Bifurcation method for solving multiple positive solutions to Henon equation

Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.     

Multiple internal resonances of rotating composite cylindrical shells under varying temperature fields

Applied Mathematics and Mechanics - Composite cylindrical shells, as key components, are widely employed in large rotating machines. However, due to the frequency bifurcations and dense frequency...     

拟弧长延拓法在静电激励MEMS吸合特性研究中的应用

在静电激励微机电系统MEMS(micro-electro-mechanical systems)吸合特性研究中,基于应变梯度理论的微梁结构的控制方程是非线性高阶微分方程,给方程的求解带来了困难.由于该问题的数学模型本质上是分叉问题,方程的解支上出现奇异点,而运用局部延拓法无法通过奇异点.因此,通过运用广义微分求积法将控制方程降阶离散,结合拟弧长延拓法使迭代顺利通过奇异点,求出了整个解曲线.结果表明,拟弧长延拓法能有效并准确地求解具有分叉现象的高阶微分方程问题,为精确预测静电激励MEMS的吸合电压提供有力帮助.     

单参数非线性问题中高阶奇异点的计算

本文考虑计算单参数非线性问题中高阶奇异点的数值方法，基于确定奇异点的一个普适的扩张系统，结合同伦参数的拟弧长延拓，给出了计算各类高阶奇异点的一个统一算法，数值例子表明了算法的有效性．     

集中载荷作用下弹性球壳大范围非线性问题

采用有限元法中的伪弧长法研究了集中载荷作用下弹性球壳轴对称大范围非线性问题，变形的范围从初始状态到壳体完全翻转．文中作了计算结果与实验结果的比较     

Numerical implementation of pseudo-arclength algorithm in nonlinear finite element analysis

A numerical procedure to calculate the pre-buckling and postbuckling response of general structures is presented. This procedure is based on the pseudo-arclength algorithm suggested by E. Riks et al., which has some numerical difficulties during implementation of large applied analysis programs. To overcome these difficulties, a scheme based on rank-1 modification of the matrix is proposed. Some example show this procedure behaves well in passing through the limit point and is rather efficient. recommended by Prof. Chen Yaosong and Prof. Wu Jike     

Solutions to general forward-backward doubly stochastic differential equations

A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a incthod of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.