The stability and load-carrying capacity of incomplete shells

The survey is devoted to problems on the stability and load-carrying capacity of imperfect shells in a nonhomogeneous stress-strain state. Methods recently developed at the Institute of Mechanics (Kiev, Ukraine) are briefly described. The approaches proposed are based on the generalized Euler criterion. Special attention is focused on numerical methods. The stability and load-carrying capacity of shells with symmetric and asymmetric, local and regular imperfections are considered. The data presented are compared with the well-known theoretical results and experimental data. At the end of the review, an analytical method (of reduced stiffness) is presented for predicting the lower bounds of sensitivity to imperfection in elastic buckling of longitudinally compressed stiffened shells with a nearly cylindrical shape. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 36–59, July, 2000.     

硅藻壳孔状结构的摩擦学性能研究

鉴于硅藻壳精细的孔状结构和良好的力学性能,选取较为典型的圆筛藻为研究对象,对其摩擦学性能进行了流固耦合分析(FSI).首先建立了圆筛藻壳壁的三维模型,然后应用计算流体动力学理论分析了圆筛藻壳不同孔径、孔深、孔距和速度下,其承载力(抵抗水压的能力)、摩擦力和摩擦系数等性能,并将该结构与无孔结构性能对比.结果表明:相对于无孔壳,硅藻壳的精细孔状结构可以增大其承载力,减小其与水环境间的摩擦.且在选取的尺寸范围内,随着硅藻壳体孔径或孔深的增大,其承载力增大,摩擦系数减小.     

Non-linear response of geometrically imperfect sandwich curved panels under thermomechanical loading

This paper deals with the non-linear response of sandwich curved panels exposed to thermomechanical loadings. The mechanical loads consist of compressive/tensile edge loads, and a lateral pressure while the temperature field is assumed to exhibit a linear variation through the thickness of the panel. Towards obtaining the equations governing the postbuckling response, the Extended Galerkin’s Method is used. The numerical illustrations concern doubly curved, circular cylindrical and as a special case, flat panels, all the edges being simply supported. Moveable and immoveable tangential boundary conditions in the directions normal to the edges are considered and their implications upon the thermomechanical load-carrying capacity are emphasized. Effects of the radii of curvature and of initial geometric imperfections on the load-carrying capacity of sandwich panels are also considered and their influence upon the intensity of the snap-through buckling are discussed. It is shown that in special cases involving the thermomechanical loading and initial geometric imperfection, the snap-through phenomenon can occur also in the case of flat sandwich panels.     

加权残值法分析轴压圆柱薄壳后屈曲问题

本文首次应用了样条配点法分析了受到轴向压力的圆柱形薄壳的后屈问题,壳体的方程是L.H.Donnell的非线性正交异性圆柱形壳体方程,壳体的挠度试函数及应力函数试函数都是于轴向用了五次B样条函数基函数,周向用余弦函数。计算模型是周向为半个波长的壳块,可适应后屈曲实验变形跳跃现象。非线性代数方程组用了Newton—Rophson迭代法求解。由此所得的理论上的后屈曲曲线与国外近代实验相符。     

Static load-carrying capacity of circular rigid-plastic plates under gaussian distribution of pressure

Static load-carrying capacities of circular rigid-plastic plates subjected to Gaussian distributions of pressure are presented in this paper. The effects of varying the load distribution as well as the boundary conditions are determined. Curves are presented which bound the load-carrying capacity for boundary conditions between the ideal cases of clamped and simply supported.     

润滑薄油膜承载力的测量

利用面接触润滑油膜测量系统研究了固定倾角滑块轴承承载力问题.在滑块倾角和载荷固定不变的条件下测得油膜厚度与速度的关系,经过参数转换,得到无量纲承载量曲线.这不同于传统方法中在不同收敛比下对油膜压力的直接测量.结果表明:在薄油膜条件下实际承载量曲线和理论曲线表现了相同的变化趋势;实测值小于理论值;理论认为无量纲承载量唯一由收敛比决定,而实验结果表明无量纲承载量曲线受滑块倾角、载荷和润滑油性质的影响.     

Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor

Conveyors are important equipment in the painting shop. Conveyors with cantilever beams have low load-carrying capacity and can carry small cars. To solve this problem, this paper presents a novel conveyor that uses redundantly actuated parallel manipulators. A method is proposed to obtain the maximum dynamic load-carrying capacity of the conveyor by optimizing the internal forces of the redundantly actuated parallel manipulators. To improve the dynamic load-carrying capacity, approaches using counterweights are utilized and compared. Furthermore, the maximum dynamic load-carrying capacity of the redundant parallel manipulator is compared with that of its nonredundant counterpart.     

平行间隙的热楔承载机理分析

本文研究了在4类表面温度边界条件下的热密度楔和热黏度楔对承载能力的影响,指出平行间隙内的油膜也具有承载能力,并与传统的几何楔进行了比较,分析了热密度楔和热黏度楔的关系及其重要性.除了用传统的表面温度差原理来解释平行间隙的承载机理外,还通过数值分析提出了1种补充理论,指出即使2个平行表面之间没有温度差但因油膜内部温度分布不均匀油膜也会产生承载力.     

Shallow flow simulation on dynamically adaptive cut cell quadtree grids

A computationally efficient, high‐resolution numerical model of shallow flow hydrodynamics is described, based on dynamically adaptive quadtree grids. The numerical model solves the two‐dimensional non‐linear shallow water equations by means of an explicit second‐order MUSCL‐Hancock Godunov‐type finite volume scheme. Interface fluxes are evaluated using an HLLC approximate Riemann solver. Cartesian cut cells are used to improve the fit to curved boundaries. A ghost‐cell immersed boundary method is used to update flow information in the smallest cut cells and overcome the time step restriction that would otherwise apply. The numerical model is validated through simulations of reflection of a surge wave at a wall, a low Froude number potential flow past a circular cylinder, and the shock‐like interaction between a bore and a circular cylinder. The computational efficiency is shown to be greatly improved compared with solutions on a uniform structured grid implemented with cut cells. Copyright © 2006 John Wiley & Sons, Ltd.     

倒三角形截面板管连接式钢圆弧拱在平面内的稳定承载力研究

采用理论推导与数值模拟相结合的方法,对倒三角形截面板管连接式钢圆弧拱在平面内的弹性屈曲和弹塑性屈曲进行了深入研究。首先,理论推导了拱的截面剪切刚度,并提出了拱在全跨均布径向荷载作用下的弹性屈曲公式。此外,还提出了避免连接板和弦杆在拱发生整体弹性失稳之前发生局部失稳的限制条件。然后,分别研究了在全跨均布径向荷载和全跨均布竖向荷载作用下,拱的整体弹塑性失稳机理。结果表明,在全跨均布径向荷载下,拱在1/4跨和3/4跨附近的弦杆会发生屈服,最终发生拱的整体弹塑性失稳。基于数值结果,建立了拱在全跨均布径向荷载作用下的稳定曲线,并针对拱发生整体弹塑性屈曲提出了相应的稳定承载力设计公式。在全跨均布竖向荷载作用下,钢拱发生整体失稳时,在拱脚两端附近的下弦杆会进入屈服。同样地,本文也提出了拱在全跨均布竖向荷载作用下,发生整体弹塑性失稳时的稳定极限承载力设计公式。本文所建议的公式与有限元结果符合得较好,可供实际工程设计参考。     

泡沫金属固支夹芯圆板的大挠度变形分析

论文分析了大挠度情况下固支夹芯圆板在准静态中心荷载作用下的承载能力.提出了考虑芯层强度影响的夹芯结构屈服条件,应用该条件,并基于边界条件和平板的初始变形机制假设夹芯板的速度场,推导了夹芯圆板考虑弯曲和膜力联合作用的大挠度响应,并应用数值算例验证了分析模型的合理性,在此基础上,分析和讨论了面板厚度、芯层厚度和芯层强度对夹芯圆板承载能力的影响.     

