弹性力学的插值型重构核粒子法

采用具有离散点插值特性的重构核粒子法形函数, 较精确地重构弹性体 变形的位移试函数, 再与弹性力学的最小势能原理相结合, 形成新的分析弹性力 学平面问题的插值型重构核粒子法. 由于插值型重构核粒子法形函数具有点插值特性和不低于核函数 的高阶光滑性, 因而既克服了多数无网格方法处理本质边界条件的困难, 也保证了较高的数值精度. 与早期的无网格方法相比, 本方法具有精度高、解题规模较小、可直接施加边界条件等优点. 通过对典型弹性力学问题数值模拟, 验证了所提方法的有效性和正确性.     

轴对称构件受力分析的插值粒子法

面对土木工程与机械工程中广泛存在的轴对称力学问题, 采用具有离散点插值特性的无网格方法形函数, 结合弹性力学空间轴对称问题的最小势能原理, 建立了轴对称构件力学分析的插值粒子法. 本文无网格法方法构造形函数不依赖网格, 也具有像有限元法一样可直接施加边界条件的优点. 本方法能直接获得全域连续应力场, 避免了有限元法应力后处理二次拟合带来的计算误差. 最后通过实例分析, 验证了所建立的无网格方法的有效性.     

弹性力学的重构核粒子边界无单元法

将重构核粒子法(RKPM)和边界积分方程方法结合，提出了一种新的边界积分方程无网格方法——重构核粒子边界无单元法(RKP-BEFM).对弹性力学问题，推导了其重构核粒子边界无单元法的公式，研究其数值积分方案，建立了重构核粒子边界无单元法离散化边界积分方程，并推导了重构核粒子边界无单元法的内点位移和应力积分公式.重构核粒子法形成的形函数具有重构核函数的光滑性，且能再现多项式在插值点的精确值，所以本方法具有更高的精度.最后给出了数值算例，验证了本方法的有效性和正确性. 关键词： 重构核粒子法 弹性力学 边界无单元法     

弹性力学的复变量重构核粒子法

在重构核粒子法的基础上,提出了复变量重构核粒子法.复变量重构核粒子法的优点是采用一维基函数建立二维问题的修正函数.然后,将复变量重构核粒子法应用于弹性力学,提出了弹性力学的复变量重构核粒子法,并推导了相关公式.与传统的重构核粒子法相比,复变量重构核粒子法具有计算量小、效率高的优点.最后给出了数值算例证明了该方法的有效性. 关键词： 重构核粒子法 复变量重构核粒子法 弹性力学 无网格方法     

The complex variable reproducing kernel particle method for elasto-plasticity problems

On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM) is discussed in this paper.The advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is formed.Then the CVRKPM is applied to solve two-dimensional elasto-plasticity problems.The Galerkin weak form is employed to obtain the discretized system equation,the penal...     

Improved reproducing kernel particle method for piezoelectric materials

In this paper, the normal derivative of the radial basis function(RBF) is introduced into the reproducing kernel particle method(RKPM), and the improved reproducing kernel particle method(IRKPM) is proposed. The method can decrease the errors on the boundary and improve the accuracy and stability of the algorithm. The proposed method is applied to the numerical simulation of piezoelectric materials and the corresponding governing equations are derived. The numerical results show that the IRKPM is more stable and accurate than the RKPM.     

Analysis of variable coefficient advection-diffusion problems via complex variable reproducing kernel particle method

The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method （RKPM） and the element- free Galerkin （EFG） method.     

瞬态热传导问题的复变量重构核粒子法

在重构核粒子法的基础上,引入复变量,讨论了复变量重构核粒子法.复变量重构核粒子法的优点是在构造形函数时采用一维基函数建立二维问题的修正函数.然后,将复变量重构核粒子法应用于瞬态热传导问题的求解,结合瞬态热传导问题的Galerkin积分弱形式,采用罚函数法引入本质边界条件,建立了瞬态热传导问题的复变量重构核粒子法,推导了相应的计算公式.与传统的重构核粒子法相比,复变量重构核粒子法具有计算量小、精度高的优点.最后通过数值算例证明了该方法的有效性. 关键词： 重构核粒子法 复变量重构核粒子法 修正函数 瞬态热传导问题     

重构核粒子法对光滑粒子法的改进效果

光滑粒子法通过核函数进行近似估计,在计算域边界附近,核估计的精度明显下降.重构核粒子法通过校正函数对核函数进行重新构造,提高核估计方法在边界点和内点上对函数的估计精度以及计算的稳定性.研究发现,虽然校正函数的构造立足于对函数的精确估计,但这个优势同样能在对导数的估计中继续保持.通过理论研究及数学、物理模型的模拟,展示重构核粒子法的改进效果,揭示其能够提高精度的原因.     

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

On the basis of the reproducing kernel particle method (RKPM), a new meshless method, which is called the complex variable reproducing kernel particle method (CVRKPM), for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.     

An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems

In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. And the number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has a higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.     

Analysis of the equal width wave equation with the mesh-free reproducing kernel particle Ritz method

In this paper,we analyse the equal width(EW) wave equation by using the mesh-free reproducing kernel particle Ritz(kp-Ritz) method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.     

SPH核函数光滑长度最优选取和自适应准则研究

基于小波分析理论和RKPM再生核函数研究无网格方法SPH中多尺度诊断工具,多尺度再生核函数使得数值计算在不同尺度上的响应分离,并通过动态伸缩窗函数给出计算域不同位置的时频特性,实现在无网格体系下构造网格计算方法的“自适应网格”,从而达到对不同流场位置多分辨率分析的目的.利用多尺度诊断工具中的小波分解算法给出SPH核函数在频域内能量残差估计,发展一种核函数光滑长度最优选取准则.最后,基于可压缩流场激波稀疏波共存的现象,针对传统的光滑长度自适应的缺陷,构造一种避免数值计算“拖尾”现象的自适应准则.     

The choosing of reproducing kernel particle shape function with mathematic proof

Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle (RKP) method is based on the Garlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.     

An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems

In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.     

On reproducing kernels and quantization of states

Quantization of a mechanical system with the phase space a Kähler manifold is studied. It is shown that the calculation of the Feynman path integral for such a system is equivalent to finding the reproducing kernel function. The proposed approach is applied to a scalar massive conformal particle interacting with an external field which is described by deformation of a Hermitian line bundle structure.     

改进的物理粘性SPH方法及其在溃坝问题中的应用

在低雷诺数物理粘性SPH方法基础上引入再生核粒子法进行密度重构,既避免了用人工粘性所导致的数值耗散问题,又提高了低雷诺数物理粘性SPH方法的数值稳定性;以溃坝问题为例,对比分析低雷诺数物理粘性SPH方法和本文方法的仿真结果表明,本文方法可有效消除数值不稳定,压强和速度分布更加光滑,粒子秩序更好,可应用于雷诺数较高或粘性不可忽略的流动问题.     

Homotopy deform method for reproducing kernel space for nonlinear boundary value problems

In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.     

Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

In this paper, the complex variable reproducing kernel particle (CVRKP) method and the finite element (FE) method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.     

Radiative decays of heavy mesons with heavy quark symmetry

The radiative decays of heavy mesons are considered in heavy quark symmetry formalism. Introducing the interpolating fields for the heavy mesons we obtain the transition matrix element and the corresponding decay widths in the heavy quark symmetry limits. The Isgur-Wise function present in the expression is determined by ISGW quark model. The results obtained agree reasonably well with other estimations.