Stability of linearly viscoelastic bars made from polymer materials of variable cross section

The critical viscoelastic forces for hinged bars made from polymer materials of variable cross section changing in accordance with a power law are obtained. It is shown that these forces are proportional to the critical elastic forces of bars of variable cross section.VMEL "Lenin," Sofia. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 540–546, May–June, 1973.     

Stochasic stability of viscoewtic bars

This paper is devoted to the investigation of stability of viscoelsstic bars compressed by stochastic forces at infinite time interval, The problem of the bar buckling is considered in dynamic statement. Some sufficient conditions of mean square stability of viscoelastic bars are derived for arbitrary relaxation measure and different types of the end fixing     

Axisymmetric trawl cod-ends made from netting of a generalized mesh shape

The equations governing the geometry of axisymmetric trawl cod-endsmade from netting of meshes of a particular generalized structureare derived. From this, by suitable setting of the initial meshbar lengths, the equations governing the geometry of cod-endsthat are of importance to the fishing industry can be readilydeduced. It is assumed that arbitrary membrane forces act normalto the edges of the mesh elements, that there is no shear forceacting on the edge of a mesh element and that the twine thatmakes up the netting is extensible. The case where there isslackness in the mesh bars in the circumferential directionis dealt with and it is demonstrated how the finite structureof a knot can be taken into account. The case where the membraneforces arise solely as a result of and can be expressed by theappropriate components of the tensions in the mesh bars is alsoexamined and numerical solutions are found for a range of examples.     

High-order accurate equations describing vibrations of thin bars

A method for deriving one-dimensional wave propagation equations in thin inhomogeneous anisotropic bars based on the mathematical homogenization theory for periodic media is used to obtain equations governing the longitudinal and transverse vibrations of a homogeneous circular bar. The equations are derived up to O(ε⁸) terms and take into account variable body forces and surface loads. Here, ε is the ratio of the bar’s typical thickness to the typical wavelength.     

Variational statement of deformation problems for a composite latticed plate with various types of lattices

The variational statement of various boundary value problems for tangential displacements and forces in a latticed plate with an arbitrary piecewise smooth contour is investigated. The lattice consists of several families of bars made of a homogeneous composite material with a matrix of relatively low shear stiffness. The energy method reduces the problem to the variational problem of minimizing the energy functional. The conditions on the plate contour are established under which the functional is minimal and positive definite, which ensures that the problem is well posed.     

Bond of FRP Reinforcement in Concrete - a Challenge

The bond of ordinary steel reinforcement in concrete depends on many factors, such as the pullout resistance, the geometry of a concrete member, the placement of a bar in the member cross section, the cover splitting, the confinement caused by concrete and the surrounding reinforcement, the order of bond-crack appearance, and the bond-stress distribution along the bond length. The bond of FRP reinforcement depends on even a greater number of factors. Moreover, the types of FRP bars are numerous. Their surface is weaker than that of steel bars and may fracture by bond forces. The surface of FRP bars is softer and does not create as high local stress concentrations in bond contact points to concrete as the harder steel bars do. This fact often delays the appearance of cover splitting cracks along the bars. However, the load necessary for developing the crack pattern of ultimate splitting failure in concrete is then very dependent on whether the bar surface is glossy or rough. The FRP reinforcement can also be used for external shear and/or flexural strengthening of existing members. For this application, FRP bars are placed in grooves cut on the surface of the member to be strengthened and are fixed there with a cement mortar or epoxy paste. In such an application, the performance of bond between the FRP rod and the mortar or resin and then between the mortar or resin and concrete is critical for the effectiveness of the technique. The presence of two interfaces increases the number of parameters needed to characterize the global joint behavior and introduces new possible failure modes. The fundament for the bond resistance estimation should be an accepted bond philosophy linked to appropriate models. A system of bond tests should provide necessary coefficients for the models.     

