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
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 constructs a new two-dimensional arbitrary polygonal stress hybrid dynamic(APSHD)element for structural dynamic response analysis.Firstly,the energy function is established based on Hamilton's principle...This paper constructs a new two-dimensional arbitrary polygonal stress hybrid dynamic(APSHD)element for structural dynamic response analysis.Firstly,the energy function is established based on Hamilton's principle.Then,the finite element time-space discrete format is constructed using the generalized variational principle and the direct integration method.Finally,an explicit polynomial form of the combined stress solution is give,and its derivation process is shown in detail.After completing the theoretical construction,the numerical calculation program of the APSHD element is written in Fortran,and samples are verified.Models show that the APSHD element performs well in accuracy and convergence.Furthermore,it is insensitive to mesh distortion and has low dependence on selecting time steps.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
路基工后沉降直接关乎公路的安全性能,蠕变行为的预测对保障路基工程的长期安全具有重要意义。对蠕变行为进行有限元数值模拟时,复杂结构模型的网格划分需要耗费大量的计算资源,且计算量大计算时间长。提出了一种考虑蠕变的任意多边形...路基工后沉降直接关乎公路的安全性能,蠕变行为的预测对保障路基工程的长期安全具有重要意义。对蠕变行为进行有限元数值模拟时,复杂结构模型的网格划分需要耗费大量的计算资源,且计算量大计算时间长。提出了一种考虑蠕变的任意多边形杂交应力新单元(polygonal hybrid stress element method,PHSEM),用于工程中的路基沉降问题研究。基于杂交应力元法及路基土的蠕变行为,推导PHSEM的单元基本格式,分析表明该单元引入了高阶应力场,能更好地提高计算精度,进一步建立路基蠕变的数值计算模型,结合有限元软件MARC开展对比分析。研究表明:PHSEM的数值仿真曲线拟合良好,验证了考虑蠕变的任意多边形杂交应力单元的有效性;PHSEM在划分网格时形状可以是任意边数的多边形,能够很好地模拟多种介质的路基模型,真实地计算出不同部位的应力分布情况;PHSEM的构造为实际工程中的蠕变研究提供了一种可参考的新思路。展开更多
基于泰森多边形理论,提出了一种鞋垫参数化设计方法,并探索了其在足底压力缓解方面的应用。研究通过自适应加权分割与有限元分析相结合的方法,对比了蜂窝结构和泰森多边形结构鞋垫的性能。结果表明,两者均可将足底压强降低至48 k Pa以下...基于泰森多边形理论,提出了一种鞋垫参数化设计方法,并探索了其在足底压力缓解方面的应用。研究通过自适应加权分割与有限元分析相结合的方法,对比了蜂窝结构和泰森多边形结构鞋垫的性能。结果表明,两者均可将足底压强降低至48 k Pa以下,但泰森多边形结构的压强分布更均匀,集中于24 k Pa左右。进一步分析发现,在相同压强分布条件下,泰森多边形结构鞋垫能够更精确地贴合脚部轮廓,适应不同区域的压强分布,展现出更好的缓压性能,尤其适用于定制化鞋垫设计。展开更多
采用有限元法分别对锂离子电池的荷电状态(state of charge,SOC)、内部缺陷(气泡缺陷、析锂缺陷和浸润不完全缺陷)与超声透射特性之间的影响规律进行了仿真分析。首先,利用Voronoi多边形建立了锂离子电池内部的多层多孔结构;其次,在仿...采用有限元法分别对锂离子电池的荷电状态(state of charge,SOC)、内部缺陷(气泡缺陷、析锂缺陷和浸润不完全缺陷)与超声透射特性之间的影响规律进行了仿真分析。首先,利用Voronoi多边形建立了锂离子电池内部的多层多孔结构;其次,在仿真过程中,通过改变正负极材料的力学参数(杨氏模量和密度)实现了锂离子电池不同荷电状态下超声透射特性的提取。仿真结果表明,随着荷电状态的增加,快纵波的声强幅值和慢纵波的声强幅值均呈现线性增加的规律,慢纵波的渡越时间呈现线性减小的规律。随后,对锂离子电池内部不同缺陷形式进行仿真分析。通过对比正常电池和缺陷电池的声透射信息可以发现:当锂离子电池底部存在气泡缺陷时,透射信号的声强幅值显著衰减,且随着气泡厚度的增加,声强幅值的衰减也在增加;此外,随着气泡位置的改变,透射信号的声强幅值也呈现规律性变化;当锂离子电池内部存在析锂缺陷时,透射信号的声强幅值和渡越时间均随着析锂厚度的增加而逐渐减小;当锂离子电池内部存在浸润不完全缺陷时,仿真模型将退化为单相多孔介质,频域中也只存在一个频率成分,且声强幅值存在衰减。研究内容解决了用有限元法对锂离子电池荷电状态、内部缺陷进行模拟处理的问题,且慢纵波波速的仿真结果与理论结果吻合良好。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
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.
