Strip Model Research Articles

Full Stand Modeling and Tension Control for the Hot Strip Finishing Mill

We describe a looper controller design for a hot strip finishing mill in steel plants. The main function of the looper system is to balance the mass flow of the strip by accumulating material in the middle of the stands. Another function is to control the strip tension which influences the width of the strip. To ensure strip quality, it is very important to control the tension of the hot strip finishing mill. However, because there is a mutual interaction between the looper angle and the strip tension, it is difficult to control the looper system. Previous researches examined only the operation of a single stand. But it is not sufficient to examine the operation and effect of whole stands because the operation is wholly interdependent. In this paper, we present a full model of the hot strip finishing mill in order to more effectively control strip tension. We propose several control methods for the full-stand hot strip finishing mill, denoted as conventional PI, PI with cross gain, and coefficient diagram method (CDM) PID control. In the real plants, there are some problems by using higher order controllers such as LQ, LQG and H∞. By comparison, the PID controller is very simple and easy to apply to all real plants. To that end, we present our findings on PID controls and their potential use in the hot strip finishing mill.

Strip yield zones around ring-shaped crack in transversely isotropic thick layer

A ring-shaped crack under uniform load in an infinitely long elastic–perfectly plastic thick layer is considered. The problem is formulated for a transversely isotropic material by using integral transform technique. Due to the geometry of the configuration, Hankel integral transform technique was chosen and the problem was reduced to a singular integral equation which is solved numerically by using Gaussian Quadrature Formulae and the values were evaluated at discrete points. The plastic zone widths were obtained by using the plastic strip model after stress intensity factors were obtained. Numerical results are plotted for various ring-shaped crack sizes and transversely isotropic materials. It was found that the width of the plastic zone at the inner edge of the crack was greater than the outer one.

Analysis of the Elastoplastic Deformation of the Material in the Process Zone

By the method of digital correlation of speckle images, we record the displacements in the vicinity of the crack tip in plane specimens of D16AT alloy. The field of elastoplastic displacements is determined in the vicinity of the crack tip under static loading. By using the distribution of displacements, we compute the levels of strains ey on the continuation of the crack. The theoretical results are in good agreement with the experimental data in estimating the length of the plastic zone for the limiting equilibrium state. For the application of the concepts of fracture mechanics in the engineering practice of evaluation of the residual strength of structures, it is necessary to have efficient procedures aimed at the estimation of the crack resistance of materials (ability of the material to resist the process of crack propagation) [1, 2]. The characteristics of crack resistance of plastic materials in the case where a plastic zone (comparable with the crack length) is formed in the vicinity of the crack tip are computed on the basis of the δc-model by using the criterion of critical crack-tip opening displacement and the model of plastic strips [3]. The critical crack opening displacement ( δc ) describes the crack resistance of the material and plays the role of a parameter of the model. To find δ c , it is necessary to measure the displacements of two points of the opposite crack lips at the crack tip or at a certain distance from the tip [4, 5]. Note that the crack opening displacement is a function of the distance from the tip and the conditions of elastoplastic deformation of the specimen affecting the value of δc . The shape and sizes of the plastic zone formed near the crack tip in the process of deformation of the body depend on its mechanical properties, geometric sizes, and stressed state. The data of measurements of the opening displacements by using standard procedures do not enable one to study the mechanisms of formation of the plastic zone and crack initiation in the process of active loading up to fracture. The aim of the present work is to develop a method aimed at the investigation of the process of deformation of materials near the crack tips and determine the characteristic sizes of the process zone according to the data of evaluation of elastoplastic displacements based on the correlation processing of the electron speckle images of this zone.

On the full stand modeling and tension control for the hot strip finishing mill with PID structure

We describe a looper controller design for a hot strip finishing mill in steel plants. The main function of the looper system is to balance the mass flow of the strip by accumulating material in the middle of the stands. Another function is to control the strip tension which influences the width of the strip. To ensure strip quality, it is very important to control the tension of the hot strip finishing mill. However, because there is a mutual interaction between the looper angle and the strip tension, it is difficult to control the looper system. Previous researches examined only the operation of a single stand. But it is not sufficient to examine the operation and effect of whole stands because the operation is wholly interdependent. In this paper, we present a full model of the hot strip finishing mill in order to more effectively control strip tension. We propose several control methods for the full-stand hot strip finishing mill, denoted as conventional PI, PI with cross gain, and coefficient diagram method (CDM) PID control. In the real plants, there are some problems by using higher order controllers such as LQ, LQG and H∞. By comparison, the PID controller is very simple and easy to apply to all real plants. To that end, we present our findings on PID controls and their potential use in the hot strip finishing mill.

