FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling

With the increasing demand of higher quality hot rolled strips, flatness defects occurred on the strips during the cooling process on the run-out table have received significant attention and should be considered in the online shape control model. Non-uniform temperature distribution and cooling across the strip width are the main reasons why the strip becomes unflatten after cooling process although the strip is rolled flat at the finishing mill. A thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS Finite Element Software. In this model, Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation by means of the user subroutine program HETVAL. An elasto-plasticity constitutive model of the material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were taken into account, was derived and realized using the user subroutine program UMAT. The conclusion that the flatness of the steel strip will develop to edge wave defect under the functions of the different thermal and microstructural behaviors across strip width direction during the run-out table cooling procedure was acquired through the analysis results of this model. The calculation results of this analysis model agree with the actual measurements and observation, therefore this model has a high accuracy. To better control the flatness quality of hot rolled steel strip, the shape compensation control strategy of slight center wave rolling is proposed based on the analysis result. This control strategy has been verified by actual measurements, and applied in actual production.     

Optical fibre sensors for assessing food quality in full scale production ovens — a principal component analysis and artificial neural network based approach

This paper reports on a method of classifying the spectral data from an optical fibre based sensor system as used in the food processing industry for monitoring food products as they are cooked in large scale continuous ovens. The method uses a feed-forward back-propagation artificial neural network. The sensor monitors the food colour online as the product cooks by examining the reflected light, in the visible region, from both the surface and the core of the product. Results based on the combined use of Principal Component Analysis (PCA) and standard back-propagation artificial neural networks are presented. Results are also reported for a wide range of food products which have been cooked in the full scale industrial oven. PCA is performed on the reflected spectra, which form a “colour scale” — a scale developed to allow the quality of several products of similar colour to be monitored, i.e. a single classifier is trained, using the colour scale data, that can classify several food products. The results presented show that the classifier performs well.     

Phase transition for models of an elastic medium with residual stress

A variational problem on martensite-austenite phase transitions in a continuous medium is considered. The energy functional of this problem depends on two parameters: the temperature, which runs all real values, and the positive surface tension coefficient. A half-plane is divided into three open zones. In the first zone, only the martensite one-phase equilibrium state is realized. In the second zone, only the austenite one-phase equilibrium state is realized, whereas, in the third zone, any equilibrium state is a two-phase one. On the interface surfaces separating the zones, only those equilibrium states are realized that are typical for adjoining zones. In the homogeneous and isotropic case, the explicit solution to the problem is given provided that the surface tension coefficient is zero. Bibliography: 12 titles. Illustrations: 4 figures. Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 153–191.     

A sand surface element for efficient modeling of residual stress in castings

This article describes a method to efficiently predict residual stresses in foundry castings. We replace explicit modeling of the sand mold during stress analysis by using a locally applied boundary condition element. Methods are given for assigning appropriate values to the individual elements, and we present several example problems. In these test problems, we also evaluate several constitutive models for the sand. We find that plastic strains and displacements in the casting do not depend strongly on the sand constitutive model. Further, the stress states produced, when using the new surface elements, are generally in good agreement with those found using a full mold. The computational advantages of the new element are demonstrated.     

Further analysis of minimum residual iterations

The convergence behaviour of a number of algorithms based on minimizing residual norms over Krylov subspaces is not well understood. Residual or error bounds currently available are either too loose or depend on unknown constants that can be very large. In this paper we take another look at traditional as well as alternative ways of obtaining upper bounds on residual norms. In particular, we derive inequalities that utilize Chebyshev polynomials and compare them with standard inequalities. Copyright © 2000 John Wiley & Sons, Ltd.     

Recovery of residual stress in a vertically heterogeneous elastic medium

We study the problem of identifying residual stress within athin subsurface layer in an elastic medium occupying a region = {(x₁, x₂, x₃) , R³: 0 < x₃ < L, where L } in space,where all parameters depend only on the depth x₃. Under thetheoretical framework of linear elasticity with initial stress,the incremental elasticity tensor of each material point iswritten as a sum of two terms, namely the elasticity tensorand the acoustoelastic tensor, both of which are taken hereas isotropic functions of their arguments. By imposing impulsiveloads and measuring the displacements at the boundary x₃ = 0,we recover the residual stress and its gradient there. If theresidual stress has a diagonal form, we can recover the residualstress inside the subsurface layer.     

