Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains

In present work, a kind of spectral meshless radial point interpolation (SMRPI) technique is applied to the time fractional nonlinear Schrödinger equation in regular and irregular domains. The applied approach is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. It is proved the scheme is unconditionally stable with respect to the time variable in and also convergent by the order of convergence , . In the current work, the thin plate spline are used as the basis functions and to eliminate the nonlinearity, a simple predictor‐corrector (P‐C) scheme is performed. It is shown that the SMRPI solution, as a complex function, is suitable one for the time fractional nonlinear Schrödinger equation. The results of numerical experiments are compared to analytical solutions to confirm the reliable treatment of these stable solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1043–1069, 2017     

船舶结构优化设计方法的研究进展

船舶结构设计，具有较强的综合性、经验性和创造性。运用经典优化方法加以处理，虽然也取得了一定成果，但要建立真正有效的船舶结构优化设计方法，必须与实际工程特点、现代数学理论以及最新计算机技术有机结合。目前，研究工作已取得了初步进展。本文综述了有关研究情况。     

正交复合材料面层夹层板非线性理论及应用

针对复合材料面层夹层板的构造和变形特点，考虑横向剪应力在面层和芯层粘结处的连续条件，应用Ｈａｍｉｌｔｏｎ原理建立了基于五个未知函数的正交铺设复合材料面层夹层板的非线性精化理论。对静力学问题，控制方程化简为由四个基本未知函数表述。文中还分析了简支正交铺设复合材料面层夹层板的非线性弯曲，给出了载荷—挠度特征关系和板中应力的分布状况。数值计算表明，夹层板面层和芯层粘结处的层间剪应力在工程设计中是十分重要的。     

弹性力学混合状态方程的小波解法

应用小波理论求解弹性力学混合状态方程，讨论了解的收敛性。从文中的数值算例不难看出，该方法不失为混合状态方程一种新的求解途径。     

概说并行计算结构力学

基于向量机（ｖｅｃｔｏｒｃｏｍｐｕｔｅｒｓ）和并行机（ｐａｒａｌｌｅｌｃｏｍｐｕｔｅｒｓ）两大类并行计算机，对线性静力和动力问题，非线性静力和动力问题，本文概说了相应于这两大类并行机一般的求解方法。     

爆轰波拐角传播三维数值模拟

为了研究爆轰波在拐角中的传播特性以及拐角爆轰低压流场现象,用LSDYNA 3D程序对三种常见的拐角装药的爆轰波传播特性进行了数值模拟,清晰显示了爆轰波因拐角处爆轰波传播面积的变化而产生的衰减 增长过程,讨论了侧向三通中爆速的变化情况,并得到了拐角处低压爆轰区的尺寸。     

欧拉流体力学数值方法中的界面计算

本文所提算法适用于二维和三维多介质流体力学两步欧拉数值方法中输运计算的混合网格(包括自由面网格)界面处理。在一个混合网格中，界面被近似地看作直线(二维)或平面(三维)。整个方法分为三步：(1)第一步，用混合网格周围的八个网格的介质面积份额(二维)或二十六个网格的介质体积份额(三维)确定界面的法线方向；第二步，用混合网格的本身的介质面积份额(二维)或体积份额(三维)确定界面的方程(位置)；第三步，用此直线方程求出通过网格边界的流以及下一时刻网格的面积份额(二维)或体积份额(三维)。最后给出了用此方法所做的一些数值计算及与SLIC算法的比较。     

An empirical model for tractive performance of rubber-tracks in agricultural soils

Mathematical models capable of describing the interaction between traction devices and soils have been effective in predicting the performance of off-road vehicles. Such a model capable of predicting the performance of bias-ply tires in agricultural soils was first developed by Brixius [Brixius WW. Traction prediction equations for bias-ply tires. ASAE Paper No. 871622. St. Joseph, MI: ASAE; 1987]. When the soil and vehicle parameters are known, this model uses an iterative procedure to predict the tractive performance of a vehicle including pull, tractive efficiency, and motion resistance. Al-Hamad et al. [Al-Hamad SA, Grisso RD, Zoz FM, Von Bargen K. Tractor performance spreadsheet for radial tires. Comput Electron Agr 1994:10(1):45–62] modified the Brixius equations to predict the performance of radial tires. Zoz and Grisso [Zoz, FM, Grisso RD. Traction and tractor performance. ASAE Distinguished Lecture Series #27. St. Joseph, MI: ASAE; 2003] have demonstrated that the use of spreadsheet templates is more efficient than the original iterative procedure used to predict the performance of 2WD and 4WD/MFWD tractors. As tractors equipped with rubber-tracks are becoming popular, it is important that we have the capability to predict the performance for off-road vehicles equipped with rubber-tracks during agricultural operations. This paper discusses the development of an empirical model to accomplish this goal and its validity by comparing the predicted results with published experimental results.     

双材料界面应力分析的局部杂交法

本文用云纹干涉法测取双材料高梁受集中载荷时沿ｘ，ｙ轴的位移场ｕ，ｖ．以其作为界面局部微区的边界条件，用有限元计算此微区内界面上的应力分量．与光弹性及全梁有限元法比较，发现局部杂交法的精度最高．     

On the general expression of Fredholm Integral Equations Method in elasticity

In this paper, the concept of covering domain is introduced to develop a general expression for the Fredholm Integral Equations Method, by which elasticity problems of arbitrarily shaped bodies loaded by external forces can be solved. Some special expressions are given for a body with non-zero remote stresses, or subjected to some concentrated forces on its boundary. The relationship between the loading forces and solutions are also discussed. Some analytical solutions can be obtained for simple cases. When numerical computations are needed for the solution, the method proves to have high precision and fast convergency.