Buckling and Postbuckling Behavior of Cross-Ply Composite Plate Subjected to Nonuniform In-Plane Loads

This paper presents a study of buckling and postbuckling behaviour of simply supported composite plates subjected to nonuniform in-plane loading. The mathematical model is based on higher order shear deformation theory incorporating von Kármán nonlinear strain displacement relations. Because the applied in-plane edge load is nonuniform, in the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using these stress distributions, the governing equations for postbuckling analysis of composite plates are obtained through the theorem of minimum potential energy. Adopting Galerkin’s approximation, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations in the case of postbuckling analysis, and homogeneous linear algebraic equations in the case of buckling analysis. The critical buckling load is obtained from the solution of associated linear eigenvalue problem. Postbuckling equilibrium paths are obtained by solving nonlinear algebraic equations employing the Newton-Raphson iterative scheme. Explicit expressions for the plate in-plane stress distributions within the prebuckling range are reported for isotropic and composite plates subjected to parabolic in-plane edge loading. Buckling loads are determined for three plate aspect ratios (a/b = 0.5, 1, 1.5) and three different types of in-plane load distributions. The effect of shear deformation on the buckling loads of composite plate is reported. The present buckling results are compared with previously published results wherever possible.     

Analysis of Thick Circular Plates Undergoing Large Deflections

This investigation considers the effect of transverse shear deformation on bending of the axisymmetrically loaded isotropic and orthotropic circular and annular plates undergoing large deflection. The analysis treats the nonlinear terms of lateral displacement as fictitious loads acting on the plate. The solution of a von Kármán‐type plate is, therefore, reduced to a plane problem in elasticity and a linear plate‐bending problem. Results are presented for simply supported and clamped plates and are in good agreement with the available solutions. For plates considered in this study, the influence of shear deformation on lateral displacement becomes more significant as the orthotropic parameter increases. The linear and nonlinear solutions for orthotropic plates deviate at a low value of the maximum deflection‐to‐thickness ratio (w/h). Consequently, the extent of w/h within which the small‐deflection theory is applicable to orthotropic plates is much lower than the value of about 0.4 typically used for isotropic plates, and it depends, in general, on the degree of orthotropy. The technique employed in this study is well suited for the analysis of nonlinear plate problems.     

New approach for prediction of roll force in rod rolling

Abstract

An approximate model is presented in which the equation for computing roll force in an oval-round (or round-oval) pass rolling sequence has been formulated with a new approach. The fundamental idea considered is to introduce the concept of a weak plane strain condition which gives a two-dimensional approximation of the three-dimensional deformation problem in rod or bar rolling. The generality and robustness of the model have been examined by conducting a two-pass low speed bar rolling experiment and a four-pass continuous high speed rod rolling test with various rolling temperatures, roll gaps (pass height), rolling speeds, and steel grades. The predicted roll forces were in good agreement with those experimentally measured, although the prediction was less good when the roll gap (pass height) varied. The proposed model was very fruitful in solving the three-dimensional deformation problem in rod or bar rolling.     

Postbuckling Analysis of Plates Resting on a Tensionless Elastic Foundation

The buckling and large deflection postbuckling behavior of plates laterally constrained by a tensionless foundation and subjected to in-plane compressive forces are investigated. A nonlinear finite-element formulation based on Marguerre’s nonlinear shallow shell theory, modified by Mindlin’s hypothesis, is employed to model the plate response. To overcome difficulties in solving the plate–foundation equilibrium equations together with the inequality constraints due to the unilateral contact condition, two different approaches are used: (1) the unilateral constraint is accounted for indirectly by a bilinear constitutive law and (2) the problem is formulated as a mathematical programming problem with inequality constraints from which a linear complementarity problem is derived and solved by the Lemke algorithm. To obtain the nonlinear equilibrium paths, the Newton–Raphson algorithm is used together with path-following strategies. Plate–foundation interaction leads to interesting deformation sequences, characterized by the variation of the contact and noncontact zones along the postbuckling path, leading sometimes to sudden changes in the deformation pattern. The results have a remarkable dependence on the plate aspect ratio, foundation stiffness, and buckling shape. The effects of geometric imperfections on the nonlinear response of the plate are also investigated. From these results, a number of insightful conclusions regarding the behavior of such plate–foundation systems are drawn.     