畴数理论在纤维空间的应用

In this paper, we improve a result of James′ paper [1], and get the theorem; If P:E→B is a fibration, B is a normal space, and catB= n, then the composition of n filre-trivial maps is section homolopic.     

Propagation of polarization in elastodynamics with residual stress and travel times

 We show that knowing the displacement-to-traction map associated to the equations of isotropic elastodynamics with residual stress we can determine the lens maps of compressional and shear waves. We derive several consequences of this for the inverse problem of determining the residual stress and the Lamé parameters from the displacement-to-traction map. Received: 6 December 2001 / Revised version: 29 October 2002 / Published online: 8 April 2003 RID="⋆" ID="⋆" The author thanks the Department of Mathematics at the University of Washington for its hospitality during his visit in fall 2000. RID="⋆⋆" ID="⋆⋆" Partly supported by NSF grant DMS-0070488 and a John Simon Guggenheim fellowship. The author also thanks MSRI for partial support and for providing a very stimulating environment during the inverse problems program in fall 2001.     

Fracture analysis of cladded components considering residual stresses

The present study is concerned with an experimental and numerical investigation of the behavior of sub–clad and surface cracks in cladded components considering the residual stress field due to the welding and heat treatment processes. For this purpose, two large–scale tests on cladded cracked specimens have been performed and analyzed numerically. It is observed that the fracture process is initiated in the heat affected zone of the base metal underneath the cladding whereas the cladding remains intact even in case of a brittle crack extension and arrest in the base material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lifetime analysis with allowance for bond stress distribution

A fracture model consisting of a set of bonds assigned various stress concentration coefficients is proposed. The bond lifetime is determined from Zhurkov's equation; the relative number of bonds with a particular _* being taken in accordance with a Weibull distribution. The model explains the similarity of the shapes of the submicrocrack accumulation and creep curves.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 227–231, March–April, 1973.     

Convergence analysis of multigrid methods with residual scaling techniques

In this paper, multigrid methods with residual scaling techniques for symmetric positive definite linear systems are considered. The idea of perturbed two-grid methods proposed in [7] is used to estimate the convergence factor of multigrid methods with residual scaled by positive constant scaling factors. We will show that if the convergence factors of the two-grid methods are uniformly bounded by σ (σ<0.5), then the convergence factors of the W-cycle multigrid methods are uniformly bounded by σ/(1−σ), whether the residuals are scaled at some or all levels. This result extends Notay’s Theorem 3.1 in [7] to more general cases. The result also confirms the viewpoint that the W-cycle multigrid method will converge sufficiently well as long as the convergence factor of the two-grid method is small enough. In the case where the convergence factor of the two-grid method is not small enough, by appropriate choice of the cycle index γ, we can guarantee that the convergence factor of the multigrid methods with residual scaling techniques still has a uniform bound less than σ/(1−σ). Numerical experiments are provided to show that the performance of multigrid methods can be improved by scaling the residual with a constant factor. The convergence rates of the two-grid methods and the multigrid methods show that the W-cycle multigrid methods perform better if the convergence rate of the two-grid method becomes smaller. These numerical experiments support the proposed theoretical results in this paper.     

Finite volume analysis of adaptive beams with piezoelectric sensors and actuators

This paper presents a finite volume (FV) formulation for the free vibration analysis and active vibration control of the smart beams with piezoelectric sensors and actuators. The governing equations based on Timoshenko beam theory are discretized using the finite volume method. For the purpose of forced vibration control of beam structures, the negative velocity feedback controller is designed for the single-input, single-output system. To achieve the best effect, the piezoelectric sensors and actuators are coupled with the host structure in different positions and then the performance of the designed control system is evaluated for each position. In the test examples, first the shear locking free feature of the present formulation is demonstrated. This has been performed by doing static and natural frequency analysis of some reference models. Then, the capability of the proposed method for the prediction of uncontrolled forced vibration response and active vibration control of a beam structure is studied.     

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb-Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction ? and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.     

Virtual modeling of residual stress in drawn wire due to the skin pass effect

The wire drawing technological process is wide use in industry. The effect of skin‐pass is apply for reduction of residual stress in final product. The finite element method is applied to simulate the effect of skin‐pass in wire drawing process. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of certain technological factors on residual stress formation in stiffened glass-reinforced plastic shells

Conclusions Residual stress formation in stiffened composite shells has a nonmonotonic character determined by the fabrication technology, by the structural geometry and by the relations between the thermophysical and mechanical characteristics of the materials of which the individual elements are composed. For a given temperature regime a residual stress distribution favorable with respect to strength can be obtained by using auxiliary devices with specially selected properties.Moscow Power-Engineering Institute. Translated from Mekhanika Polimerov, No. 1, pp. 34–39, January–February, 1978.     

