Closed form solutions for free vibrations of rectangular Mindlin plates

A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate.     

Reflection of an impulsive torsional wave by a moving boundary

Reflection of an impulsive torsional wave by a uniformly moving surface/boundary is discussed. Applying the Cagniard–de Hoop technique, the solution for the reflected wave is obtained in the closed form and a new wave that runs along the moving boundary has been found. Its wave front singularity is stronger than those of the incident and the regular reflected waves. This new wave has the cylindrical surface, but the shape of the disturbed region is a torus with a triangular-like cross section.     

基于辛弹性力学解析本征函数的有限元应力磨平方法

在实际工程结构的结构强度与优化等力学数值分析中,应力计算结果的精度是非常重要的。有限元法是得到最广泛应用的一类数值方法,并形成了众多通用的有限元程序系统。这些程序系统采用的几乎都是基于最小总势能的位移法,虽然其分析给出的有限元位移场具有较高的精度,但所得到的有限元应力场的精度较位移场大大降低。基于极坐标辛对偶体系所提供的平面弹性力学的解析辛本征展开解,并借用有限元程序系统所得到的节点位移,本文提出了一个应力分析的改进方法。数值结果表明,本方法给出的应力分析精度得到大幅提高,并具有良好的数值稳定性,可用于有限元程序系统的后处理,以提高应力尤其是关键区域应力的分析精度。     

椭圆孔口外受集中力和力偶时的新解法

文中给出了无限平板带椭圆孔又受集中力和力偶时的弹性分析。所讨论问题归结为复变函数的一个特殊问题，即令一个复变函数（单位圆外有奇点）的值和另一个复变函数（单位圆外为解析）的共轭值沿着单位圆相等。最后，得出了闭合形式的解。     

黄河口裸置管线在位稳定性数值模拟研究

基于Biot固结理论,并结合接触算法,考虑了海水流经管线时的尾流效应,建立了波浪荷载作用下裸置管线与周围土体相互作用的有限元模型,使计算结果更加符合实际情况。将此模型应用于黄河口埕岛油田裸置管线在位稳定性计算,分析了尾流效应对裸置管线稳定性的影响,在此基础上提出了适用于黄河口不同地质分区的裸置管线稳定性校核曲线。     

A note on the determination of critical loads for flexible noncircular cylindrical shells with clamped edges

An approach is proposed to determine the upper and lower bounds of the critical load for flexible noncircular long cylindrical shells with clamped longitudinal edges under nonuniform loading. An exact analytical solution is designed. Its critical points are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 78–87, November 2005.     

Elastoplastic stress analysis for cylindrical shell with flat strip imperfection

Based on unequidistant B-spline function, generalized spline subdomain displacement mode of rotational shell is obtained by taking double-direction interpolation of spline. The elastoplastic constitutive equation of shells is established by using the endochronic theory.According to the initial deflection theory of shells, the elastoplastic stress analysis of cylindrical shells with flat strip geometrical imperfection is studied. Numerical results show that the geometrical imperfection has a great effect on the stress distribution of shells.     

Residual stress field and reduction of stress intensity factors in cold-worked holes

Closed-form and semi-analytical solutions are obtained for the residual stress distributions in a plate caused by pressure acting on a central circular hole, representing the cold-work process. The material is elastic–perfectly plastic. Both Tresca and von Mises yield criteria are used and the corresponding residual stress distributions are compared. The relation between the dimension of the plastic zone and the value of internal pressure is presented. The relation between the magnitude of the residual stresses and the remote uniform tensile stress required to open symmetrical radial cracks is also presented. The reduction of the stress intensity factors of cracked open and riveted holes as a function of the internal pressure applied (or mandrel radial displacement) is investigated using numerical models for both an elastic–perfectly plastic material and for an Al 2024-T3 Alclad aluminum alloy.     

PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is co…     

轴压随机几何缺陷圆柱壳可靠性分析

轴压随机几何缺陷圆柱壳屈曲的失效函数具有较强的非线性,对于该结构已应用的可靠性分析方法不能同时满足计算精度和计算效率的要求。本文发展一个修正的ＭｏｎｔｅＣａｒｌｏ法,由两个步骤执行：应用一阶可靠性方法计算Ｈａｓｏｆｅｒ－Ｌｉｎｄ可靠性指标β;将简单ＭｏｎｔｅＣａｒｌｏ法的采样区域限制在基本随机变量构成的ｎ维β－球外部,采样点由一个χ２分布的随机半径Ｒ≥β和（－１,１）均匀分布的随机方向组成,该修正的ＭｏｎｔｅＣａｒｌｏ法用于轴压随机几何缺陷圆柱壳屈曲强度可靠性分析表明,在相同精度的情况下修正的ＭｏｎｔｅＣａｒｌｏ法的样本容量比简单ＭｏｎｔｅＣａｒｌｏ法要低３个数量级,一阶可靠性方法的计算误差随着与分支屈曲模态一致的初始几何缺陷项数的增加越来越显著     

不确定初始几何缺陷壳的动态屈曲分析

研究了动载作用下含有不确定初始几何缺陷壳的动态屈曲问题.给出了不确定初始几何缺陷在椭球描述和区间描述下,壳的动态响应和安全因子的界限估计.从数学证明和数值算例两方面,讨论了基于不确定性初始几何缺陷两种描述的凸模型方法和区间分析方法所得壳动态响应及安全因子的界限的关系,为判断壳的动态屈曲失效提供了依据.     

考虑周长约束的圆柱薄壳初始几何缺陷随机场建模方法

利用随机场对圆柱薄壳结构的初始几何缺陷进行建模,并据此建立了一种用于含初始几何缺陷轴压圆柱薄壳屈曲分析的随机分析方法.首先,指出已有将圆柱薄壳初始几何缺陷表征为二维高斯随机场的方法会导致与实际不相符的初始几何缺陷,如圆柱周长显著增大或缩小的几何缺陷.其次,提出一种考虑周长不变约束的随机场建模方法,以剔除与实际不相符的随...     

Membrane fusion based on the geometry of the stalk model

It is a commonly accepted assumption that membrane fusion involves an hourglass-shaped local contact between two monolayers of opposing membranes, an intermediate structure called a stalk. The shape of the stalk is considered as an axisymmetrical figure of revolution in 3D space, with a planar geometry in the initial configuration. The total energy of the stalk is evaluated from the assumption that the stalk has a constant curvature. Its negative value due to the presence of spontaneous curvature promotes hemifusion. An extension of the original model developed in Markin and Albanesi [23] is proposed, in which any geometrical feature of the stalks can be expressed in explicit form, by considering the stalks as nodoid surfaces. The local stresses and induced internal moments due the membrane bending are evaluated based on the adopted parameterization.     

几何缺陷浅拱的动力稳定性分析

研究了几何缺陷对粘弹性铰支浅拱动力稳定性能的影响。从达朗贝尔原理和欧拉-贝努利假定出发推导了粘弹性铰支浅拱在正弦分布突加荷载作用下的动力学控制方程,并采用Galerkin截断法得到了可用龙格-库塔法求解的无量纲化非线性微分方程组。同时引入能有效追踪结构动力后屈曲路径的广义位移控制法,对含几何缺陷浅拱的响应曲线进行几何、材料双重非线性有限元分析。用这两种方法分析了前三阶谐波缺陷对浅拱动力稳定性能的影响,其中动力临界荷载由B-R准则判定。主要结论有:材料粘弹性使浅拱动力临界荷载增大且结构响应曲线与弹性情况差别很大;二阶谐波缺陷影响显著,它使动力临界荷载明显下降且使得浅拱粘弹性动力临界荷载可能低于弹性动力临界荷载。     

用广义样条子域法分析具有环形初始几何缺陷的圆柱壳

基于壳体初挠曲理论,对具有环形初始几何缺陷的圆柱壳进行了静力分析。整个缺陷区段视为由若干斜锥段组成。利用广义样条子域法建立了位移模式,该模式具有自由度少,结点设置灵活之特点。计算结果与有限元计算所得结果基本吻合。     

隧道工程解析方法及解析模型研究进展

封闭或解析形式解答可以实现隧道工程的快速初步设计、获得参数影响的函数形式,并为数值方法提供正确性验证手段,与其共同完成工程问题的可靠预测．本文针对各类静动力问题,从经典方法以及近十年来的最新进展入手,阐述了隧道工程常用的解析方法和求解思路,全面综述了可解问题、解答和最新研究进展,并展望了解析研究发展方向．本文内容涵盖了隧道解析研究的重要领域,涉及弹性、弹塑性、各向异性、流变岩体中的隧道问题、衬砌和锚杆支护以及多物理场相关的问题．通过系统介绍以上成果,可以深入了解隧道问题解析研究思路和解答,推动更具价值的解析解的发展．