Theoretical contact angles on a nano-heterogeneous surface composed of parallel apolar and polar strips.

Neumann-Good's parallel strip model (J. Colloid Interface Sci. 1972, 38, 341) was used to analyze the contact angle hysteresis for a liquid on a heterogeneous surface composed of alternatively aligned horizontal apolar (theta = 70 degrees ) and polar (theta = 0 degree ) strips. The critical size of the strip width, below which the contact angle hysteresis disappears, was determined on the basis of the analysis of the activation energy for wetting to be from 6 to 12 nm. This calculated value of the critical strip size is 1 order of magnitude smaller than that of 0.1 microm, which has been commonly considered as the limit of heterogeneity size causing the appearance of the contact angle hysteresis.

Finite strip modeling for optimal design of prestressed folded plate structures

The optimal limit state design of prestressed thin-walled folded plate structures under multiple loading conditions is presented. The design variables include (a) geometrical quantities, like the thickness and the dimensions of the structural members, (b) topological parameters, which define the location and the connectivity of such elements, and (c) the characteristics of the eventual prestressing system, described by the prestressing forces and the cables profile. Besides the physical and technological limits on such variables, the design constraints account for given limit states on both the stress and the displacement states which define the structural behavior. The objective of the design process is to find the structural layout which minimizes the structural volume and/or the total prestressing force according to the mentioned side and behavioral constraints. The solution of the corresponding non-linear optimization problem is achieved by using a numerical procedure based on the complex method. The structural analyses required during the optimization process are performed by using the finite strip method. Some applications to the optimal design of beams, vaults and box-girder bridges show the effectiveness of the proposed procedure.

Method of singular integral equations in linear and elastoplastic problems of fracture mechanics

A brief survey of investigations carried out at the Karpenko Physicomechanical Institute of the Ukrainian National Academy of Sciences and devoted to the application of the method of singular integral equations to the solution of two-dimensional problems of fracture mechanics is presented. Special attention is given to the integral equations defined on piecewise smooth closed or open contours appearing in the boundary-value problems of the theory of elasticity for angular domains. We propose a new method aimed at the solution of dynamic problems by using finite differences with respect to time and singular integral equations on the boundary contours. Integral equations also appear in the elastoplastic problems of fracture mechanics solved by using the model of plastic strips and in the general case of continual plastic zones.

Finite strip modeling for optimal design of prestressed folded plate structures

The optimal limit state design of prestressed thin-walled folded plate structures under multiple loading conditions is presented. The design variables include (a) geometrical quantities, like the thickness and the dimensions of the structural members, (b) topological parameters, which define the location and the connectivity of such elements, and (c) the characteristics of the eventual prestressing system, described by the prestressing forces and the cables profile. Besides the physical and technological limits on such variables, the design constraints account for given limit states on both the stress and the displacement states which define the structural behavior. The objective of the design process is to find the structural layout which minimizes the structural volume and/or the total prestressing force according to the mentioned side and behavioral constraints. The solution of the corresponding non-linear optimization problem is achieved by using a numerical procedure based on the complex method. The structural analyses required during the optimization process are performed by using the finite strip method. Some applications to the optimal design of beams, vaults and box-girder bridges show the effectiveness of the proposed procedure.

Study on Dependence of AC Transport Current Losses in YBCO Coated Conductors on Distributions of Critical Current Density and n Value

We measured AC transport current losses in three kinds of thin film YBCO coated conductors made by different processes. The results showed that the loss characteristics were different and that some of the conductors did not follow the Norris strip model which was generally considered to well explain the loss characteristics of YBCO conductors. In the paper, an analytical model in which distribution of critical current density and n value of the conductor are taken into consideration is proposed to describe the AC transport current loss characteristics more generally than the Norris strip and elliptical models. It is shown that the analytical model well explain the measured loss characteristics of the three kinds of the conductors.

514 傾斜機能圧電層が接着された積層複合帯板の非定常圧電熱弾性問題(OS-4 熱弾性・等温弾性(1))

In this study, the theoretical analysis of transient piezothermoelasticity is developed for laminated composite strip bonded to a functionally graded piezoelectric layer(FGPL), subject to nonuniform heat supply in the width direction. Using the analytical procedure of a laminated of composite strip model, we obtain the solution for the two-dimensional temperature change in a transient state, and piezothermoelasticity of simply supported combined strip under the state of plane strain. Some numerical results for the temperature change, the displacement, the stress, and electric potential distributions when the thermoelastic displacement is not controlled or controlled are shown in figures.

