曲柄滑块机构综合的三周期牛顿混沌法研究

为了提高牛顿混沌迭代Julia点的求解效率,构造了基于三周期混沌求解Julia点的逆像迭代方法,提出了一种新的牛顿混沌迭代法,该方法可以求出解非线性方程组全部解.对平面曲柄-滑块机构综合进行了研究,计算实例表明该方法的正确性与有效性.     

平面上不可压缩的Navier-Stokes方程五模截断方程组的标准型

把广义的类Lorenz系统推广到五维,给出了平面上不可压缩的Navier-Stokes方程五模截断方程组广义的类Lorenz系统的标准型;讨论了截断方程组标准型的形式统一性。     

Constitutive equations and finite element implementation of strain localization in sand deformation

A recently proposed model coupling with the solid-fluid of the saturated sand was utilized to study the deformation band. Based on the critical state plasticity model by Borja and Andrade, the hydraulic conductivity tensor was naturally treated as a function of the spatial discretization matrix about the displacement and the stress field, allowing a more realistic representation of the physical phenomenon. The fully Lagrangian form of the Darcy law was resolved by Piola algorithm, and then the flow law was gained, leading to the implementation of a modified model of the saturated sand. Then the criterion for the onset of localization was derived and utilized to detect instability. The constitutive model was implemented in a finite element program coded by FORTRAN, which was used to predict the formation and development of shear bands in plane strain compression of saturated sand. At last, the formation mechanism of the shear band was discussed. It is shown that the model works well, and the simulation sample bifurcates at 1.18% axial strain, which is in a good qualitative agreement with the experiment. The pore pressure greatly affects the onset and development of the deformation band, and it obviously increases around the localization-prone regions with the direction toward the outer side of the normal of the shear band, while the pore stress flows nearly horizontally and is distributed equally far away the shear band region. Foundation item: Project(2006G007-C) supported by the Foundation of the Science and Technology Section of Ministry of Railway of China; Project(77206) supported by the Excellent PhD Thesis Innovation Foundation of Central South University, China     

带阻尼项的二阶强迫非线性微分方程的区间振动准则

利用Riccati技巧和变分原理,对带阻尼项的二阶强迫非线性微分方程建立了新的区间振动准则,推广和改进了已有的一些结果．     

一类分数阶微分方程组的L^p稳定性

讨论了一类分数阶微分方程组的L^p稳定性,给出了分数阶微分方程组在有限时间情况下L^p稳定的充分条件,其主要是利用了一类特殊卷积的性质．     

吸收介质表面Brewster定律的数值解

讨论了吸收介质表面的Fresnel公式,对介质表面的Brewster定律进行了数值求解。总结了吸收介质表面发生Brewster反射时的规律,得到了三维数值解曲面图,使复杂的问题简单化、直观化。     

带跳随机延迟微分方程半隐式Milstein数值方法的均方稳定性

研究带跳随机延迟微分方程半隐式Milstein数值方法的均方稳定性.将半隐式Milstein数值方法应用到补偿泊松过程及维纳过程驱动下的非线性随机延迟微分方程上进行讨论,给出了半隐式Milstein方法MS-稳定的条件.     

利用Liapanov直接方法判定差分方程稳定性

研究差分方程稳定性的强有力的方法是Liapanov直接方法,这一方法的核心思想是针对所研究的方程,构造出其相应的Liapanov函数,利用它来判定方程的稳定性．     

修正Helmholtz方程的小波配点区域分解法

将小波配点法和区域分解结合用于求解修正Helmholtz方程。该方法克服了在求解大规模问题时用一般的全域小波配点法所带来的配置矩阵为非对称满阵,且高度病态的问题。给出小波配点求解修正Helmholtz方程解的存在唯一性。通过数值结果表明该算法在降低了系数矩阵条件数的同时,也能够降低误差,并达到满意的收敛效果。     

半离散Newton分裂方法的Kantorovich型定理

本文在Kantorovich型定理的条件下,给出了一种半离散Newton型分裂方法的存在性收敛性定理.