微分求积方法对于桩基大变形分析的应用

本文基于大变形的理论,采用弧坐标首先建立了具有初始位移的桩基的非线性数学模型,一组强非线性的微分-积分方程,其中,地基的抗力采用了Winkeler模型;其次,引入变数变换将微分-积分方程转化为一组非线性微分方程,并用微分求积方法离散了方程组,得到一组离散化的非线性代数方程;最后用Newton-Raphson迭代方法对离散化方程进行了求解,得到了桩基变形前后的构形、弯矩和剪力.计算中选取了两种不同类型的初始位移,并考察了它们对桩基大变形力学行为的影响.     

多体系统动力学方程违约修正的数值计算方法

多体系统动力学方程为微分代数方程,一般将其转化成常微分方程组进行数值计算,在数值积分的过程中约束方程的违约会逐渐增大.本文对具有完整、定常约束的多体系统,在修改的带乘子Lagrange正则形式的方程的基础上,根据Baumgarte提出的违约修正的方法,给出了一种多体系统微分代数方程违约修正法和系统的动力学方程的矩阵表达式.通过对曲柄-滑块机构的数值仿真,计算结果表明本文给出的方法在计算精度和计算效率上好于Baumgarte提出的两种违约修正的方法.     

DIFFERENTIAL-ALGEBRAIC APPROACH TO COUPLED PROBLEMS OF DYNAMIC THERMOELASTICITY

An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.     

弱形式方程中分片函数奇异性的光滑化分析

研究弱形式方程中的分片光滑函数因求导数出现的奇异性问题，意在为得到离散格式时正确处理这一问题提供依据。在不改变拟合性质的情况下，将分片函数光滑化，则分步积分公式仍然有效。通过光滑后的函数讨论其积分的性质，总结出了几条计算规则。文中的典型例子说明这些计算规则是合理而有效的。     

非线性粘弹性拟静态问题与非线性弹性静力问题对应原理

本文应用多重单边拉氏变换导出了非线性粘弹性拟静态问题与非线性弹性静力问题的对应关系,从而把过去认为只有线性条件下存在的粘弹性——弹性对应原理拓展到了非线性范畴     

一种通过改进Canny算子提取光弹条纹骨架线的方法

光弹性法是确定应力集中系数的有效手段，在实际工程中应力参数都是通过分析光弹干涉条纹图获得的，由于光弹干涉条纹图的复杂性，且影响成像质量的因素较多，因此如何从光弹干涉条纹图中撇开其复杂性，较高精度的提取骨架线，是一项较困难的工作，本文提出一种由改进的Canny算子对条纹方位图进行直接运算提取光弹条纹骨架线的算法，实验表明此方法对光弹条纹图很有效。     

UPWIND LOCAL DIFFERENTIAL QUADRATURE METHOD FOR SOLVING COUPLED VISCOUS FLOW AND HEAT TRANSFER EQUATIONS

The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method.     

A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS

IntroductionExtensive research works have been published for solving nonlinear mathematicprogramming problems.Nonetheless,it is still difficult to find an effective and universalapproach for general programming problems with multiple design variables and …     

用同伦方法反演非饱和土中溶质迁移参数

非饱和土中溶质迁移参数反演问题可以归结为非线性算子方程的求解问题. 将同伦方法 引入该问题的求解，通过构造线性同伦将原问题转化为求解同伦函数最小值的无约束优化问 题. 同时在分析了同伦参数正则化效应的基础上，提出一种两段同伦参数修正方法. 即在求 解的初始阶段，根据拟Sigmoid函数调整同伦参数，以追踪同伦路径，保证计算稳定地进行； 在迭代的后期，采用与残差相关的同伦参数修正方法，以抵抗观测噪声对求解的影响. 数值 算例为求解带有平衡及非平衡吸附效应的一维非饱和土中溶质迁移模型参数反演问题，计算 结果表明了该方法的大范围收敛性及较强的抵抗观测噪声的能力.     

论可积微分约束引入的循环积分

 对循环坐标和多余坐标间存在一类线性可积微分约束的力学系统，导出了循环积分的一般表 达式. 采用实例分析了产生循环积分的原因，并解释了该循环积分的物理意义.