Stability of Thin-Walled Open Beams Under Nonconservative Loads

ABSTRACT

A finite element formulation for free-vibration analysis of straight prismatic beams of general thin-walled open cross-section, under conservative and nonconservative loads, is presented. The formulation is used to calculate the flutter load for a number of beam problems and is verified by comparison with pre-existing numerical solutions.     

Spatial Stability of Layered Anisotropic Cylindrical Shells Under Compressive Loads

International Applied Mechanics - An approach to solving spatial problems of the stress–strain state and stability of layered anisotropic cylindrical shells is developed. The anisotropy is...     

Stability of an Elastic Layer Stack Between Two Half-Spaces Under Compressive Loads

A stability problem is solved for a multicomponent medium consisting of a layer stack and two structurally homogeneous half-spaces. The analysis is made within the framework of the piecewise-homogeneous model and the three-dimensional linearized theory of stability for small subcritical strains. The properties of isolated elements of the medium are determined within the framework of the orthotropic linearly elastic model. Specific numerical results are obtained for the case of plane strain     

用广义阶梯函数简化计算简支圆板在复杂荷载作用下的极限荷载

本文将广义阶梯函数应用于薄板的塑性极限分析问题，用以简化计算简支圆板在复杂荷载作用下的极限荷载。文中针对简支圆板在任意局部均布荷载和线性分布荷载共同作用下的塑性极限分析问题，并考虑荷载的五种不同的分布形式，给出相应的极限荷载的计算公式。     

弹性细杆螺旋线平衡的动态稳定性

本文从动力学观点讨论具有初扭率的非圆截面弹性细杆的螺旋线平衡稳定性。弹性杆平衡的动态稳定性建立在以弧坐标s和时间坐标t为双自变量的离散系统的Lyapunov稳定性概念基础上。对于两端约束状况固定不变的弹性杆,若静态稳定性条件已满足,其与弧坐标对应的本征值可根据端部约束条件确定。则螺旋线平衡的动态稳定性由时间域的本征值判断。在缓慢受扰运动条件下,引入尺度缩小的时间变量T=εt,可将动力学过程视为对平衡状态的摄动。证明在ε^2计算精度范围内,当螺旋线平衡的一次近似静态稳定性条件得到满足时,考虑动力学因素的稳定性条件必也同时满足。     

模型外载与自重并存变动外载的光弹性分析法

提出一个变动模型外载，分析大模型在外载与自重共同作用时的尤弹性法。它与用离心力模拟自重试验的传统方法完全不同，只要在大模型上变动外载，就可以获得上述两种载荷共同作用下的应力分析结果。此法避免了用离心模型自重受模型尺寸限制等诸多因素影响的缺点，为自重不可的大型复杂空间工程结构模型试验应力分析提出了一条新的途径。文中给出了本方法的基本原理及其简要的实验验证和工程应用结果。     

Small Delay Inertial Manifolds Under Numerics: A Numerical Structural Stability Result

In this paper we formulate a numerical structural stability result for delay equations with small delay under Euler discretization. The main ingredients of our approach are the existence and smoothness of small delay inertial manifolds, the C ¹-closeness of the small delay inertial manifolds and their numerical approximation and M.-C. Li's recent result on numerical structural stability of ordinary differential equations under the Euler method.     

非圆截面弹性细杆的螺旋线平衡及稳定性

本文研究端部受力和力矩作用，且存在初曲率和初扭率的非圆截面弹性细杆的螺旋线平衡及其稳定性。描述弹性细杆平衡状态的Kirchhoff方程存在与杆的螺旋线平衡状态相对应的特解。直杆和圆环杆为螺旋线状态的两种特例。文中分析了螺旋线的几何特性与作用力和力矩之间的相互关系，并导出螺旋线平衡的一次近似解析形式稳定性判据。分析表明，松弛状态下弹性杆可处于螺旋线状态，直杆只有在轴向压力的作用下才能保持螺旋线平衡。无初曲率和初扭率弹性杆的螺旋线平衡稳定性必要条件是杆截面绕副法线轴的抗弯刚度大于或等于绕法线轴的抗弯刚度。此条件也适用于带初扭率的圆环杆及更普遍情形。无初曲率和初扭率的圆截面杆的螺旋线平衡恒稳定。     

四种非正交边界板考虑初始荷载效应的后期荷载位移近似解

基于考虑初始荷载效应情况下板的一般形式的静力平衡微分方程,运用坐标变换得到了轴对称情形,考虑初始荷载效应后圆形板的极坐标形式的静力平衡微分方程。运用Galerkin法解得了简支等边三角形板、固支椭圆板、固支圆形板和简支圆形板四种非正交边界板考虑初始荷载效应的后期荷载位移近似解。运用相关文献提出的有限元法验证了近似解的正确性。各位移近似解表达式简单、物理意义明确,清楚地反映了初始荷载及相关因素对后期荷载位移的影响。计算分析表明：初始荷载效应提高了板的弯曲刚度,减小了板的后期荷载位移;板的初始荷载效应主要受初始荷载、跨厚比及边界条件等因素的影响。     

非圆截面弹性细杆的平衡稳定性与分岔

本文研究存在初始曲率或挠率的非圆截面弹性细杆的平衡及稳定性问题,在两端受力矩单儿作用的条件下,杆的平衡微分方程可转换为用欧拉角表述的一阶自治系统,并有可能利用相平面的奇点理论分析弹性细杆平衡状态的稳定性,文中对杆截面的对称性,以及杆的初始曲率和挠率对平衡状态性的影响进行了定性分析,导出了解析形式的稳定性判据,揭示了杆平衡状态的列态分岔现象。     

