共查询到20条相似文献,搜索用时 562 毫秒
1.
2.
Combining the radial point interpolation method (RPIM), the dual reciprocity method (DRM) and the hybrid boundary node method (HBNM), a dual reciprocity hybrid radial boundary node method (DHRBNM) is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square (MLS) in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it's computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM. 相似文献
3.
几何精确NURBS有限元中边界条件施加方式对精度影响的三维计算分析 总被引:2,自引:1,他引:1
非均匀有理B样条(NURBS)有限元法把计算机辅助几何设计(CAGD)中的NURBS几何构形方法与有限元方法有机结合起来,有效消除了有限元离散模型的几何误差,提高了计算精度。但是由于NURBS基函数不是插值函数,直接在控制节点上施加位移边界条件会引起较大误差。本文详细讨论了NURBS基函数的插值特性,在NURBS有限元分析中采用罚函数法施加位移边界条件,提高了收敛率和计算精度。结合典型三维弹性力学问题,对两种施加位移边界条件的方法进行了对比和分析。计算结果表明,直接施加位移边界条件会导致收敛率和精度的明显降低,而基于罚函数法的NURBS有限元分析则能达到最优收敛率,并具有更高的精度。 相似文献
4.
5.
Summary A variant of the boundary element method, called the boundary contour method, offers a further reduction in dimensionality.
Consequently, boundary contour analysis of 2-D problems does not require any numerical integration at all. In a boundary contour
analysis, boundary stresses can be accurately computed using the approach proposed in Ref. [1]. However, due to singularity,
this approach can be used only to calculate boundary stresses at points that do not lie at an end of a boundary element. Herein,
it is shown that a technique based on the displacement/velocity shape functions can overcome this drawback. Further, the approach
is much simpler to apply, requires less computational effort, and provides competitive accuracy. Numerical solutions and convergence
study for some well-known problems in linear elasticity and Stokes flow are presented to show the effectiveness of the proposed
approach.
This research was supported in part by the 2004 Ralph E. Powe Junior Faculty Enhancement Award from Oak Ridge Associated Universities
and by the University of South Alabama Research Council. 相似文献
6.
数值流形方法(numerucal manifold method,NMM)通过引入数学覆盖和物理覆盖两套系统来统一处理连续和非连续问题. 通过用移动最小二乘插值(moving least squares interpolation,MLS)中的节点影响域构造数学覆盖,得到了基于数值流形方法的无网格伽辽金法(element free Galerkin,EFG). 该方法在保证前处理简单的同时,又能方便处理如裂纹等不连续问题. 建立了适用于小变形和大变形的裂纹扩展计算格式,并通过对曲折裂纹(kinked crack)的处理,在不加密的情况下实现了任意小步长的裂纹扩展,大大提高了在固定网格中模拟裂纹扩展的实用性. 大小变形的结果对比表明,按照不考虑构型变化的小变形计算,结果可能偏于危险. 相似文献
7.
In this article, adaptive mesh refinement (AMR) is performed to simulate flow around both stationary and moving boundaries. The finite-difference approach is applied along with a sharp interface immersed boundary (IB) method. The Lagrangian polynomial is employed to facilitate the interpolation from a coarse to a fine grid level, while a weighted-average formula is used to transfer variables inversely. To save memory, the finest grid is only generated in the local areas close to the wall boundary, and the mesh is dynamically reconstructed based on the location of the wall boundary. The Navier-Stokes equations are numerically solved through the second-order central difference scheme in space and the third-order Runge-Kutta time integration. Flow around a circular cylinder rotating in a square domain is firstly simulated to examine the accuracy and convergence rate. Then three cases are investigated to test the validity of the present method: flow past a stationary circular cylinder at low Reynolds numbers, flow past a forced oscillating circular cylinder in the transverse direction at various frequencies, and a free circular cylinder subjected to vortex-induced vibration in two degrees of freedom. Computational results agree well with these in the literature and the flow fields are smooth around the interface of different refinement levels. The effect of refinement level has also been evaluated. In addition, a study for the computational efficiency shows that the AMR approach is helpful to reduce the total node number and speed up the time integration, which could prompt the application of the IB method when a great near-wall spatial resolution is required. 相似文献
8.
Convergence improvement and superconvergence behaviour, obtained by the simple boundary node correction (BNC) procedure for certain stress-like variables of smoothed FEM solutions, are reported in this paper. The effectiveness of BNC is shown through three examples of steady flow problems, and a posterior error analysis based on the multiple-mesh extrapolation technique has been used for estimating the convergence rates. 相似文献
9.