Theoretical and numerical analysis of a minimal residual solver for 2D Boltzmann transport equation

Relying on the splitting of the collision operator introduced in (M2AN 34 (2000) 1109; (M2AN 32 (1998) 341), we prove theoretical convergence for an infinite dimensional adaptation of the minimal residual algorithm for Boltzmann transport equation in dimension two. Then we compare numerically this method with existing nonaccelerated schemes. It gives good results which could even be further improved by adding a DSA or SOR acceleration.     

A structure for the Bayes analysis of the performance of detection systems with multiple sensors and sites

The usual Bayes analysis for optimum detection systems is extended to include the costs of equipment, location, maintenance, and other features of operation, in addition to the customary preassigned costs of correct and incorrect decisions, when multiple receiving sites (Q) and sensors (M) are employed for acquisition and ultimately joint processing of data for simple binary (i.e.,yes orno) decisions as to the presence or absence of a signal source. A risk formalism is constructed which indicates how the expected overall costs of both decision and operation can be generally determined for a variety of realistic cost models. Since the expected cost or average risk of decision is a monotonically decreasing function ofM andQ, while the associated costs of operation are reasonably described by monotonically increasing functions ofM andQ, values ofM andQ may also exist for which the total average cost (or risk) can be minimized, as well as the cost of decision itself (i.e., for a Bayes decision system). In any case, the physics of the particular detection situation (radar, radio, seismic, acoustic, etc.) is included in the usual way, under the important constraint of decision optimality (i.e., Bayes decision). Thus, one purpose of this introductory study is to provide some possible models for system evaluation and comparison which specifically include the often controlling factors of operational costs (vis-à-vis those of decision). A simple analytic example is used to illustrate the approach, which is, however, capable of handling much more general examples, both conceptually and quantitatively. In these more general cases, it is expected that computer aids will be needed.This work was supported by the United States Air Force, Project RAND, Contract No. F44620-67-C-0045.     

Local analysis of a spectral correction for the Gauss-Newton model applied to quadratic residual problems

A simple spectral correction for the Gauss-Newton model applied to nonlinear least squares problems is presented. Such a correction consists in adding a sign-free multiple of the identity to the Hessian of the Gauss-Newton model, being the multiple based on spectral approximations for the Hessians of the residual functions. A detailed local convergence analysis is provided for the resulting method applied to the class of quadratic residual problems. Under mild assumptions, the proposed method is proved to be convergent for problems for which the convergence of the Gauss-Newton method might not be ensured. Moreover, the rate of linear convergence is proved to be better than the Gauss-Newton’s one for a class of non-zero residue problems. These theoretical results are illustrated by numerical examples with quadratic and non-quadratic residual problems.     

New variational-asymptotic formulations for interlaminar stress analysis in laminated plates

A new approach for the three-dimensional stress analyses in composite laminates is presented. The method of composite expansions along with Hellinger-Reissner variational formulation is employed to derive the interior and edge layer problems for high order approximations. A new method of finite element analysis for solving the edge layer problem is developed based on the modified mixed-hybrid method. Comparison of the present solution with an assumed displacement finite element solution is made to demonstrate the accuracy and efficiency of the present approach.

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Zusammenfassung Eine neue Methode zur dreidimensionalen Spannungsanalyse von Verbundlaminaten wird dargelegt. Die Methode der gewünschten Entwicklungen zusammen mit dem Hellinger-Reissner'schen Variationsprinzip führt zur Herleitung des inneren Problems und des Grenzschichtproblems für höhere Näherungen. Eine neue Methode wird entwickelt, welche mit Hilfe von finiten Elementen, vom gemischt hybriden Verfahren ausgehend, das Grenzschichtproblem löst. Der Vergleich, der hier vorgeschlagenen Lösung mit einer klassischen, auf Verschiebungselementen beruhenden Lösung zeigt die Genauigkeits- und Effizienzvorteile der hier dargelegten neuen Methode.

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This research was supported by Technion V. P. R. fund (grant No. 030-717), New York Metropolitan research fund.