積層圧電帯板の非定常圧電熱弾性解析 : 電極層を考慮した場合(OS3-7 圧電材料、き裂,OS3 先端機能性構造材料の力学的挙動に関する数理解析とマルチスケールアナリシスへの進展)

In this study, the theoretical analysis of transient piezothermoelasticity is developed for laminated composite strip bounded to a piezoelectric layer and the electrode layers, subject to nonuniform heat supply in the width direction. Using the analytical procedure of a laminated of composite strip model, we obtain the solution for the two-dimentional temperature change in a transient state, and piezothermoelasticity of simply supported combined strip under the state of plane strain. Some numerical results for the effects of the electrode layers on the temperature change and piezothermoelastic behavior when the thermoelastic displacement is not controlled or controlled are shown in figures.

The foundation and the future of wind engineering of long span bridges—the contributions of Alan Davenport

The pioneering work of Alan Davenport in the area of wind effects on long span bridges is reviewed, beginning with his Ph.D. research at Bristol University in the UK. Alan's resurrection of statistical concepts developed by Taylor and Von Kármán, describing the properties of the turbulent wind and the stochastic approach to the response of structures was key to his future work and to those researchers that followed. Simplification of the suspension bridge to a “line-like” structure permitted the focusing on fundamental areas of the response such as the resonant and quasi-steady components. This marriage between a sound theoretical understanding of the physical processes of the load and that of the response is characteristic of Alan's work and the experimental approaches that have been developed in the intervening time. His innovations with experimental techniques involving Section Models, Full Aeroelastic Models and his development of the Taut Strip Model approach are discussed. The incorporation of experimental results from these different approaches into the design methodology and codification is also outlined. Current research by Alan and his colleagues on the pressure fields on bridge decks promises to provide new insights into the effects of vortex shedding and flutter as well as turbulent buffeting. Some areas of future research are suggested with Alan's vision of the rational treatment of the problems associated with the wind engineering of long span bridges.

Plastic Analysis and Design of Steel Plate Shear Walls

A revised procedure for the design of steel plate shear walls is proposed. In this procedure the thickness of the infill plate is found using equations that are derived from the plastic analysis of the strip model, which is an accepted model for the representation of steel plate shear walls. Comparisons of experimentally obtained ultimate strengths of steel plate shear walls and those predicted by plastic analysis are given and reasonable agreement is observed. Fundamental plastic collapse mechanisms for several, more complex, wall configurations are also given. Additionally, an existing codified procedure for the design of steel plate walls is reviewed and a section of this procedure which could lead to designs with less-than-expected ultimate strength is identified. It is shown that the proposed procedure eliminates this possibility without changing the other valid sections of the current procedure.

Transport ac loss studies of YBCO coated conductors with nickel alloy substrates

Transport alternating current (ac) loss measurements were performed on a series of rolling-assisted biaxially textured substrate (RABiTS) processed YBa2Cu3Ox (YBCO) coated conductors at 77 K. While each sample possessed a 1 µm layer of YBCO and a 3 µm silver cap layer, two different nickel alloy substrates were used and their impact on the ac loss was examined. Both substrates possessed a 75 µm Ni–5 at%W base, but one substrate also had a 2 µm nickel overlayer as part of the buffer layer architecture. The ac losses, which were determined by thermal and electrical measurements, contained two dominant contributions: superconductive hysteresis in the YBCO and ferromagnetic hysteresis in the substrates. The superconductive component followed the Norris elliptic model for the substrate with the nickel overlayer and the Norris thin strip model for the substrate without the nickel overlayer. The substrates' ferromagnetic loss was determined separately through magnetization measurements, which showed that this loss contribution was independent of the presence of the nickel overlayer for effective ac currents less than 50 A. While the overall loss was lower for the thin-strip-like conductor with no nickel overlayer, further research is necessary to strengthen this connection.

Comparison of numerical techniques for 3D flutter analysis of cable-stayed bridges

This paper presents the results of a comparison study of the numerical techniques of structural and aerodynamic force models developed based on the spline finite strip method with the conventional finite element approach in three-dimensional flutter analysis of cable-stayed bridges. In the new formulation, the bridge girder is modelled by spline finite strips. The mass and stiffness properties of the torsional behaviour of complex bridge girder, which have a significant influence on the wind stability of long-span bridges, are modelled accurately in the formulation. The effects of the spatial variation of the aerodynamic forces can be taken into account in the proposed numerical model by distributing the loads to the finite strips modelling the bridge deck. The numerical example of a 423 m long-span cable-stayed bridge is presented in the comparison study. The accuracy and effectiveness of the proposed finite strip model are compared to the results obtained from the equivalent beam finite element models. The advantages and disadvantages of these different modelling schemes are discussed.