The plastica: The large elastic-plastic deflection of a strut

An extension of the theory of the Elastica is developed to determine the shape of a strut (or a cantilever) which undergoes large plastic deflection. The equations governing such a behaviour and known as the Plastica equations are set up and then solved by a perturbation method and by numerical integration. The post-buckling elastic-plastic deformation of a strut after initial elastic buckling is analysed, and some numerical results are given to show the variation of its load-carrying capacity with the development of the plastic region.     

Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials

A numerical method is developed to simulate complex two-dimensional crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. Potential cracks are represented by pre-inserted cohesive elements with tension and shear softening constitutive laws modelled by spatially-varying Weibull random fields. Monte Carlo simulations of a concrete specimen under uni-axial tension were carried out with extensive investigation of the effects of important numerical algorithms and material properties on numerical efficiency and stability, crack propagation processes and load-carrying capacities. It was found that the homogeneous model led to incorrect crack patterns and load–displacement curves with strong mesh-dependence, whereas the heterogeneous model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing the variance of the tensile strength random fields with increased heterogeneity led to reduction in the mean peak load and increase in the standard deviation. The developed method provides a simple but effective tool for assessment of structural reliability and calculation of characteristic material strength for structural design.     

Inverse doubly periodic problem of the theory of bending of a plate with elastic inclusions

Based on the balanced strength principle, a problem of determining the optimal interference for fitting elastic inclusions into holes of an isotropic elastic plate weakened by a doubly periodic system of circular holes is solved. A closed system of algebraic equations is derived, which allows solving this problem. The resultant interference increases the load-carrying capacity of the composite plate being bent. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 153–161, July–August, 2006.     

狭缝节流气体静压轴颈-止推轴承静态特性分析

在气体静压轴颈 -止推轴承的离散化过程中 ,采用有限元方法 ,利用加权余量法将其二阶偏微分方程降低一阶 ,使利用三角单元线性插值函数成为可能 ,简化了压力分布方程式的计算 ,给出了轴承的静态特性 ,分析了结构工艺尺寸、狭缝宽度和轴承间隙等因素对径向和轴向承载性能的影响 ,揭示了轴颈和止推轴承之间的相互影响规律 ,并且研究了轴承内部气膜压力分布的规律 .最后 ,通过实测值对计算结果进行了验证     

Buckling of cracked composite columns

A crack in a structural element introduces a significant local flexibility which enhances the instability. Buckling of an edge-notched beam is studied for isotropic and anisotropic composites. The local compliance due to the presence of cracks in an anisotropic medium is formulated as a function of the crack-tip stress intensity factors and the elastic constants of the material. The general integration of the non-linear differential equations expressing the buckling model of an eccentrically loaded composite beam is derived for two different types of hinged supports ; namely freely approaching and fixed span. The effect of reducing rigidity on the load-carrying capacity and the post-buckling behavior of the beam is discussed and exemplary numerical solutions are provided. The study indicates that the instability increases with the beam slenderness and the crack length. In addition, the material anisotropy conspicuously reduces the load-carrying capacity of an externally cracked member.     

Stress Concentration in an Axially Compressed Cylindrical Shell of Medium Thickness with an Elliptic Opening

Stress concentrations at the periphery of elliptic and circular openings are determined experimentally by the photoelastic method for three compressed cylindrical shells of medium thickness made of epoxy resin. The experimental values are compared with numerical values obtained by the theory of thin shells     

STRUCTURE DESIGN AND ANALYSIS OF A COMPETITION MODEL FOR THE 10th INTER-UNIVERSITY INVITATION CIVIL ENGINEERING COMPETITION1)

第十届亚洲土木工程邀请赛的题目为制作一个可承受静载荷和动载荷的弯桥,要求模型具有足够的承载力和合理的刚度,且模型质量尽可能小。针对西南交通大学代表队的参赛作品,从材料力学性能、桥梁概念设计、数值优化等几方面,阐述了结构优化步骤和方法,对比了静、动力仿真分析 和实体模型试验,总结了模型设计的优点和不足。本文可为今后的类似赛事提供参考。     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.