A new model for the analysis of reinforced concrete members with a coupled HdBNM/FEM

As a truly boundary-type meshless method, the hybrid boundary node method (HdBNM) does not require ‘boundary element mesh’, either for the purpose of interpolation of the solution variables or for the integration of ‘energy’. In this paper, the HdBNM is coupled with the finite element method (FEM) for predicting the mechanical behaviors of reinforced concrete. The steel bars are considered as body forces in the concrete. A bond model is presented to simulate the bond-slip between the concrete and steels using fictitious spring elements. The computational scale and cost for meshing can be further reduced. Numerical examples, in 2D and 3D cases, demonstrate the efficiency of the proposed approach.     

Account of the Cross-Sectional Deplanation of a Composite Bar in Determining the Critical Force

A method for determining the critical force for an axially compressed composite bar with account of deplanation of its cross sections is considered. It is proposed to consider the cross-sectional deplanation, which decreases the critical force, by lowering the basic flexural stiffness of the bar by the value resulting from this effect. General relationships for calculating this value for composite bars are obtained. Numerical results are presented, which show the decrease in the critical force as a function of some parameters for transversely isotropic bars of rectangular cross section.     

具有凸缘加劲肋圆孔的应力分析

本文讨论无限平面内具有凸缘加劲肋圆孔的应力分析问题。所谓凸缘加劲肋系指孔周用型钢或其他形状的构件加劲,进行应力分析时难以将其视为板的一部分来处理的加劲肋。文中讨论了两种荷载情形:一为薄板在无限远点处应力σ_X(∞),σ_Y(∞)及τ_XY(∞)的作用;另一为薄板受线性应力的作用。分析方法是:将加劲肋视为圆形杆件,把加劲肋与薄板间相互作用之径向力q₀(θ)及切向力t₀(θ)表示成三角级数,分别求出加劲肋轴线之位移与具有圆孔薄板孔周之位移,利用加劲肋与薄板孔周变形一致的变形协调条件,确定径向力q₀(θ)及切向力t₀(θ),从而得到加劲肋及薄板之位移和内力的算式。     

复合材料大层数层压矩形截面杆的扭转问题分析

本文根据有效弹性模量理论［１］，采用三维八节点等参数有限元和整体—局部方法，对复合材料大层数矩形厚截面层压杆的扭转问题及其自由边缘效应进行了分析研究，通过算例计算给出了剪切应力在横截面内的分布规律、杆的扭转变形及其在自由边缘区域层间应力的分布情况·由于本文的分析方法可根据需要仅在应力梯度较大的局部区域，按单层逐层划分单元或在单层内再细化单元，以求得单层内精确的应力场和位移场，因此能显著节约计算量与机时，为具有大层数层压杆的扭转强度计算提供了一种有效的方法·     

The method of decomposition over velocities in the dynamics of extended systems

We propose a new method of solving multimodal problems of the dynamics of nonlinear extended shells, plates, and bars in a field of distributed mass and surface forces. We study the mode of motion of a towed system with the body in the steady state and under acceleration. We propose a new version of the method of decomposition based on identifying the characteristic times of propagation of various modes in the system, which can be used with success in the early stage of design of shell and bar structures, and also in problems of control of towed systems. Translated fromDinamicheskie Sistemy, No. 13, 1994. pp. 73-2-80.     

无约束平面框架结构冲击响应分析(Ⅱ)——数值算例分析

利用第(Ⅰ)部分推得的公式,对一无约束平面框架结构受运动刚体冲击时的瞬态响应进行了数值计算分析．计算了结构与运动刚体之间的冲击力时程曲线、梁中的剪力及弯矩分布、轴力杆件中的轴力分布．分析了杆中的纵波、Timoshenko梁中弯曲波及剪切波的传播现象．数值分析表明:冲击力的延续时间主要是由挠曲波及纵波控制的;在结构的冲击响应分析中,梁的剪切效应不容忽略．     

From single obstacles to wall roughness: some fundamental investigations based on DNS results for turbulent channel flow

Turbulent flow through a plane channel with only one smooth wall is analyzed based on DNS results for three Reynolds numbers. The opposite wall has 2D bars of size k ×  k attached with the distance to each other as the crucial parameter. When they are close together they act as a wall roughness whereas they are single obstacles in character when they are far apart. These two extreme cases show very different coherent structures in the vicinity of the wall attached bars. The categories single obstacles and wall roughness are introduced as an alternative to the often used categorization in terms of k- and d-type roughness. Visualization of the coherent structures is achieved by introducing constant local entropy generation as a parameter. Finally it is discussed whether results gained in a channel with one rough wall can be transferred to the more realistic case when both walls are rough.     

封闭薄壁截面空间曲杆的双力矩

讨论了各向异性材料薄壁截面空间曲杆的双力矩,给出了一般解法及平面曲杆受竖向载荷作用的双力矩公式。     

L形和十形截面杆的抗扭刚度

本文是作者前三篇论文的一个继续[1-3].利用调和函数延拓方法,L形和+形截面杆的抗扭刚度很容易求得.数值结果如表1-3所示.     

A new Branch and Bound method for a discrete truss topology design problem

Our paper considers a classic problem in the field of Truss Topology Design, the goal of which is to determine the stiffest truss, under a given load, with a bound on the total volume and discrete requirements in the cross-sectional areas of the bars. To solve this problem we propose a new two-stage Branch and Bound algorithm. In the first stage we perform a Branch and Bound algorithm on the nodes of the structure. This is based on the following dichotomy study: either a node is in the final structure or not. In the second stage, a Branch and Bound on the bar areas is conducted. The existence or otherwise of a node in this structure is ensured by adding constraints on the cross-sectional areas of its incident bars. In practice, for reasons of stability, free bars linked at free nodes should be avoided. Therefore, if a node exists in the structure, then there must be at least two incident bars on it, unless it is a supported node. Thus, a new constraint is added, which lower bounds the sum of the cross-sectional areas of bars incident to the node. Otherwise, if a free node does not belong to the final structure, then all the bar area variables corresponding to bars incident to this node may be set to zero. These constraints are added during the first stage and lead to a tight model. We report the computational experiments conducted to test the effectiveness of this two-stage approach, enhanced by the rule to prevent free bars, as compared to a classical Branch and Bound algorithm, where branching is only performed on the bar areas.     

New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers

In the one-dimensional cutting stock problem with usable leftovers (1DCSPUL), items of the current order are cut from stock bars to minimize material cost. Here, stock bars include both standard ones bought commercially and old leftovers generated in processing previous orders, and cutting patterns often include new leftovers that are usable in processing subsequent orders. Leftovers of the same length are considered to be of the same type. The number of types of leftovers should be limited to simplify the cutting process and reduce the storage area. This paper presents an integer programming model for the 1DCSPUL with limited leftover types and describes a heuristic algorithm based on a column-generation procedure to solve it. Computational results show that the proposed approach is more effective than several published algorithms in reducing trim loss, especially when the number of types of leftovers is limited.     

Experimetal study on the FRP-concrete bond behavior under repeated loadings

In this study, the effects of repeated loads on the FRP-concrete bond strength were investigated experimentally by direct pull out tests according to CSA S806-02. A conventional reinforcing steel bar and two types of glass-fiber-reinforced plastic (GFRP) bars were embedded in concrete and tested under four different loading patterns. The bond strength–slip curves of the bars were obtained and analyzed. The results showed that the maximum bond strengths under the repeated loads differed from those obtained under monotonic ones. In addition, noticeable differences in degradation of the bond strength with respect to the magnitude of slip were observed between the different bar types tested. On the basis of an image analysis of failure surfaces, they were attributed to the different bond failure mechanisms associated with the steel and GFRP bars.     

Anwendung des Galerkinschen Verfahrens auf nichtkonservative Stabilitätsprobleme des elastischen Stabes

Summary The paper deals with the application ofGalerkin's method to non-conservative stability problems of elastic bars. Two results established byBeck andPflüger by means of other methods are verified.