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funded by the National Natural Science Foundation of China(Grant No.12072135).
文摘This paper constructs a new two-dimensional arbitrary polygonal stress hybrid dynamic(APSHD)element for structural dynamic response analysis.Firstly,the energy function is established based on Hamilton's principle.Then,the finite element time-space discrete format is constructed using the generalized variational principle and the direct integration method.Finally,an explicit polynomial form of the combined stress solution is give,and its derivation process is shown in detail.After completing the theoretical construction,the numerical calculation program of the APSHD element is written in Fortran,and samples are verified.Models show that the APSHD element performs well in accuracy and convergence.Furthermore,it is insensitive to mesh distortion and has low dependence on selecting time steps.
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.
文摘路基工后沉降直接关乎公路的安全性能,蠕变行为的预测对保障路基工程的长期安全具有重要意义。对蠕变行为进行有限元数值模拟时,复杂结构模型的网格划分需要耗费大量的计算资源,且计算量大计算时间长。提出了一种考虑蠕变的任意多边形杂交应力新单元(polygonal hybrid stress element method,PHSEM),用于工程中的路基沉降问题研究。基于杂交应力元法及路基土的蠕变行为,推导PHSEM的单元基本格式,分析表明该单元引入了高阶应力场,能更好地提高计算精度,进一步建立路基蠕变的数值计算模型,结合有限元软件MARC开展对比分析。研究表明:PHSEM的数值仿真曲线拟合良好,验证了考虑蠕变的任意多边形杂交应力单元的有效性;PHSEM在划分网格时形状可以是任意边数的多边形,能够很好地模拟多种介质的路基模型,真实地计算出不同部位的应力分布情况;PHSEM的构造为实际工程中的蠕变研究提供了一种可参考的新思路。
文摘基于泰森多边形理论,提出了一种鞋垫参数化设计方法,并探索了其在足底压力缓解方面的应用。研究通过自适应加权分割与有限元分析相结合的方法,对比了蜂窝结构和泰森多边形结构鞋垫的性能。结果表明,两者均可将足底压强降低至48 k Pa以下,但泰森多边形结构的压强分布更均匀,集中于24 k Pa左右。进一步分析发现,在相同压强分布条件下,泰森多边形结构鞋垫能够更精确地贴合脚部轮廓,适应不同区域的压强分布,展现出更好的缓压性能,尤其适用于定制化鞋垫设计。
文摘采用有限元法分别对锂离子电池的荷电状态(state of charge,SOC)、内部缺陷(气泡缺陷、析锂缺陷和浸润不完全缺陷)与超声透射特性之间的影响规律进行了仿真分析。首先,利用Voronoi多边形建立了锂离子电池内部的多层多孔结构;其次,在仿真过程中,通过改变正负极材料的力学参数(杨氏模量和密度)实现了锂离子电池不同荷电状态下超声透射特性的提取。仿真结果表明,随着荷电状态的增加,快纵波的声强幅值和慢纵波的声强幅值均呈现线性增加的规律,慢纵波的渡越时间呈现线性减小的规律。随后,对锂离子电池内部不同缺陷形式进行仿真分析。通过对比正常电池和缺陷电池的声透射信息可以发现:当锂离子电池底部存在气泡缺陷时,透射信号的声强幅值显著衰减,且随着气泡厚度的增加,声强幅值的衰减也在增加;此外,随着气泡位置的改变,透射信号的声强幅值也呈现规律性变化;当锂离子电池内部存在析锂缺陷时,透射信号的声强幅值和渡越时间均随着析锂厚度的增加而逐渐减小;当锂离子电池内部存在浸润不完全缺陷时,仿真模型将退化为单相多孔介质,频域中也只存在一个频率成分,且声强幅值存在衰减。研究内容解决了用有限元法对锂离子电池荷电状态、内部缺陷进行模拟处理的问题,且慢纵波波速的仿真结果与理论结果吻合良好。
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.
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。
