An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error b...An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuum- based shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.展开更多
Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It lead...Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.展开更多
In[A NURBS-enhanced finite volume solver for steady Euler equations,X.C.Meng,G.H.Hu,J.Comput.Phys.,Vol.359,pp.77–92],aNURBS-enhanced finite volume method was developed to solve the steady Euler equations,in which the...In[A NURBS-enhanced finite volume solver for steady Euler equations,X.C.Meng,G.H.Hu,J.Comput.Phys.,Vol.359,pp.77–92],aNURBS-enhanced finite volume method was developed to solve the steady Euler equations,in which the desired high order numerical accuracy was obtained for the equations imposed in the domain with a curved boundary.In this paper,the method is significantly improved in the following ways:(i)a simple and efficient point inversion technique is designed to compute the parameter values of points lying on a NURBS curve,(ii)with this new point inversion technique,the h-adaptive NURBS-enhanced finite volume method is introduced for the steady Euler equations in a complex domain,and(iii)a goal-oriented a posteriori error indicator is designed to further improve the efficiency of the algorithm towards accurately calculating a given quantity of interest.Numerical results obtained from a variety of numerical experiments with different flow configurations successfully show the effectiveness and robustness of the proposed method.展开更多
V&V(Verification and Validation),即模型验证与确认,是一种量化复杂数值模拟结果置信度的系统方法.大规模的数值模拟往往不能确保高置信度,数值模拟结果的置信度需要一种严格量化的方法.对于有限元模拟问题,获得近似解后,如果直...V&V(Verification and Validation),即模型验证与确认,是一种量化复杂数值模拟结果置信度的系统方法.大规模的数值模拟往往不能确保高置信度,数值模拟结果的置信度需要一种严格量化的方法.对于有限元模拟问题,获得近似解后,如果直接对这个解进行误差分析,可以得到一个整体的误差估计.而对于以有限元模拟为辅助手段的设计改进而言,通常都有特别关心的专门设计量,所有的模拟实验过程都是为检验这个量而服务的.面向目标的误差估计方法就是专门针对如何准确和经济地估算特定值误差的一种方法.本文通过线性化简后,把这种估计方法针对有限元模拟成功实现,为在实际工程应用中数值实现这种最接近于解决实际问题的方法作了准备.展开更多
Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It lea...Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method （XFEM）, which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10876100)
文摘An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuum- based shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.
基金Project supported by the National Natural Science Foundation of China (No. 10876100)
文摘Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.
基金supported by the National Natural Science Foundation of China(Grant No.12101057)the Scientific Research Fund of Beijing Normal University(Grant No.28704-111032105)+4 种基金the Start-up Research Fund from BNU-HKBU United International College(Grant No.R72021112)supported by FDCT of the Macao S.A.R.(0082/2020/A2)National Natural Science Foundation of China(Grant Nos.11922120,11871489)the Multi-Year Research Grant(MYRG2020-00265-FST)of University of Macaoa grant from Department of Science and Technology of Guangdong Province(2020B1212030001).
文摘In[A NURBS-enhanced finite volume solver for steady Euler equations,X.C.Meng,G.H.Hu,J.Comput.Phys.,Vol.359,pp.77–92],aNURBS-enhanced finite volume method was developed to solve the steady Euler equations,in which the desired high order numerical accuracy was obtained for the equations imposed in the domain with a curved boundary.In this paper,the method is significantly improved in the following ways:(i)a simple and efficient point inversion technique is designed to compute the parameter values of points lying on a NURBS curve,(ii)with this new point inversion technique,the h-adaptive NURBS-enhanced finite volume method is introduced for the steady Euler equations in a complex domain,and(iii)a goal-oriented a posteriori error indicator is designed to further improve the efficiency of the algorithm towards accurately calculating a given quantity of interest.Numerical results obtained from a variety of numerical experiments with different flow configurations successfully show the effectiveness and robustness of the proposed method.
文摘V&V(Verification and Validation),即模型验证与确认,是一种量化复杂数值模拟结果置信度的系统方法.大规模的数值模拟往往不能确保高置信度,数值模拟结果的置信度需要一种严格量化的方法.对于有限元模拟问题,获得近似解后,如果直接对这个解进行误差分析,可以得到一个整体的误差估计.而对于以有限元模拟为辅助手段的设计改进而言,通常都有特别关心的专门设计量,所有的模拟实验过程都是为检验这个量而服务的.面向目标的误差估计方法就是专门针对如何准确和经济地估算特定值误差的一种方法.本文通过线性化简后,把这种估计方法针对有限元模拟成功实现,为在实际工程应用中数值实现这种最接近于解决实际问题的方法作了准备.
基金Project supported by the National Natural Science Foundation of China(No.10876100)
文摘Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method （XFEM）, which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.