A nonlinear problem for penetrant diffusion with relaxation in polymers is considered. A numerical approach to solving this type of problems is developed. The proposed numerical scheme based on a finite element domain approximation and a time difference method can be used for numerical simulation of the considered penetrant diffusion in 2-D and 3-D domains. A numerical procedure and a corresponding computer code are created and tested for some examples in 1-D and 2-D domains. 相似文献
10.
11.
Simulation of a 2-D Rightmyer–Meshkov instability (RMI), including inviscid, viscous and magnetic field effects was conducted
comparing recently developed sixth-order filter schemes with various standard shock-capturing methods. The suppression of
the inviscid gas dynamics RMI in the presence of a magnetic field was investigated by Samtaney and Wheatley et al. Numerical
results illustrated here exhibit behavior similar to the work of Samtaney. Due to the different amounts and different types
of numerical dissipation contained in each scheme, the structures and the growth of eddies for the chaotic-like inviscid gas
dynamics RMI case are highly grid size and scheme dependent, even with many levels of refinement. The failure of grid refinement
for all studied numerical methods extends to the viscous gas dynamics case for high Reynolds number. For lower Reynolds number,
grid convergence has been achieved by all studied methods. To achieve similar resolution, standard shock-capturing methods
require more grid points than filter schemes and yet the CPU times using the same grid for all studied methods are comparable.
This paper is based on work that was presented at the 17th International Shock Interaction Symposium (ISIS17), Rome, Italy,
4–8 September 2006. 相似文献
12.
自适应一致性高阶无单元伽辽金法 总被引:5,自引:4,他引:1
近来提出的一致性高阶无单元伽辽金法通过导数修正技术大幅度减少了所需积分点数目,并能够精确地通过线性和二次分片试验,显著改善标准无单元伽辽金法的计算效率、精度和收敛性.本文在此基础之上,充分利用无单元法易于在局部区域添加节点的优势,发展了一致性高阶无单元伽辽金法的h型自适应分析方法.根据应变能密度梯度该方法自适应地确定需节点加密的区域,基于背景积分网格的局部多层细化要求生成新的计算节点,同时考虑了节点分布由密到疏渐进过渡的情形.采用相邻两次计算的应变能的相对误差作为自适应过程的停止准则,将所发展自适应无网格法应用于由几何外形、边界外载和体力等因素造成的应力集中问题的计算分析.数值结果表明,所发展方法能够自适应地对高应力梯度区域进行节点加密,自动给出合理的计算节点分布.与已有的标准无网格法的自适应分析相比,所发展方法在计算效率、精度和应力场光滑性等方面均展现出显著优势.与采用节点均匀分布的一致性高阶无单元伽辽金法相比,它大幅度地减少了计算节点数目,有效提高了一致性高阶无单元伽辽金法在分析应力集中等存在局部高梯度问题时的计算效率和求解精度. 相似文献
13.
In recent years, three higher‐order (HO) bounded differencing schemes, namely AVLSMART, CUBISTA and HOAB that were derived by adopting the normalized variable formulation (NVF), have been proposed. In this paper, a comparative study is performed on these schemes to assess their numerical accuracy, computational cost as well as iterative convergence property. All the schemes are formulated on the basis of a new dual‐formulation in order to facilitate their implementations on unstructured meshes. Based on the proposed dual‐formulation, the net effective blending factor (NEBF) of a high‐resolution (HR) scheme can now be measured and its relevance on the accuracy and computational cost of a HR scheme is revealed on three test problems: (1) advection of a scalar step‐profile; (2) 2D transonic flow past a circular arc bump; and (3) 3D lid‐driven incompressible cavity flow. Both density‐based and pressure‐based methods are used for the computations of compressible and incompressible flow, respectively. Computed results show that all the schemes produce solutions which are nearly as accurate as the third‐order QUICK scheme; however, without the unphysical oscillations which are commonly inherited from the HO linear differencing scheme. Generally, it is shown that at higher value of NEBF, a HR scheme can attain better accuracy at the expense of computational cost. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD FOR THREE-DIMENSIONAL ELASTICITY WITH BODY FORCE 总被引:1,自引:0,他引:1
Combining Dual Reciprocity Method (DRM) with Hybrid Boundary Node Method (HBNM), the Dual Reciprocity Hybrid Boundary Node Method (DRHBNM) is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems. 相似文献
15.
采用径向基函数配点法分析考虑剪切效应的梁板弯曲问题,该方法利用径向基函数作为近似函数,基于配点法离散方程,通过最小二乘法求解.径向基函数配点法在离散和计算过程中不需要划分任何形式的网格,是一种真正的无网格法;径向基函数可以用一元函数来描述多元函数,存在明显的储存和运算简单的特点;而基于配点法求解不需要积分,提高了计算效率.分析考虑剪切效应的薄梁板问题时,传统的有限元法或无网格法求解均会存在剪切锁闭问题,而径向基函数在全域内存在无限连续性,能够准确地满足Kirchhoff约束条件,因此径向基函数配点法能够消除剪切锁闭现象,而且不会出现应力波动.该方法的优势在于,其不仅易于离散、精度高,而且具有指数收敛率,计算效率高.数值算例验证了上述结论和该方法的稳定性. 相似文献
16.
