点式压电智能结构的模型修正与振动主动控制

提出了在点式压电智能结构中应用摄动有限元方法对结构的有限元模型进行修正 ,从而达到提高建模精度 ,改善实际结构振动主动控制效果的目的。通过对一悬臂梁在模型修正前后进行振动主动控制的不同的控制效果验证了该方法的有效性     

Reliable solutions to the problem of periodic oscillations of an elastoplastic beam

We consider time-periodic oscillations of a beam with a spatially inhomogeneous Prandtl–Ishlinskii constitutive law describing the elastoplastic hysteresis. The data (mass density, Prandtl–Ishlinskii distribution, external load) are assumed to be uncertain. It is shown that a unique solution exists and is stable with respect to the data variation. Considering the total dissipated energy as a measure for the accumulated material fatigue, we identify and estimate from above the ‘worst scenario’ case, where the dissipation over one period is maximal within an admissible set of data obtained from inaccurate measurements.     

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.The project supported by the National Outstanding Youth Science Foundation of China (10425208), the National Natural Science Foundation of China and Institute of Engineering Physics of China (10376002) The English text was polished by Keren Wang.     

Large thermal deflections of Timoshenko beams under transversely non-uniform temperature rise

Geometrically non-linear deformation of axially extensional Timoshenko beams subjected mechanical as well thermal loadings were characterized by a system of 7 coupled and highly non-linear ordinary differential equations, which results in a complicated two-point boundary-value problem. By using shooting method this kind of problem can be numerically solved efficiently. Based on the above-mentioned mathematical formulation and numerical procedure, analysis of large thermal deflections for Timoshenko beams, subjected transversely non-uniform temperature rise and with immovably pinned–pinned as well as fixed–fixed ends, is presented. Characteristic curves showing the relationships between the beam deformation and temperature rise are illustrated. Especially, the effects of shear deformation on the bending and buckling response are quantitatively investigated. The numerical results show, as we know, that shear deformation effects become significant with the decrease of the slenderness and with the increase of the shear flexibility.     

含水砂层对堆积体稳定性的影响研究

受复杂地质环境的影响,我国西南岷江上游沿岸普遍发育一种前缘多分布有一层或多层具一定厚度含水砂层的特殊堆积体。大量工程实践表明,工程开挖的扰动可导致砂层出现明显侧向变形,进而导致整个堆积体的失稳破坏。本文采用数值计算的方法,结合某典型堆积体对开挖条件下砂层影响其整体稳定性的作用机理进行了较为深入的分析和探讨。     

软土地区人工冻土无侧限瞬时抗压强度的试验研究

冻结法施工在上海隧道建设中(如隧道旁通道、地下泵房等的设计与施工)得到广泛应用,也曾引发过严重的地质灾害(如上海地铁4号线外滩段的地质灾害)。因此安全、经济、合理地将冻结法用于上海软土地区隧道建设中已经成为上海工程建设中的一个重要的研究课题。本文以上海复兴东路越江隧道旁通道冻结法施工中遇到的第⑥层粉质粘土及第⑦层粉细砂为研究对象,针对设计冻结壁重要强度参数无侧限瞬时抗压强度,进行了室内试验研究,揭示了两种土的冻结强度随温度的变化关系,同时研究了粉细砂的冻结强度随含水率的变化规律。     

复变量移动最小二乘法及其应用

提出了复变量移动最小二乘法，并详细讨论了基于正交基函数的复变量移动最小二乘 法. 然后，将复变量移动最小二乘法和弹性力学的边界无单元法结合，提出了弹性力学的复 变量边界无单元法，推导了相应的公式，并给出了数值算例. 基于正交基函数的复变量移动 最小二乘法的优点是不形成病态方程组、精度高，所形成的无网格方法计算量小. 复变量边 界无单元法是边界积分方程的无网格方法的直接列式法，容易引入边界条件，且具有更高的 精度.     

一种梁柱非线性分析新方法

提出了一种等截面梁柱非线性分析的新方法，即采用按幂函数的变截面法模拟梁柱截面刚度，建立了梁柱非线性分析的简化数学计算模型，并研究了梁柱从弹性到塑性状态时梁柱截面刚度的变化规律，通过与Chen法的比较证明了截面刚度按幂函数模拟的变截面法的正确性。在此基础上进一步应用变截面法讨论了单边塑性情况下偏心受压梁柱随偏心轴力P值的变化规律。此方法为进一步研究非线性梁柱结构提供了一种新的思路。     

PARTITION OF UNITY FINITE ELEMENT METHOD FOR SHORT WAVE PROPAGATION IN SOLIDS

IntroductionIt is known that standard finite element procedure is unable to simulate the wavepropagation with high oscillations or gradients in space in the media with reasonableefficiency and accuracy due to the nature of polynomial interpolation approxi…     

A nonlinear oscillatory system subjected to driving forces of elliptic type

The aim of this paper is to show how Jacobi elliptic functions in combination with the averaging and the harmonic balance methods can be applied to obtain the approximate solution of two coupled, ordinary differential equations having a spring with cubic nonlinearity and subjected to driving forces of elliptic type. By an appropriate choice of the system parameter values, it is possible to show that our derived solution represents the exact steady-state solution of the undamped Duffing equation with driving force of elliptic type. At the end of this work, we also demonstrate the validity of our derived solution by comparing the amplitude–time response curves with those of the numerical integration solutions.