Vibration and Stability of Thick Plates on Elastic Foundations

Natural frequencies and buckling stresses of a thick isotropic plate on two-parameter elastic foundations are analyzed by taking into account the effect of shear deformation, thickness change, and rotatory inertia. Using the method of power series expansion of the displacement components, a set of fundamental dynamic equations of a two-dimensional, higher-order theory for thick rectangular plates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are used to solve the eigenvalue problems of a simply supported thick elastic plate. To assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling stress are examined in detail. The distribution of modal transverse stresses are obtained by integrating the three-dimensional equations of motion in the thickness direction. The present approximate theories can accurately predict the natural frequencies and buckling stresses of thick plates on elastic foundations as compared with Mindlin plate theory and classical plate theory.     

模拟热轧板带三维变形的条层法及仿真实例

提出一种模拟板带轧制过程三维变形的新的数值方法———条层法。首先沿高向将变形区均匀地划分为若干层 ,然后再沿着金属的流动轨迹将变形区内的每层带材划分为若干流线条元 ,为了方便分析和计算 ,又将流线条元映射为矩形条元。横向位移的纵向分布被构造为四次曲线 ,横向分布用三次样条插值函数表示 ,高向分布用二次曲线拟合。根据塑性力学流动理论 ,分析推导了变形区三维变形和应力的数学模型。与本文作者曾经提出的流线条元法相比 ,考虑了应力与变形沿高向的不均匀分布 ,实现了精确的三维分析和计算。关于热带钢连轧和厚板轧制的仿真实例表明 ,提出的方法和模型符合实际 ,为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。     

A 2.5-dimensional Analytical Model of Cold Leveling for Plates with Transverse Wave Defects

Waves occurring in cold-rolled plates or sheets can be divided into longitudinal and transverse waves. Classical leveling theories merely solve the problem of longitudinal waves, while no well accepted method can be employed for transverse waves. In order to investigate the essential deformation law of leveling for plates with transverse waves, a 2.5-dimensional(2.5-D) analytical approach was proposed. In this model, the plate was transversely divided into some strips with equal width; the strips are considered to be in the state of plane strain and each group of adjacent strips are assumed to be deformation compatible under stress. After calculation, the bending deformation of each strip and the leveling effect of overall plate were obtained by comprehensive consideration of various strips along with the width. Bending of roller is a main approach to eliminate the transverse waves, which is widely accepted by the industry, but the essential effect of bending of roller on the deformation of plates and the calculation of bending of roller are unknown. According to the 2.5-D analytical model, it can be found that, for plates, it is neutral plane offsetting and middle plane elongation or contraction under inner stress that can effectively improve plate shape. Taking double side waves as an example, the appropriate values of bending of roller were obtained by the 2.5-D analytical model related to different initial unevenness, which was applicable to the current on-line adjusting of bending of roller in rolling industry.     

Frequency of Functionally Graded Plates with Three-Dimensional Asymptotic Approach

The harmonic vibration problem of functionally graded plates is studied by means of a three-dimensional asymptotic theory formulated in terms of transfer matrix. Instead of using multiple time scales expansion, the frequency is determined in a much simpler way that renders the asymptotic method to be practically validated for finding any higher-order solutions. This is illustrated by applying the refined formulation to a functionally graded rectangular plate with simply supported edges. The locally effective material properties are estimated by the Mori–Tanaka scheme. Accurate natural frequencies associated with flexural, extensional, and thickness-stretching modes are provided.     

Vibration of Laminate-Faced Sandwich Plate by a New Refined Element

An efficient six-noded triangular element based on refined plate theory is developed for the analysis of sandwich plates with stiff laminated face sheets and it is applied to a free vibration problem in this paper. The plate theory represents parabolic through thickness variation of transverse shear stresses with continuity at the layer interfaces, which introduces discontinuity at these interfaces for the shear strains. It is to be noted that the plate theory requires unknowns at the reference plane only. Moreover, it ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for an accurate modeling of laminated sandwich plates. The plate theory suffers from a problem in its finite element implementation since it requires C1 continuity of transverse displacement at the element interfaces. As very few elements based on this plate theory exist and they possess certain disadvantages, an attempt has been made to develop this new element. It has been utilized to study some interesting problems of laminated sandwich plate.     

