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     

求解Kuramoto-Sivashinsky方程的平移基无单元Galerkin方法

Kuramoto-Sivashinsky方程是一种可以描述复杂混沌现象的高阶非线性演化方程.方程中高阶导数项的存在,使得传统无单元Galerkin方法采用高次多项式基函数构造形函数时,形函数违背了一致性条件.因此,本文提出了一种采用平移多项式基函数的无单元Galerkin方法.与传统无单元Galerkin方法相比,该方法在方程离散时依然采用Galerkin进行离散,但形函数的构造采用了基于平移多项式基函数的移动最小二乘近似.通过对具有行波解和混沌现象的Kuramoto-Sivashinsky方程的数值模拟,验证了本文方法的有效性.     

无网格方法的研究进展与展望

目前正在发展的无网格方法采用基于点的近似,可以彻底或部分地消除网格,因此在处理不连续和大变形问题时可以完全抛开网格重构。无网格方法是目前科学和工程计算方法研究的热点,也是科学和工程计算发展的趋势。本文首先简单地阐述了无网格方法,然后详细叙述了目前提出的各种无网格方法的研究进展,最后对目前无网格方法存在的问题进行了探讨,提出了今后的研究方向。     

Carrier element-free coprecipitation (CEFC) method for the separation, preconcentration and speciation of chromium using an isatin derivative

A new, simple, rapid and sensitive separation, preconcentration and speciation procedure for chromium in environmental liquid and solid samples has been established. The present speciation procedure for Cr(III) and Cr(VI) is based on combination of carrier element-free coprecipitation (CEFC) and flame atomic absorption spectrometric (FAAS) determinations. In this method a newly synthesized organic coprecipitant, 5-chloro-3-[4-(trifluoromethoxy) phenylimino]indolin-2-one (CFMEPI), was used without adding any carrier element for coprecipitation of chromium(III). After reduction of chromium(VI) by concentrated H₂SO₄ and ethanol, the procedure was applied for the determination of total chromium. Chromium(VI) was calculated as the difference between the amount of total chromium and chromium(III). The optimum conditions for coprecipitation and speciation processes were investigated on several commonly tested experimental parameters, such as pH of the solution, amount of coprecipitant, sample volume, etc. No considerable interference was observed from the other investigated anions and cations, which may be found in natural water samples. The preconcentration factor was found to be 40. The detection limit for chromium(III) corresponding to three times the standard deviation of the blank (N = 10) was found 0.7 μg L⁻¹. The present procedure was successfully applied for speciation of chromium in several liquid and solid environmental samples. In order to support the accuracy of the method, the certified reference materials (CRM-TMDW-500 Drinking Water and CRM-SA-C Sandy Soil C) were analyzed, and standard APDC-MIBK liquid-liquid extraction method was performed. The results obtained were in good agreement with the certified values.     

A novel interpolating element-free Galerkin (IEFG) method for two-dimensional elastoplasticity

Using the interpolating moving least-squares (IMLS) method to obtain the shape function, we present a novel interpolating element-free Galerkin (IEFG) method to solve two-dimensional elastoplasticity problems. The shape function of the IMLS method satisfies the property of Kronecker δ function, then in the meshless methods based on the IMLS method, the essential boundary conditions can applied directly. Based on the Galerkin weak form, we obtain the formulae of the IEFG method for solving two-dimensional elastoplasticity problems. The IEFG method has some advantages, such as simpler formulae and directly applying the essential boundary conditions, over the conventional element-free Galerkin (EFG) method. The results of three numerical examples show that the computational precision of the IEFG method is higher than that of the EFG method.     

三维斜置半圆形表面裂纹扩展数值模拟

以裂纹前沿局部坐标中主法平面内的最大周向拉应力作为控制参数,对第一主应力拉应力裂纹扩展准则进行了补充和修正.修正后的拉应力裂纹扩展准则称为最大周向拉应力裂纹扩展准则.它不仅可以有效地确定裂纹扩展方位、扩展方向和扩展条件,而且可以有效地确定裂纹扩展步长.根据修正的裂纹扩展准则,给出了三维裂纹曲面的数学描述方式,可以有效地模拟扩展曲面的弯折和扭曲.     

无单元法在薄板稳定问题中的应用

用无单元法研究了薄板的弹性稳定问题，从滑动最小二乘法和变分原理出发导出了薄板的无单元法几何刚度矩阵，编制了相应的计算程序，并给出了算例，结果表明，方法合理可行，且精度高于有限元。     

几何非线性分析的高效高阶无网格法

准确高效地处理几何非线性对于材料破坏等大变形过程的数值分析至关重要。考虑到无网格法具有易于形成高阶近似函数等诸多优点,本文发展了几何非线性分析的高阶无网格法。采用上一载荷步收敛的构形作为计算的参考构形,位移本质边界条件由罚函数法施加。为提高计算效率,将针对线性问题发展的二阶一致三点积分格式QC3（Quadratically Consistent 3-point integration scheme）拓展到考虑构形变化的几何非线性分析,大幅度减少了所需的积分点数目。数值结果表明,本文发展的高阶无网格法能够准确有效地处理几何非线性问题,而且在计算效率、精度以及应力场光滑性等方面均表现出显著优势。     

基于正交基函数的薄板弯曲无单元法MLS导函数及其应用

针对采用正交基函数的无单元方法插值函数的导函数进行了详细推演，给出适用于薄板弯曲(C^1)问题的导函数递推计算公式，并首次将其应用于地基板的计算分析中。将计算结果与Rayleigh—Ritz法结果进行比较，两者较好的一致性表明了所得导函数及其递推公式的正确性，同时也说明了基于正交基函数的无单元方法应用于C^1问题的可行性和合理性。