Timoshenko梁弯曲分析的一种新方法

本文给出了Ｔｉｍｏｓｈｅｎｋｏ梁弯曲的混合状态方程及其解的一般表达式．算例表明：本文方法求解简单，明显优于以往的分析方法．     

弹性力学混合状态方程的弱形式及其边值问题

导出了弹性力学混合状态方程和边界条件弱形式的统一方程，此法使函数的选择无需事先完全满足边界条件，对于各种不同的边值问题可以用统一形式处理，这使得求解弹性力学问题的形式得以扩大和统一     

轴对称层合圆柱壳混合状态方程的弱形式及其边值问题

从Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理出发，在柱坐标系中，导出圆柱壳轴对称问题的弱形式混合状态方程和边界条件，联用状态空间法给出强厚度叠层柱壳的解析解，此法使得求解该类问题的形式得以扩大和统一。     

叠层连续柱壳热应力问题的弱形式研究

建立了弹性力学基本方程的弱形式,从而得到叠层连续柱壳混合状态方程的边界条件放在一起的算子方程,扩大了求解空间,给出叠层连续闭口柱壳在热荷载和机械荷载作用下的解析解。     

一种基于凸集-概率混合模型的结构可靠性分析法

本文建立一种凸集-概率混合模型下的结构可靠性分析方法。考虑椭球模型和区间模型两种不同类型的凸集模型，在标准空间内通过拉丁超立方抽样生成样本点，通过矩阵变换将其转换到凸集空间内，得到凸集变量的样本点；将凸集变量样本点代入极限状态方程，从而混合可靠性模型转变为纯概率可靠性模型；利用Laplace渐进积分法对每个极限状态方程进行失效概率求解，统计结果的最大值和最小值，得到失效概率的上、下界，研究了凸集变量的个数对结果的影响，通过失效概率的变异系数描述计算结果的稳定性；通过三个算例验证了计算结果的精度，并采用混合模型的蒙特卡洛法进行对比计算。研究表明：本文所提方法计算精度和效率均较高；凸集模型的类型会对结果产生较大影响；为使结果趋于稳定，椭球模型所需的凸集样本点个数多于区间模型；若凸集样本点数目相同，椭球模型的失效概率计算结果变异系数较小，稳定性高于区间模型。     

基于Kriging模型的结构可靠性分析

在结构极限状态方程(LSF)未知的情况下,通常采用响应面法(RSM)模拟结构的极限状态方程,逐步修正求解。由于响应面法对于极限状态方程的多项式假定,使其在计算精度上存在一定的缺陷。本文通过随机选取的部分结构响应,采用K rig ing模型模拟未知状态的结构响应,然后附以最优化的方法求解可靠性指标。该方法突破了极限状态方程的形式对于可靠性计算的制约,避免数学表达式的不同对于可靠性计算的影响。通过数值算例,可以看到本文的方法具有较高的精度和稳定性。     

一期水管冷却效应的数值模拟新方法

采用有限单元离散空间域，视冷却水管所在单元为子结构，其它单元为常规单元，然后，把混凝土结构瞬态温度场的有限元控制方程表示成状态方程，最后，利用精细积分法求解．结果表明，子结构、状态方程和精细积分技术的引用降低了对计算机贮存量的要求和提高了冷却水管附近温度梯度的精度，显示出极大的优越性．     

用状态方程直接积分法求解饱和土Biot固结方程

试采用状态方程直接积分法求解饱和土Biot固结问题,首次得到以位移未知量表示的状态方程、位移和孔隙流体压力的计算公式。算例结果表明,本方法的计算效率较高,同时精确可靠。     

A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua

通过把固支边上的边界位移函数作为状态变量引入状态方程,得到了含固支边矩形单层与叠层厚板的精确解. 在求解过程中,将非齐次状态方程的求解变为齐次状态方程的求解,省略了求解待定常数的中间过程,使求解过程变得简单. 所得到的解能够严格满足固支边界条件,在同一材料层内不需作分层处理,因而更加精确. 此外,对固支边的应力提出了新的计算方法,能够得到更精确的边界应力. 算例表明,本文解比现有精确解收敛快,与有限元解吻合的更好,尤其是在固支边处体现得更加明显.     

层状横观各向同性饱和土的非轴对称动力响应

通过方位角的Fourier变换，将圆柱坐标系下横观各向同性饱和土的Biot非轴对称波动方 程转化为一组一阶常微分方程组. 然后基于径向Hankel变换,建立问题的状态方程；求解状态方程后,得到传递矩阵. 进而利用传递矩阵，结合饱和层状地基的边界条件、排水条件及层间接触和连续条件,求解 了任意震源力作用下层状横观各向同性饱和地基频域动力响应问题. 时域解可通过频率的Fourier积分得到.     