Hygrothermoelastic Postbuckling Response of Laminated Composite Plates

The paper deals with the effect of moisture and temperature on the postbuckling response of a laminated composite plate subjected to hygrothermomechanical loadings. Mechanical loading consists of uniaxial, biaxial, shear, and their combinations. The distribution of temperature and moisture on the surface is considered to be uniform. The degradation in material properties due to moisture and temperature is taken into account using a micromechanical model. The mathematical formulation is based on higher order shear deformation theory and von Karman’s nonlinear kinematics. The quadratic extrapolation technique and fast converging finite double Chebyshev series are used for linearization and spatial discretization of the governing nonlinear equations of equilibrium, respectively. The effects of temperature rise, moisture concentration, fiber-volume fraction, and plate parameters on buckling and postbuckling response of the plate are presented.     

离散时间多智能体系统的协调最优预见跟踪

在互联拓扑包含一棵有向生成树的条件下,研究了离散时间多智能体系统的协调最优预见跟踪问题.首先利用状态增广技术把协调跟踪问题转化为一个增广系统的全局最优调节问题.然后应用离散时间线性二次型调节理论的相关结果给出了使增广系统的闭环系统渐近稳定的控制器,并由此得到原系统实现跟踪一致性的全局最优预见控制器.仿真结果不仅验证了所设计控制器的有效性,并且表明适当增加预见步长对保证准确跟踪领导者的输出是至关重要的.      

Wellbore Stability Analysis: From Linear Elasticity to Postbifurcation Modeling

This paper reviews some of the progress made on wellbore stability modeling during the last two decades. First we demonstrate the improvement made on mud-pressure predictions by moving from analytic elastic solutions to finite element elastoplastic modeling. We show this progress, presenting a finite element model based on a generalized plane strain formulation for analyzing efficiently the three-dimensional problem of stability in deviated wellbores. On a more research oriented work, we present results from two advanced theories capable of modeling localization of deformation in shear bands, which causes borehole breakouts. The first theory is based on a more established approach, the Cosserat continuum. The second theory, called gradient elastoplasticity, is being developed to resolve some of the drawbacks of gradient plasticity theories. Gradient elastoplasticity is a unified theory where both elastic and plastic parts are of gradient type. We demonstrate that both theories, in addition to localization, can also model the scale effect observed in thick-walled cylinder tests.     

Stability Analysis of Composite Plates with Through-the-Width Delamination

In this paper, the compressive bucking and postbuckling behavior of composite laminates with through-the-width delamination are investigated. The analytical method is based on the first-order shear deformation theory, and its formulation is developed on the basis of the Rayleigh-Ritz approximation technique by the implementation of the polynomial series, which has been used for the first time in the case of the mixed mode of buckling. Both local buckling of the delaminated sublaminate and global buckling of the whole plate are investigated. Also, the contact among sublaminates is taken into account. The three-dimensional finite-element analysis is performed by using ANSYS5.4 general-purpose commercial software just to compare the finite-element method results with those obtained by the analytical model. It is noted that the significance and contribution of the current paper lies in the fact that for a rather complicated problem, very good results are obtained by using a fairly small number of degrees of freedom through the application of complete polynomial series.     

Hygrothermal Effects on the Nonlinear Bending of Shear Deformable Laminated Plates

The influence of hygrothermal effects on the nonlinear bending of shear deformable laminated plates subjected to a uniform or sinusoidal load is investigated using a micro-to-micromechanical analytical model. The material properties of the composite are affected by the variation of temperature and mositure, and are based on a micromechanical model of a laminate. The governing equations of a laminated plate are based on Reddy’s higher-order shear deformation plate theory with von Kármán-type kinematic nonlinearity, and including hygrothermal effects. A perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The results presented show the effects of temperature rise, the degree of moisture concentration, and fiber volume fraction on the nonlinear bending behavior of the plate.     

Mental rotation of representations of two-dimensional and three-dimensional objects.

