PFE)to solve a two-dimensional(2D)incompressible steady fluid problem in a cavity square.It is a well-known standard benchmark(i.e.,lid-driven cavity flow)-to evaluate the numerical methods in solving fluid problems controlled by the Navier-Stokes(N-S)equation system.The approximation solutions provided in this research are based on our developed equal-order mixed PFE,called Pe1Pe1.It is an exciting development based on constructing the mixed scheme method of two equal-order discretisation spaces for both fluid pressure and velocity fields of flows and our proposed stabilisation technique.In this research,to handle the nonlinear problem of N-S,the Picard iteration scheme is applied.Our proposed method’s performance and convergence are validated by several simulations coded by commercial software,i.e.,MATLAB.For this research,the benchmark is executed with variousReynolds numbers up to the maximum Re=1000.All results then numerously compared to available sources in the literature.
基金The authors gratefully acknowledges support for this research by the“German Research Foundation”(DFG)in(i)the Collaborative Research Center CRC 1153 and(ii)the Priority Program SPP 2020.
文摘The virtual element method(VEM)can be seen as an extension of the classical finite element method(FEM)based on Galerkin projection.It allows meshes with highly irregular shaped elements,including concave shapes.So far the virtual element method has been applied to various engineering problems such as elasto-plasticity,multiphysics,damage and fracture mechanics.This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations.Within this framework,we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape.The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior.Generally the construction of a virtual element is based on a projection part and a stabilization part.While the stiffness matrix needs a suitable stabilization,the mass matrix can be calculated using only the projection part.For the implicit time integration scheme,Newmark-Method is used.To show the performance of the method,various two-and three-dimensional numerical examples in are presented.
基金supported by the National Science and Technology Major Project(J2019-IV-0003-0070)the National Natural Science Foundation of China(Grant No.12102320)+1 种基金the Advanced Aviation Power Innovation Workstation Project(HKCX2019-01-003)China Postdoc-toral Science Foundation(2021M692571).
文摘Avirtual wall thicknessmethod is developed to simulate the temperature field of turbine bladeswith thermal barrier coatings(TBCs),to simplify the modeling process and improve the calculation efficiency.The results show that the virtualwall thickness method can improve themesh quality by 20%,reduce the number ofmeshes by 76.7%and save the calculation time by 35.5%,compared with the traditional real wall thickness method.The average calculation error of the two methods is between 0.21%and 0.93%.Furthermore,the temperature at the blade leading edge is the highest and the average temperature of the blade pressure surface is higher than that of the suction surface under a certain service condition.The blade surface temperature presents a high temperature at both ends and a low temperature in themiddle height when the temperature of incoming gas is uniformand constant.The thermal insulation effect of TBCs is the worst near the air film hole,and the best at the blade leading edge.According to the calculated temperature field of the substrate-coating system,the highest thermal insulation temperature of the TC layer is 172.01 K,and the thermal insulation proportions of TC,TGO and BC are 93.55%,1.54%and 4.91%,respectively.
基金supported by the National Natural Science Foundation of China(Nos.11871009,12271055)the Foundation of LCP and the Foundation of CAEP(CX20210044).
文摘Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadratic serendipity element shape function is introduced from the linear generalized barycentric coordinates,and the quadratic serendipity element function space based on Wachspress coordinate is selected as the trial function space.Moreover,we construct a family of unified dual partitions for arbitrary convex polygonal meshes,which is crucial to finite volume element scheme,and propose a quadratic serendipity polygonal finite volume element method with fewer degrees of freedom.Finally,under certain geometric assumption conditions,the optimal H1 error estimate for the quadratic serendipity polygonal finite volume element scheme is obtained,and verified by numerical experiments.
基金The research of Juan Cao was supported by the National Natural Science Foundation of China(Nos.61872308,61972327,and 62272402)the Xiamen Youth Innovation Funds(No.3502Z20206029)Yongjie Jessica Zhang was supported in part by NSF CMMI-1953323 and a Honda grant.
文摘Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes.This enables simple and efficient implementation,but in turn,restricts the representation capability of the deformation,often leading to unsatisfactory warping results.We present a novel,flexible polygonal finite element(poly-FEM)method for content-aware image warping.Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image.This allows highly adaptive meshes and smoother warping with fewer degrees of freedom,thus significantly extending the flexibility and capability of the warping representation.Benefiting from the continuous formulation of image deformation,our polyFEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations.We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-ofthe-art methods.
文摘In this study, Virtual Reality (VR)-based plastic injection molding training system (VPIMTS), which can be modeled as an integrated system with a task planning module, an intelligent instruction module, a simulation module, and virtual envi-ronment (VE) module, was developed. Presented in this paper are an architecture of VPIMTS, a practical knowledge modelling approach for modelling the training scenarios of the system by using Petri nets formalism and key techniques (FEM, injection molding procedure modelling) which have been developed independently. The utilization of the Petri net model realized the environment where the trainee can behave freely, and also made it possible to equip the system with the function of showing the next action of the trainee whenever he wants. The overall system is a powerful approach for highly improving the trainee’s comprehension and injection molding study-efficiency by building digital, intelligent, knowledgeable, and visual aids.
文摘应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。