Mindlin中厚板的辛求解方法

在Mindlin板混合能函数的基础上,通过引入混合变量及对混合能变分原理的修正,在全状态下建立了Mindlin板的Hamilton正则方程,进而采用直接法给出了两对边简支板的解析解,并通过具体例题说明了方法的有效性．     

弹性力学Hamilton方法广义解的适定性

首先引入了Hamilton体系中平面应力弹性力学问题正则方程的Galerkin变分方程,证明了Galerkin变分方程和目前文献中所用的Ritz变分方程的等价性,以及相应广义解的适定性,从而为目前的数值方法提供了理论基础。从证明过程中可以看到广义解实际上是Ritz变分泛函的一个鞍点。     

里卡提微分方程解的奇异性分析

本文处理有限长时间的里卡提微分方程。指出可以用区段混合能合并消元之法来得出它的解,在t_f处边界条件可以放在最后一步进行处理。这样就可以避免从奇点开始数值积分的困难。还可以据此分析t_f处的奇性。     

Convergence of Anisotropically Decaying Solutions of a Supercritical Semilinear Heat Equation

We consider the Cauchy problem for a semilinear heat equation with a supercritical power nonlinearity. It is known that the asymptotic behavior of solutions in time is determined by the decay rate of their initial values in space. In particular, if an initial value decays like a radial steady state, then the corresponding solution converges to that steady state. In this paper we consider solutions whose initial values decay in an anisotropic way. We show that each such solution converges to a steady state which is explicitly determined by an average formula. For a proof, we first consider the linearized equation around a singular steady state, and find a self-similar solution with a specific asymptotic behavior. Then we construct suitable comparison functions by using the self-similar solution, and apply our previous results on global stability and quasi-convergence of solutions.     

四边简支各向同性矩形厚板的插值矩阵法解

针对强厚度矩形板四边简支情况,论文根据状态变量法思想,基于三维弹性理论基本方程,以3个位移分量及3个应力分量按双三角级数展开,将三维弹性力学控制方程转化为常微分方程边值问题.尽管一些各向异性弹性矩形厚板早已由状态空间法获得分析解,可是各向同性厚板的分析解至今难以获得,因为状态空间解法中特征方程有重根问题而不易于收敛.论文提出采用插值矩阵法直接对常微分方程进行求解,获得各向同性矩形厚板在四边简支边界条件下三维理论的位移和应力解,并与有限元精细结果进行比较,证明了本文解的准确性.     

Hopf Bifurcation in a Diffusive Logistic Equation with Mixed Delayed and Instantaneous Density Dependence

A diffusive logistic equation with mixed delayed and instantaneous density dependence and Dirichlet boundary condition is considered. The stability of the unique positive steady state solution and the occurrence of Hopf bifurcation from this positive steady state solution are obtained by a detailed analysis of the characteristic equation. The direction of the Hopf bifurcation and the stability of the bifurcating periodic orbits are derived by the center manifold theory and normal form method. In particular, the global continuation of the Hopf bifurcation branches are investigated with a careful estimate of the bounds and periods of the periodic orbits, and the existence of multiple periodic orbits are shown.     

Diffraction of P-wave by crack in an elastic strip at asymmetric position

Scattering of P-wave by a Griffith Crack in a long elastic strip situated at an asymmetric position has been studied in this paper. Using Fourier transform, the mixed boundary value problem has been reduced to the solution of dual integral equations which finally has been reduced to the solution of a Fredholm integral equation of second kind. Solving this integral equation numerically, stress intensity factors have been calculated and illustrated graphically to show the effect of asymmetry of position of the crack.     

Flow and heat transfer due to impulsive motion of a cone in a viscous fluid

Numerical solution has been obtained for the development of the flow over a cone which is impulsively set into motion. Initially the flow is described by the solution of Rayleigh and then it tends to the ultimate steady state solution of Falkner-Skan equation. But due to the leading edge effect the semi-similar equation describing the transient flow changes its character after certain time and the solution depends also on the ultimate steady state solution of the Falkner-Skan equation. A second-order upwind difference scheme has been used for discretisation. The temperature distribution and heat transfer has also been obtained for constant wall temperature as well as for constant heat flux at the wall. With the increase ofm, Falkner-Skan parameter, the magnitude of skin friction and wall heat transfer increases. It has been found that form≥?0.275 flow separation does not occur.