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.     

Spline-based meshfree method with extended basis

In this work, an extension has been performed on the analysis basis of spline-based meshfree method (SBMFM) to stabilize its solution. The potential weakness of the SBMFM is its numerical instability from using regular grid background mesh. That is, if an extremely small trimmed element is produced by the trimming curves that represent boundaries of the analysis domain, it can induce an excessively large condition number in global system matrix. To resolve the instability problem, the extension technique of the weighted extended B-spline (WEB-spline) is implemented in the SBMFM. The basis functions with very small trimmed supports are extrapolated by neighboring basis functions with some special scheme so that those basis functions can be condensed in the solution process. In order to impose essential boundary conditions in the SBMFM with extended basis, Nitsche's method is implemented. Using numerical examples, the presented SBMFM with extended basis is shown to be valid and effective. Moreover, the condition number of the system is well-managed guaranteeing the stability of the numerical analysis.     

基于配点型无网格法的金属挤压过程数值模拟

阐述了配点型无网格法的基本原理,及其用于求解偏微分方程的步骤和方法,对Al在挤压成形过程中的塑性变形情况进行了三维无网格法模拟。该方法避免了有限元法因网格畸变需要重新划分网格的问题,同时解决了伽辽金型无网格法计算效率低的问题。计算实例表明,配点型无网格法可以利用初始节点完成全部计算,得到与有限元法相吻合的结果,是模拟金属塑性变形过程的一种有效的新方法。     

Application of Particle Methods to Static Fracture of Reinforced Concrete Structures

Particle methods for modeling reinforced concrete are described. The reinforcements are modeled by finite elements and are coupled to the particle method by Lagrange multipliers. The method is applicable to nonlinear problems, problems with moderate to severe cracking and deformable interfaces. Applications to the static response of reinforced concrete structures where the concrete is discretized with particles and the reinforcement with elements are described. The method is also tested for several static problems where no relative displacements between the concrete and the reinforcement are allowed.     

A meshfree Hermite‐type radial point interpolation method for Kirchhoff plate problems

A meshfree computational method is proposed in this paper to solve Kirchhoff plate problems of various geometries. The deflection of the thin plate is approximated by using a Hermite‐type radial basis function approximation technique. The standard Galerkin method is adopted to discretize the governing partial differential equations which were derived from using the Kirchhoff's plate theory. The degrees of freedom for the slopes are included in the approximation to make the proposed method effective in enforcing essential boundary conditions. Numerical examples with different geometric shapes and various boundary conditions are given to verify the efficiency, accuracy, and robustness of the method. Copyright © 2005 John Wiley & Sons, Ltd.     

A smoothed particle hydrodynamics and coarse‐grained molecular dynamics hybrid technique for modelling elastic particles and breakable capsules under various flow conditions

In this work, a hybrid numerical approach, which combines elements of SPH and coarse‐grained molecular dynamics, is used to investigate the effect of various flow conditions to deformable and breakable shell‐structures such as capsules, vesicles or biological cells. Copyright © 2014 John Wiley & Sons, Ltd.     

金属体积成形过程的自适应无网格方法

采用动态显式自适应无网格RKPM方法的计算格式，在有效误差估计模型的基础上进行节点加密，采用区域分解思想确定新的计算模型中节点的影响域半径，对金属体积成形过程进行了全过程的计算机模拟。Taylor Bar冲击的自适应无网格计算结果与实验结果吻合良好，有效地验证了该方法的正确性和可行性。挤压算例的计算结果也表明该算法能提高计算精度和改善板内应变能误差。     

MESHFREE METHOD BASED ON POINT COLLOCATION FOR METAL FORMING SIMULATION

A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.     

A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems

In part I of this paper, we have established the G space theory and fundamentals for W² formulation. Part II focuses on the applications of the G space theory to formulate W² models for solid mechanics problems. We first define a bilinear form, prove some of the important properties, and prove that the W² formulation will be spatially stable, and convergent to exact solutions. We then present examples of some of the possible W² models including the SFEM, NS‐FEM, ES‐FEM, NS‐PIM, ES‐PIM, and CS‐PIM. We show the major properties of these models: (1) they are variationally consistent in a conventional sense, if the solution is sought in a proper H space (compatible cases); (2) They pass the standard patch test when the solution is sought in a proper G space with discontinuous functions (incompatible cases); (3) the stiffness of the discretized model is reduced compared with the finite element method (FEM) model and possibly to the exact model, allowing us to obtain upper bound solutions with respect to both the FEM and the exact solutions and (4) the W² models are less sensitive to the quality of the mesh, and triangular meshes can be used without any accuracy problems. These properties and theories have been confirmed numerically via examples solved using a number of W² models including compatible and incompatible cases. We shall see that the G space theory and the W² forms can formulate a variety of stable and convergent numerical methods with the FEM as one special case. Copyright © 2009 John Wiley & Sons, Ltd.     

随机动力学中FPK方程的径向基点插配点方法求解

应用径向基点插配点方法对随机动力学中的FPK方程进行了求解.所求未知函数的空间插值采用径向基点插近似,而时间导数离散采用差分格式,建立具有带宽特性的代数方程,采用逐次超松弛迭代法（SOR）有效地求解所得到的代数方程.针对线性振子和杜芬振子问题的FPK方程进行了具体的数值求解,计算结果表明了方法的有效性,尤其是散点模型的计算结果表明该方法具有比其它有网格数值方法对非规则离散模型适应性更强的优点.