PZT陶瓷的断裂分析

与有限元法相比,无网格法由于只需节点不用单元而在压电分析中具有优越性。采用一个简单的包含有极化反转及电饱和影响的锆钛酸铅系压电陶瓷(PZT)的本构模型,以局部J积分作为断裂准则,应用再生核点法这一无网格数值法导出了作用电场与断裂载荷的关系曲线,该曲线的趋势与Park[1]的实验观察现象一致。计算程序采用面向对象方法实现。     

Boundary knot method for 2D and 3D Helmholtz and convection–diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non‐singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection–diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Mesh‐independent p‐orthotropic enrichment using the generalized finite element method

This paper is aimed at presenting a simple yet effective procedure to implement a mesh‐independent p‐orthotropic enrichment in the generalized finite element method. The procedure is based on the observation that shape functions used in the GFEM can be constructed from polynomials defined in any co‐ordinate system regardless of the underlying mesh or type of element used. Numerical examples where the solution possesses boundary or internal layers are solved on coarse tetrahedral meshes with isotropic and the proposed p‐orthotropic enrichment. Copyright © 2002 John Wiley & Sons, Ltd.     

针对无网格并行计算的基于模糊均值聚类的分区方法*

针对国际上普遍采用的基于回归几何二分的分区方法的缺陷,提出了基于模糊均值聚类的均匀模糊均值聚类分区算法。采用该方法对不同类型的无网格几何模型进行了分区,并根据分区信息对三维实体模型进行了并行计算。通过与基于回归几何二分法的比较,充分验证该算法的有效性和可行性。     

功能梯度材料的点插值无网格法

建立了一种新的求解功能梯度材料问题的点插值无网格法,这种无网格方法将径向基函数和多项式基函数耦合构造具有插值特性的近似函数,并将其应用于弹性力学问题Galerkin形式的无网格方法。在计算过程中,取高斯点的材料参数模拟功能梯度材料特性的变化,由于形函数及其导数的构造相对简单,并且满足Delta函数性质,所以该方法具有计算量小、精度高、可以像有限元法一样直接施加边界条件的优点。最后通过数值算例证明了该方法的有效性。     

基于无网格局部Petrov-Galekin法的板结构拓扑优化

为将无网格法的优势集成到结构拓扑优化中,基于无网格局部Petrov-Galerkin(Meshless Local Petrov-Galerkin,MLPG)法进行板结构的拓扑优化.基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP...     

用无网格方法求解声波散射问题

在均匀介质中,对软表面障碍、时间调和声波散射问题归结为Helmholtz方程的Dirichlet外问题.应用无网格方法求解Helmholtz方程的Dirichlet外问题,并给出了一个数值例子,与Nystrom方法进行了对比,表明该方法是较精确的.     

Dynamic flow‐based particle splitting in smoothed particle hydrodynamics

In this work, a dynamic procedure for local particle refinement to be used in smoothed particle hydrodynamics (SPH) is presented. The algorithm is able to consistently produce successive levels of particle splitting in accordance to a flow‐based criterion. It has been applied together with accurate and robust formulations for variable spatial resolution in the framework of a semi‐implicit, truly incompressible scheme for SPH. Different test cases have been considered to assess the capabilities and advantages of the proposed procedure, namely, the laminar flow around circular and square obstacles in a plane channel for various regimes. Such flow cases entail the simulation of attached and separated shear layers, recirculating flow, vortex shedding and surface discontinuities. The results obtained for two levels of particle splitting have demonstrated that significant improvements may be obtained with respect to uniform particle spacing solutions in a variety of situations, thus presenting an excellent trade‐off between accuracy and computational cost. Copyright © 2015 John Wiley & Sons, Ltd.     

空间碎片高速撞击的数值模拟方法评述

计算机数值模拟是实现空间碎片撞击效应地面模拟的重要手段之一。撞击速度增加,撞击的物理机制和效应将发生改变,计算机数值模拟方法也应随之丰富和全面。介绍了基于有网格和无网格方法的高速撞击数值模拟发展历程,并针对数值模拟中常用的有限元法和SPH法进行了分析比较,阐述了高速撞击计算机模拟中无网格法的计算优势,并提出量子力学在未来无网格法数值模拟中的可能应用。为空间碎片高速撞击更加真实可靠的数值模拟提供参考。     

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions.