Static analysis of functionally graded beams using higher order shear deformation theory

Displacement field based on higher order shear deformation theory is implemented to study the static behavior of functionally graded metal–ceramic (FGM) beams under ambient temperature. FGM beams with variation of volume fraction of metal or ceramic based on power law exponent are considered. Using the principle of stationary potential energy, the finite element form of static equilibrium equation for FGM beam is presented. Two stiffness matrices are thus derived so that one among them will reflect the influence of rotation of the normal and the other shear rotation. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick FGM beam under uniform distributed load for clamped–clamped and simply supported boundary conditions are discussed in depth. The effect of power law exponent for various combination of metal–ceramic FGM beam on the deflection and stresses are also commented. The studies reveal that, depending on whether the loading is on the ceramic rich face or metal rich face of the beam, the static deflection and the static stresses in the beam do not remain the same.     

Deformation of reinforced-plastic beams with allowance for the time factor

A method is proposed for calculating statically determinate beams made of reinforced plastics with allowance for the reinforcement ratio, the rheological properties of the resin and the reinforcement, the effect of shears, the type of reinforcement distribution, and the time factor. In constructing the corresponding laws of deformation it is assumed that both components obey the "standard solid" law.Mekhanika Polimerov, Vol. 2, No. 1, pp. 100–107, 1966     

Einige Eigenschaften von beliebigen Translationsebenen mit Scherungen

We study the automorphism-group of a not necessarily finite affine translation-plane the lines of which are all axes of non-trivial shears. We prove: Every reflection of the translation-plane can be represented as the product of three shears. Furthermore, the group which is generated by all shears is transitive on the set of lines of the translation-plane.In another section we consider conditions for such translationplanes to be Moufang-planes. One knows examples of finite planes with the above structure, which are not Moufang-planes and hence (as every Moufang-plane is already Desarguesian) not Desarguesian (Compare the results of 4],[6] and [7]).     

Bending strength of oriented glass-reinforced plastics

The authors consider the effect of the low shear strength and shear stiffness of oriented glass-reinforced plastics (GRP) on the stress distribution and type of failure in bending. On the basis of relations obtained in [1] it is shown that the effect of shears on the magnitude and law of distribution of the normal and shear stresses is important only for very short beams made of materials with a low shear stiffness. An experimental study of the nature of failure in bending has revealed that the chief cause of extension of the region of shear failure of oriented GRP is the low shear strength of the material, and has made it possible to establish the limits of this region for three typical materials. Anisotropy of the elastic properties has little effect on the type of failure in bending.Mekhanika Polimerov, Vol. 2, No. 4, pp. 535–542, 1966     

Stability of elastoplastic flat arches

The stability of flat arches with pinned and fixed ends under a uniformly distributed load is investigated on the assumption that the material obeys a linear hardening law and the geometric relations are nonlinear. The equations obtained are solved for a sinusoidal arch with a rectangular cross section using the Bubnov-Galerikn method and the method of elastic solutions. Equations are obtained for the load and deflection at which transition from the purely elastic to the elastoplastic state occurs.Tartu State University. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 887–896, September–October, 1968.     

Motion planning for a piezo-actuated structure modeling a wingsail

This contribution presents the modeling and the motion planning of a flexible interconnected beam structure representing a wingsail. The structure is equipped with spatially distributed embedded actuators. The solution of the motion planning provides a feedforward control law to realize a desired spatial-temporal out-of-plane deflection trajectory. For this, a systematic flatness-based methodology is proposed, that allows for an efficient numerical solution exploiting, e.g., finite element approximations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large deflections of tapered functionally graded beams subjected to end forces

The large deflections of tapered functionally graded beams subjected to end forces are studied by using the finite element method. The material properties of the beams are assumed to vary through the thickness direction according to a power law distribution. A first order shear deformable beam element employed the exact polynomials to interpolate the transverse displacement and rotation, is formulated in the context of the co-rotational approach. The large deflection response of the beams is computed by using the arc-length control algorithm in combination with the Newton–Raphson iterative method. The numerical results show that the formulated element is capable to assess accurately the response of the beams by using just several elements. A parametric study is given to examine the influence of the material non-homogeneity, taper ratio as well as the aspect ratio on the large deflection behaviour of the beams.     

非定常沿岸波流的有限单元分析(Ⅰ)──数学模型

本文提出了一个预测由风和波流相互作用所产生的非定常近海波流的数学模型,其基础方程组中除了传统的连续性方程、动量方程、能量方程外,还引进了色散方程及折射方程。同时,在基础方程组中本文还分析了横向剪应力、风的应力、辐射应力及海底摩擦应力的作用,因而期望它能较全面和较精确地反映波流相互作用的规律。在(Ⅱ)中将给出二步显含有限单元法及几个计算例子。     

粘弹性板混沌振动的输出变量反馈线性化控制

研究了粘弹性板混沌振动的控制问题·　应用非线性系统精确线性化控制理论导出了一类非仿射控制系统的非线性反馈控制律·　建立了描述材料非线性的粘弹性板运动的数学模型并利用Ｃａｌｅｒｋｉｎ 方法进行简化·　采用相空间曲线和频率谱密度函数说明了在特定参数条件下系统将出现混沌振动,并以位移为输出变量将混沌振动控制为给定的周期运动·     

Exact Solutions for Linearized Gravity in the Randall–Sundrum Model

We find exact solutions of the equations of motion for linearized gravity in the Randall–Sundrum model with matter on the branes and calculate the Newtonian limit of the model. The results established include the contributions of the radion and the massive gravitons, which essentially modify Newton's law at short distances. We consider the effects produced by shadow matter situated on the other brane and compare them with the effect of the usual matter for branes with positive and negative tension. We also calculate the deflection of light and Newton's law in the zero-mode approximation and explicitly isolate the contribution of the radion field.     

Modelling and experimental validation of the deflection of a leveller for hot heavy plates

In order to successfully automate levelling processes, in particular for heavy plates, the deflection of the leveller has to be compensated based on a deflection model. In this work, a detailed mathematical deflection model of a hot leveller with bending mechanism and its experimental validation are presented. The roll intermesh profiles are calculated based on the deflection of the work rolls that are elastically supported by support rolls, frames, posts and adjustment screws. The deflection model is suited to compensate the effect of deflection on the roll intermesh and the plate flatness as well as to assess the loads of critical parts, for example the support rolls. A new experimental design to measure the deflection of a leveller is presented and successfully applied for model validation. The work roll deflection is measured directly by means of displacement sensors that are inserted in cut-outs of test plates. These test plates are modelled as linear elastic stripes. For normal load levels, the relative accuracy (repeatability) of the roll intermesh prediction of the model is better than 0.08 mm.     

Resolvents of the theory of orthotropic shells with low shear stiffness in force-moments and stress functions

The problem of the theory of orthotropic layered shells with low shear stiffness is reformulated in force-moments and stress functions on the basis of new strain continuity relations constructed with allowance for transverse shears.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 950–952, September–October, 1970.     

Jittering performance of random deflection routing in packet networks

This paper reports a study of random deflection routing protocol and its impact on delay-jitter over packet networks. In case of congestion, routers with a random deflection routing protocol can forward incoming packets to links laying off shortest paths; namely, packets can be “deflected” away from their original paths. However, random deflection routing may send packets to several different paths, thereby introducing packet re-ordering. This could affect the quality of receptions, it could also impair the overall performance in transporting data traffic. Nevertheless, the present study reveals that deflection routing could actually reduce delay-jitter when the traffic loading on the network is not heavy.     

Translationsebenen der ordnung 49 mit scherungen

It is shown that there exists, up to isomorphism, exactly one non-Desarguesian translation plane of order 49 which admits non-trivial shears. Furthermore, the collineation groups of this plane and all its derived planes are described.     

Modeling of transverse shears of piecewise homogeneous composite bars using an iterative process with account of tangential loads

A nonclassical model for the stress-strain state of a piecewise homogeneous composite bar is proposed. The model is based on an iterative process and takes into account the deplanation of cross sections of the bar caused by transverse shears. Based on the shear strains of some particular approximation, higher approximation models are constructed. The model accounts for both the normal and tangential loads.Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 487–500, July–August, 2000.     

Shock waves in an elastic medium with cubic anisotropy

Low-intensity shock waves, propagating along the principal diagonal of a cube in an incompressible elastic medium possessing cubic symmetry, are considered. The form of the shock adiabatic in the phase plane of shears is obtained. Sections corresponding to non-decreasing entropy at the discontinuity and the conditions of evolutionarity of the discontinuity on it are indicated. The structure of the shock waves is investigated.     

Analysis of functionally graded plates using higher order shear deformation theory

This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.     

An analysis of turbulent film condensation on a sphere with variable wall temperature under the effect of local shear stress

This paper presents an investigation into turbulent film condensation on a sphere with variable wall temperature. Under the wide range of vapor velocity, the wall temperature and the local film shear stress were considered. The result shows that under the high velocity vapor, the increase of the temperature amplitude will bring out a larger Nusselt number, and the increase is about 2.7–5.6%. Besides, under the effect of the local film shear stress, the mean Nusselt number will decrease about 0.65–0.8%. Furthermore, the paper then discusses the influence of shears and temperature amplitudes on the local dimensionless film thickness and heat transfer characteristics. Finally, the results developed in the current study are compared with those generated by previous theoretical results.     

复合载荷下圆薄板的大挠度问题

本文引入载荷分布函数使复合载荷依单参数变化,并选取平均挠角作为单一的位移摄动参数,给出了在均布载荷和中心集中力联合作用下边缘固定夹紧的圆薄板大挠度问题的摄动解,并讨论了中心点挠度为零的特殊情况.