A perturbation finite volume (PFV) method for the convective-diffusion integral equation is developed in this paper. The PFV
scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations, with
the least nodes similar to the standard three-point schemes, that is, the number of the nodes needed is equal to unity plus
the face-number of the control volume. For instance, in the two-dimensional (2-D) case, only four nodes for the triangle grids
and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D linear and
nonlinear problems, 2-D and 3-D flow model equations. Comparing with other standard three-point schemes, the PFV scheme has
much smaller numerical diffusion than the first-order upwind scheme (UDS). Its numerical accuracies are also higher than the
second-order central scheme (CDS), the power-law scheme (PLS) and QUICK scheme.
The project supported by the National Natural Science Foundation of China (10272106, 10372106) 相似文献
17.
R. WEBSTER 《国际流体数值方法杂志》1996,22(11):1103-1123
An algebraic multigrid scheme is presented for solving the discrete Navier–Stokes equations to second-order accuracy using the defect correction method. Solutions for the driven cavity and asymmetric, sudden expansion test problems have been obtained for both structured and unstructured meshes, the resolution and resolution grading being controlled by global and local mesh refinements. The solver is efficient and robust to the extent that, for problems attempted so far, no underrelaxation of variables has been required to ensure convergence. Provided that the computational mesh can resolve the flow field, convergence characteristics are almost mesh-independent. Rates of convergence actually improve with refinement, asymptotically approaching mesh-independent values. For extremely coarse meshes, where dispersive truncation errors would be expected to prevent convergence (or even induce divergence), solutions can still be obtained by using explicit underrelaxation in the iterative cycle. 相似文献
18.
A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils 下载免费PDF全文
D. Ngo‐Cong C. M. T. Tien T. Nguyen‐Ky D.‐A. An‐Vo N. Mai‐Duy D. V. Strunin T. Tran‐Cong 《国际流体数值方法杂志》2017,85(7):404-429
In the present paper, we develop a generalised finite difference approach based on compact integrated radial basis function (CIRBF) stencils for solving highly nonlinear Richards equation governing fluid movement in heterogeneous soils. The proposed CIRBF scheme enjoys a high level of accuracy and a fast convergence rate with grid refinement owing to the combination of the integrated RBF approximation and compact approximation where the spatial derivatives are discretised in terms of the information of neighbouring nodes in a stencil. The CIRBF method is first verified through the solution of ordinary differential equations, 2–D Poisson equations and a Taylor‐Green vortex. Numerical comparisons show that the CIRBF method outperforms some other methods in the literature. The CIRBF method in conjunction with a rational function transformation method and an adaptive time‐stepping scheme is then applied to simulate 1–D and 2–D soil infiltrations effectively. The proposed solutions are more accurate and converge faster than those of the finite different method used with a second‐order central difference scheme. Additionally, the present scheme also takes less time to achieve target accuracy in comparison with the 1D‐IRBF and higher order compact schemes. 相似文献
19.
A first-order non-conforming numerical methodology, Separation method, for fluid flow problems with a 3-point exponential interpolation scheme has been developed. The flow problem is decoupled into multiple one-dimensional subproblems and assembled to form the solutions. A fully staggered grid and a conservational domain centred at the node of interest make the decoupling scheme first-order-accurate. The discretization of each one-dimensional subproblem is based on a 3-point interpolation function and a conservational domain centred at the node of interest. The proposed scheme gives a guaranteed first-order accuracy. It is shown that the traditional upwind (or exponentially weighted upstream) scheme is less than first-order-accurate. The pressure is decoupled from the velocity field using the pressure correction method of SIMPLE. Thomas algorithm (tri-diagonal solver) is used to solve the algebraic equations iteratively. The numerical advantage of the proposed scheme is tested for laminar fluid flows in a torus and in a square-driven cavity. The convergence rates are compared with the traditional schemes for the square-driven cavity problem. Good behaviour of the proposed scheme is ascertained. 相似文献
20.
Liu Ning 《Acta Mechanica Solida Sinica》1996,9(4):296-305
By taking the elastoplastic effect of structural material into account and based on 3-D elastoplastic stochastic finite element method, methods for sensitivity analysis with respect to both the distribution parameters of random variables and parameters in the limit state function are suggested. In the incremental iterative calculation, the sub-increment changingK, method and the corresponding formulas for accelerating convergence are used. The sensitivity of 3-D structural system reliability with respect to random variables is also studied. 相似文献