Salt Water Intrusion in a Three-dimensional Groundwater System in The Netherlands: A Numerical Study

Salt water intrusion is investigated in a coastal groundwater system in the northern part of the province Noord-Holland, The Netherlands. Density dependent groundwater flow is modeled in three-dimensions with MOCDENS3D. This computer code is a version of MOC3D (Konikow et al., 1996) that has been adapted to simulate transient density-driven groundwater flow. Results from the model suggests that in this Dutch hydrogeologic system a severe and irreversible salinisation is already occurring. Within a few tens to hundreds of years, the salinity of the shallow aquifer is estimated to increase substantially. This salinisation process is a result of human activities such as the reclamation of the low-lying areas during the past centuries. Without changing the present boundary conditions, seepage into the low-lying areas will decrease slightly because of predicted increases in groundwater salinity. However, the rate in salt load through the Holocene aquitard into the low-lying areas will increase significantly due to an increase in salinity in the shallow aquifer. In addition, a relative sea level rise of 0.5m per century will intensify the salinisation process, causing an enormous increase in salt load in all low-lying areas in this part of The Netherlands.     

A Method for Measuring End Load in a Pressurized Hollow Rod

Experimental Techniques -     

非局部杆纵向振动的特性研究

基于非局部理论，研究弹性杆在任意边界约束条件下的纵向振动特性．根据Chebyshev 谱级数建立非局部弹性杆的纵向位移形式．在杆的两端引入纵向约束弹簧，通过设置弹簧刚度系数，模拟经典边界及弹性边界．建立非局部杆的能量表达式，由瑞利-里兹法得到齐次线性方程组，求解对应的矩阵特征值与特征向量问题获得非局部杆的固有频率和振型．通过数值仿真计算，研究非局部特征系数与边界约束条件对非局部杆振动频率的影响．结果表明本文方法合理简便，具有良好的精度，且适用于任意弹性边界条件．     

半无限粘弹杆的广义磁热粘弹问题

应用Lord-Shulman(L-S)和Green-Lindsay(G-L)广义热弹性理论,研究了在磁场中受移动热源作用的半无限长均质各向同性粘弹杆的磁热粘弹动态响应,并与经典耦合理论进行了对比.给出了杆的广义磁热粘弹耦合的控制方程,借助拉普拉斯积分变换及其数值反变换对控制方程进行了求解,计算得到了杆内温度、应力和位移的分布规律.研究结果表明:时间、热源移动速度和磁场大小对以上分布规律都有一定的影响.     

水电站压力钢管外压稳定问题的数值仿真研究

水电站压力钢管因失稳屈曲破坏过程的复杂性及影响失稳因素的多样性,导致对该问题的研究很难进行.目前该问题的传统计算方法存在一定的局限性,有时甚至计算结果相差较大.本文用神经网络模型结合模拟退火算法对该问题进行数值仿真求解,并通过测试样本验证了算法的可行性,为压力钢管外压稳定问题的分析方法开拓了一条新的研究思路.     

Blow-Up Estimates for a Non-Newtonian Filtration System

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A Variational Rod Model with a Singular Nonlocal Potential

The classical theory of elastic rods does not account for the possibility that large deformations may involve distinct points along the rod occupying the same physical space. We develop an elastic rod model with a pairwise repulsive potential such that, if two non-adjacent points along the rod are close in physical space, there is an energy barrier which prevents contact while for points nearby along the rod the potential is describable classically. This framework is developed to prove the existence of minimizers within each homotopy class, where the idea of topological homotopy of a curve is generalized to elastic rods as framed curves. Finally, the relevant first-order optimality conditions are derived and used to investigate the regularity of minimizers.     

Three-dimensional water entry of a solid body: A computational study

Marine vessels are continuously subject to impulsive loading from impact on the water surface. Understanding and quantifying the hydrodynamics generated by the three-dimensional (3D) water impact of a solid body is central to the design of resilient and performing vessels. Computational fluid dynamics (CFD) constitutes a viable tool for the study of water entry problems, which may overcome some of the drawbacks associated with semi-analytical and experimental methods. Here, we present a new computational study of the 3D water entry of a solid body with multiple curvatures. The method of finite volume is utilized to discretize incompressible Navier-Stokes equations in both air and water, and the method of volume of fluid is employed to describe the resulting free-surface multiphase flow. Computational results are validated against available experimental findings obtained using particle image velocimetry in terms of both the flow kinetics and kinematics. Specifically, we demonstrate the accuracy of our CFD solution in predicting the overall force experienced by the hull, the pile-up phenomenon, the velocity field in the water, the distribution of the hydrodynamic loading, and the energy transfer during the impact. Our approach is expected to aid in the validation of new semi-analytical solutions and to offer a viable means for conducting parametric studies and design optimization on marine vessels.     

轴向可压缩压杆的压缩失稳实验研究

用受压变形明显的聚胺脂胶棒进行了两端铰支的压缩失稳试验。为减少铰支处的摩擦力,在胶棒的两端铰支处安装了直线轴承。试验中观察到了Euler压杆理论所不包括的一些失稳现象,如：仍然在线弹性变形范围内的压杆,没有像Euler压杆理论预测的那样发生屈曲;在较高的临界载荷作用下,柔度较小的压杆发生了亚临界屈曲,所产生的弯矩是突然失稳弯曲的杆件不能承受的,于是杆件突然卸载。另外,大柔度压杆的超临界屈曲,即类似Euler压杆的屈曲现象也被观察到了。这些实验结果与轴向可压缩压杆失稳理论所预测的相符。