固体力学边界元分析程序包BESMAP——基本结构功能

要使边界元法象有限元法那样得到广泛应用，必须开发与有限元法相媲美的大型边界元法程序包。国外虽出现少数几个边界元法程序包，但由于结构、功能等方面的原因，还不能成为边界元法广泛应用的工具。针对这种情况，本文借鉴现有的先进的有限元法程序包，研制了大型固体力学边界元法程序包ＢＥＳＭＡＰ，ＢＥＳＭＡＰ在总体设计、计算能力、使用方便和功能齐全等方面作了研究和改进。     

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.     

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.     

空位结构缺陷对C纳米管弹性性质的影响

用分子动力学方法对不同空位缺陷的扶手椅型与锯齿型单壁C纳米管杨氏弹性模量进行了计算和分析. 结果表明：扶手椅型（5, 5）, （10,10）和锯齿型（9, 0）, （18, 0） 纳米管在无缺陷时其杨氏模量分别为948,901和804,860 GPa. 随管径的增大,扶手椅型和锯齿型单壁C纳米管弹性模量分别减小和增大,表现出完全不同的变化规律. 随着C纳米管中单点空位缺陷的均匀增加,杨氏模量下降,当缺陷比率增加到一定程度时,杨氏模量下降骤然趋缓,形成一下降平台;双空位缺陷对C纳米管杨氏模量的影响与其分布方向有关;随单点空位缺陷间原子数的增加,在轴向上,杨氏模量下降到某一值小幅波动,而在周向上杨氏模量先下降,然后上升到某一稳定值. 随两单点空位缺陷的空间距离进一步增大,杨氏模量又呈微降趋势. 通过分子间σ键与π键特征及缺陷间近程电子云耦合作用规律与空位缺陷内部5-1DB缺陷的形成特点等理论对上述规律进行了分析. 关键词： 空位缺陷 C纳米管 分子动力学 杨氏模量     

Topology optimization using the improved element-free Galerkin method for elasticity

The improved element-free Galerkin(IEFG) method of elasticity is used to solve the topology optimization problems.In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin(EFG) method. The central processing unit(CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown.     

Solving unsteady Schr?dinger equation using the improved element-free Galerkin method

By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrödinger equation. In the IEFG method, the two-dimensional (2D) trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square (MLS) approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.     

加权残数法通用程序包MWRAP的开发技术与1程应用

要想使加权残数法广泛应用于工程实际问题,需要解决两方面的问题,一是精度问题,二是必须研制和开发通用软件。本文阐述了加权残数法通用程序包MWRAP的结构设计和功能设置及其前后处理技术,详细阐述了其前后处理程序的程序设计流程;在该软件中计算模块,所用的计算方法为加权残数和有限元耦合法,为此推导了加权残数和有限元耦合法的公式,从计算结果来看该方法具有较高的精度,可以满足工程需要。最后,运用MWRAP计算了钢管混凝土柱肩梁结构的位移和应力,与实验结果相比吻合较好,说明了MWRAP具有较高的精度,加上其完善的前后处理功能,可以应用于工程实际问题。     

准连续体方法研究进展

准连续体方法是一种将连续介质方法和原子模拟相耦合的多尺度模拟方法。该方法巧妙地将分子静力学与有限元法相结合,在变形梯度较小的规则区域采用代表性原子作为计算点,以此为节点形成有限元网格,其周围其他原子的位置通过插值得到。代表性原子的引入,使系统原子势能的计算大大简化。自适应手段的应用,保证了材料缺陷核心附近原子尺度的细节描述。与其他纳米力学计算方法相比,准连续体方法具有计算精度高,计算规模大等优点。本文主要介绍了准连续体方法的基本原理及发展状况,归纳并总结了这一些优点及今后的发展方向。     

Ca3Al2Ge3O12:Cr3+的光谱性质及晶场参数计算

为了解Cr3+离子在钙铝锗酸盐Ca₃Al₂Ge₃O₁₂:石榴石中的光谱性质, 合成了Ca₃Al₂Ge₃O₁₂:Cr³⁺多晶材料；测量了其X射线衍射图, 漫反射光谱, 激发、发射光谱等；分析了Cr3+离子在钙铝锗酸盐中的发光特性；计算了其晶场强度(Dq/B), Stokes位移(ΔEs)及黄昆-里斯因子(S)等. 在450 nm激发下, Ca₃Al₂Ge₃O₁₂:Cr³⁺室温发射光谱主要由三个宽带及附加其上的弱R线构成, 分别对应于Cr3+离子的4T1、 4T2、2T2到 4A2 能级跃迁. 低温时R线变得强而锐. 通过计算, Dq/B=2.43, ΔEs=1884 cm-1, S=5.21. 表明在Ca₃Al₂Ge₃O₁₂中Cr³⁺离子处于较弱的晶场强度, 电子-声子耦合较强, 为发展可调谐激光材料提供重要线索.     

接枝羧基对单壁碳纳米管弹性性质的影响

采用分子动力学方法对端口接枝不同数量羧基的扶手椅型和锯齿型单壁碳纳米管弹性模量进行了模拟研究. 结果表明, 扶手椅型(5, 5)、(10, 10)管和锯齿型(9, 0)、(18, 0)管在未接枝状态下杨氏模量分别为948、901GPa和804、860 GPa. 在接枝2-8个羧基情况下, 扶手椅型单壁碳纳米管拉伸杨氏模量基本不随接枝数量的增加而发生变化, 而锯齿型单壁碳纳米管则不同, 接枝状态下的弹性模量比未接枝状态小很多, 但随接枝数量的增加又呈略增趋势. 分别从接枝后碳纳米管变形电子密度等值线结构变化、键长变化和系统势能变化规律等方面, 对单壁碳纳米管弹性模量的接枝效应进行了分析.