Empirical and theoretical considerations suggest that representations of three-dimensional objects should be more difficult to rotate mentally than representations of two-dimensional objects. In this study, subjects were asked to make mirror-normal decisions with stimuli that differed in perceived dimensionality and in angle of rotation in the image plane. In a series of four experiments, the time to make mirror-normal decisions increased with increased orientation discrepancy between the stimuli, as found previously in the literature. In every experiment, however, response times were smaller for representations of two-dimensional shapes than for representations of three-dimensional shapes when the stimuli being compared were presented with a large angular discrepancy. Whereas response times increased linearly with orientation when representations of three-dimensional shapes were rotated, the increase in response time for representations of two-dimensional shapes was generally nonlinear. Overall, the evidence suggests that representations of three-dimensional shapes are mentally rotated at the same rate as representations of two-dimensional shapes for angles of rotation between 0° and 60°. For larger angles of rotation, however, the rate of mental rotation is greater for representations of two-dimensional shapes than for representations of three-dimensional shapes. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

2800 mm中厚板精轧机辊型开发与应用

用平面变厚度有限元方法对中厚板精轧机辊变形分析的基础上，应用模拟退火算法，建立轧辊磨损、热凸度预报模型及工作辊与支持辊辊形同步解耦设计的理论和方法，开发出PMR和PWR辊形，成功在2800mm轧机上长期稳定地使用，取得显著效果。     

Stream Surface Strip Element Method and Simulation of Three-Dimensional Deformation of Continuous Hot Rolled Strip

A new method, the stream surface strip element method, for simulating the three-dimensional deformation of plate and strip rolling process was proposed. The rolling deformation zone was divided into a number of stream surface (curved surface) strip elements along metal flow traces, and the stream surface strip elements were mapped into the corresponding plane strip elements for analysis and computation. The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal were respectively constructed to be a quartic curve and a quadratic curve, of which the lateral distributions were expressed as the third-power spline function, and the altitudinal distributions were fitted in the quadratic curve. From the flow theory of plastic mechanics, the mathematical models of the three-dimensional deformations and stresses of the deformation zone were constructed. Compared with the streamline strip element method proposed hy the first author of this paper, the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction, and realizes the precise three-dimensional analysis and computation. The simulation example of continuous hot rolled strip indicates that the method and the model accord with facts and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.     

A model for the oxide growth stress and its effect on the creep of metals

A mathematical model is developed for the effect of the oxide growth stress upon the high temperature deformation of metal. The growth stress is modeled as a volumetric strain calculated from a modified Pilling-Bedworth ratio. The model is three-dimensional and allows the metal and the oxide scale to undergo both elastic and creep deformation during oxidation. The problems of oxidizing a flat plate, a solid rod, and a curved plate are formulated and solved. Experimental results for these geometries in the Ni-NiO system at 1000 °C are well predicted, both with and without an external load. The creep properties and the stress distribution in the NiO scale are calculated.     

求解冷轧带材金属横向流动和前张应力横向分布的一种新型条元变分法

将变形区划分为许多纵向条元,根据最小能量原理,通过对单个条元的变分,由欧拉微分方程求得条元上的出口横向位移函数模式,再通过对整个变形区的变分,由一组线性方程直接求得条元节线上的出口横向位移值,进而确定前张应力的横向分布。冷轧窄带和宽带的前张应力横向分布的计算结果与实验结果吻合较好,证明了该理论模型的正确性。     

Thermal Postbuckling of Preloaded Shear Deformable Laminated Plates

Postbuckling analysis is presented for a simply supported, shear deformable laminated plate subjected to a uniform lateral pressure and thermal loading, and resting on an elastic foundation. The temperature fields considered are associated with a nonuniform tentlike and parabolic distribution over the plate surface. The material properties are assumed to be independent of temperature. The lateral pressure is first converted into an initial deflection, and the initial geometric imperfection of the plate also is taken into account. The formulations are based on Reddy's higher-order shear deformation plate theory and include the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the thermal postbuckling equilibrium paths. The numerical illustrations concern the thermal postbuckling behavior of preloaded antisymmetric angle-ply laminated plates under a tentlike temperature field and symmetric cross-ply laminated plates under a parabolic temperature field resting on Pasternak-type or softening nonlinear elastic foundations from which the results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, fiber orientation, transverse shear deformation, the plate aspect ratio, thermal load ratio, and initial geometric imperfection as well as initial lateral pressure are studied.