Morphological Butcher–Oemler Effect in the SDSS “Cut and Enhance” Galaxy Cluster Catalog

Abstract We investigated the evolution of the fractions of late-type cluster galaxies as a function of redshift using one of the largest, most uniform cluster samples available. The sample consisted of 514 clusters of galaxies in the range of $0.02 \leq z\leq 0.3$ from the Sloan Digital Sky Survey “Cut and Enhance” galaxy cluster catalog. This catalog was created using a single automated cluster-finding algorithm applied to uniform data from a single telescope, with accurate CCD photometry, thus minimizing the selection biases. We used four independent methods to analyze the evolution of the late-type galaxy fraction. Specifically, we selected late-type galaxies based on each of the rest-frame $g-r$ color, the $u-r$ color, galaxy profile fitting, and the concentration index. The first criterion corresponds to that used in classical Butcher–Oemler analyses. The last two criteria are more sensitive to the morphological type of galaxies. In all four cases, we find an increase in the fraction of late-type galaxies with increasing redshift, significant at the 99.9% level. The results confirm that cluster galaxies do change colors with redshift (the Butcher–Oemler effect) and, in addition, they change their morphology to later-type toward a higher redshift — indicating a morphological equivalence of the Butcher–Oemler effect. We also found a tendency of richer clusters to have lower fractions of late-type galaxies. This trend is consistent with a ram-pressure stripping model, where galaxies in richer clusters are affected by stronger ram pressure due to the higher temperature of clusters.

Free vibration and stability analysis of stiffened sandwich plates

Description is given of the development of a B-spline finite strip method for predicting the natural frequencies of vibration and the buckling stresses of rectangular sandwich panels. Each panel comprises a flat sandwich main plate which is reinforced by a number of longitudinal compact plate stiffeners attached to the faceplates. The core of the main plate is represented as a three-dimensional solid whilst the faceplates and the stiffening plates may in general be composite laminates which are represented, in turn, as either shear-deformable plates or classically thin plates. Details are given of the development of the elastic stiffness, geometric stiffness and consistent mass matrices of the finite strip models. The nature of the structural equations and the sophisticated procedure for their solution are discussed. Both vibrational and buckling applications of the developed analysis capability are presented and these include situations in which the corresponding mode shapes are of an overall nature and, for some of the buckling problems, of a highly localised nature.

Inelastic deformation and failure of clamped aluminium plates under pulse pressure loading

An experimental and analytical study is presented of the inelastic deformation and failure (rupture) of clamped aluminium plates measuring 0.5 m×0.5 m at the clamped edge by 1 mm thick under pulse pressure loading. The pulse loading was applied by generating a dynamic pressure gradient across the plates using a fast differential pressure device. Both static and dynamic test results are reported together with the results of an investigation of the failure surface using scanning electron microscopy. An assumed-modes, elastic–plastic analysis of the plates using a finite strip model was used to predict the maximum displacement of the plates. A simple uniaxial strain-based failure criterion was used in the analysis to predict the failure pressure of the ruptured plates. The rigid-plastic method was used to estimate the permanent deformation of some of the plates. Reasonable agreement is obtained between the predictions of the simplified elastic–plastic analysis and the experimental results. The rigid-plastic results were less accurate at predicting the permanent deformation of the plates due to the long duration of the loading relative to the fundamental natural period of the plates.

Modelling of twin‐roll strip casting processes

AbstractIn this work, a twin‐roll strip casting industrial process is analysed using a fixed‐mesh finite element formulation able to deal with unsteady incompressible thermally coupled flows including phase‐change and non‐Newtonian effects assumed to account for the flow behaviour during the whole cooling conditions. The weak form of the full Navier–Stokes equations is obtained using a generalized streamline operator in order to stabilize its numerical response while a temperature‐based algorithm is applied to describe the latent heat release. This proposed methodology is tested in a two‐dimensional analysis of a twin‐roll casting problem where an evaluation of different thermal and flow patterns is performed. Copyright © 2003 John Wiley & Sons, Ltd.

Large deflection analysis of composite laminates

A B-spline finite strip model is developed to simulate large deflection and delamination behaviour of laminated composite plates subjected to transverse loading. The model is based on a layer-wise plate theory. The geometrical non-linearity is included through use of von Karman’s non-linear strain–displacement relationship. In order to model progressive failure phenomena of composite laminates, both stress-based criteria and fracture-mechanics-based criteria are employed, and the former for delamination initiation whilst the later for delamination propagation. Comparison is made between the calculations of the present model and available analytical and experimental results.