Dynamic Analysis of Cold-Rolling Process Using the Finite-Element Method

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Sajan Kapil ◽  
Peter Eberhard ◽  
Santosha K. Dwivedy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Governing Equation ◽  
Degrees Of Freedom ◽  
Vertical Displacement ◽  
Work Roll ◽  
Equation Of Motion ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Element Method

In this work, the finite-element method (FEM) is used to develop the governing equation of motion of the working roll of a four-high rolling mill and to study its vibration due to different process parameters. The working roll is modeled as an Euler Bernoulli beam by taking beam elements with vertical displacement and slope as the nodal degrees-of-freedom in the finite-element formulation. The bearings at the ends of the working rolls are modeled using spring elements. To calculate the forces acting on the working roll, the interaction between the working roll and the backup roll is modeled by using the work roll submodel, and the interaction between the working roll and the sheet is modeled by using the roll bite submodel (Lin et al., 2003, “On Characteristics and Mechanism of Rolling Instability and Chatter,” ASME J. Manuf. Sci. Eng., 125(4), pp. 778–786). Nodal displacements and velocities are obtained by using the Newmark Beta method after solving the governing equation of motion of the working roll. The transient and steady-state variation of roll gap, exit thickness profile, exit stress, and sheet force along the length of the strip have been found for different bearing stiffnesses and widths of the strip. By using this model, one can predict the shape of the outcoming strip profile and exit stress variation which will be useful to avoid many defects, such as edge buckling or center buckling in rolling processes.

Fundamentals and Applications of the Finite-Element Method in Analyzing Structural and Nonstructural Marine Problems

1982 ◽  
Vol 19 (03) ◽  
pp. 272-292
Author(s):  
Donald Liu ◽  
Yung-Kuang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Static And Dynamic Analysis ◽  
Marine Industry ◽  
Wide Range ◽  
Element Method

The finite-element method has become a popular and effective tool not only for structural analysis, but also for a wide range of physical problems which are of particular interest to the marine industry. A brief review of the finite-element formulation for structural and nonstructural problems is presented. Applications to marine structures, including static and dynamic analysis and fracture mechanics, are given. Nonstructural applications to heat transfer and ship hydrodynamic problems are also demonstrated. Recent developments in the coupled fluid-structural interaction problem using the boundary integral method, which is considered as an extension of the finite-element method, are also described.

Renewed Inflation of Krafla Caldera, Iceland, since 2018: Sensitivity of Ground Deformation to lateral variation in Earth structure and architecture of the magmatic system explored with the Finite Element Method

2020 ◽  
Author(s):  
Chiara Lanzi ◽  
Vincent Drouin ◽  
Siqi Li ◽  
Freysteinn Sigmundsson ◽  
Halldor Geirsson ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Properties ◽  
Ground Deformation ◽  
Vertical Displacement ◽  
Magma Source ◽  
The Finite Element Method ◽  
Spherical Source ◽  
Horizontal Displacements ◽  
Element Method

<p>The Krafla volcanic area in Northern Volcanic Zone of Iceland was characterized by deflation starting in 1989, suggesting a general pressure decrease and/or volume contraction at depth, which then exponentially decayed until having no significant deformation since around 2000.  In summer 2018, the volcano behaviour changed to inflation as observed both by Global Navigation Satellite System (GNSS) geodesy  and Sentinel-1 satellite radar interferometry (InSAR). Inflation since 2018 occurs at a rate of 10-14 mm/yr, centered in the middle of the caldera. No significant change in seismicity has occurred in the area in 2018, but seismic moment release ocurrs at a higher rate since middle 2019. Gravity stations in the area were remeasured in November 2019 for allowing comparison with earlier observations, and for providing reference for later studies. Initial modelling of the geodetic data is carried out assuming that the deformation is caused by a spherical source of pressure in an uniform elastic half-space. The result suggests that the deformation can be broadly explained by a single source of magma inflow at depth around 3.9-7.5 km, with the best-fit value around 4-4.5 km. We also apply the Finite Element Method (FEM) to additionally consider modification of the deformation field caused by Earth’s elastic heterogeneities and the uncertain geometry and  depth of the magma source. A set of FEM models are built with the COMSOL Multiphysics software in a 50x50 km domain where we test three different geometries of the source: a spherical source (radius 1000 km), a prolate ellipsoid,  and an oblate ellipsoid (sill-like) source, at 2.5, 4.0 and 5.5 km of depth. We also build a model to test how the vertical and horizontal displacements may be influenced by different elastic properties (e.g. Young’s modulus; about an order of magnitude different within a caldera boundary) for these sources. The results show that lateral variations in material properites can have a significant influence on ground deformation. Low-value Young’s inside caldera boundaries compared to higher values outside caldera boundaries will in particular influence the vertical displacement: the vertical displacement is about half of of what it is the original modelling.  The ratio of vertical to horizontal displacements will thus also be modified. This can in turn influence the inferred magma source geometry as it depends on the displacement ratios. The outcome of our study will provide better constrain for the elastic properties in Krafla area, and help understand the magma intrusion rate in the area.</p>

scholarly journals A Map-plane Finite-element Model: Three Modeling Experiments

1989 ◽  
Vol 35 (119) ◽  
pp. 48-52 ◽  
Author(s):  
James L. Fastook ◽  
Judith E.. Chapman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Ice Sheet ◽  
Time Dependent ◽  
Element Formulation ◽  
Initial Surface ◽  
The Finite Element Method ◽  
Sheet Flow ◽  
Flow Law ◽  
Element Method

AbstractPreliminary results are presented on a solution of the two-dimensional time-dependent continuity equation for mass conservation governing ice-sheet dynamics. The equation is solved using a column-averaged velocity to define the horizontal flux in a finite-element formulation. This yields a map-plane model where flow directions, velocities, and surface elevations are defined by bedrock topography, the accumulation/ablation pattern, and in the time-dependent case by the initial surface configuration. This alleviates the flow-band model limitation that the direction of flow be defined and fixed over the course of the modeling experiment. The ability of the finite-element method to accept elements of different dimensions allows detail to be finely modeled in regions of steep gradients, such as ice streams, while relatively uniform areas, such as areas of sheet flow, can be economically accommodated with much larger elements. Other advantages of the finite-element method include the ability to modify the sliding and/or flow-law relationships without materially affecting the method of solution.Modeling experiments described include a steady-state reconstruction showing flow around a three-dimensional obstacle, as well as a time-dependent simulation demonstrating the response of an ice sheet to a localized decoupling of the bed. The latter experiment simulates the initiation and development of an ice stream in a region originally dominated by sheet flow. Finally, a simulation of the effects of a changing mass-balance pattern, such as might be anticipated from the expected carbon dioxide warming, is described. Potential applications for such a model are also discussed.SYMBOLS USEDa(x,y) Accumulation/ablation rate.A Flow-law parameter.B Sliding-law parameter.CijC Global capacitance matrix.f Fraction of the bed melted.Fij,F Global load vector.g Acceleration of gravity.hj,h Ice-surface elevation.H Ice thickness.k(x,y) Constitutive equation constant of proportionality.kij Global stiffness matrix.m Sliding-law exponent.n Flow-law exponent.ρ Density of ice.σ(x,y) Ice flux.t Time.U Column-average ice velocity.UF Column-average deformation (flow) velocity.US Sliding velocity.v Variational trial function.x,y Map-plane coordinates.

COMPUTATIONAL CONTACT MECHANICS BASED ON THE rp-VERSION OF THE FINITE ELEMENT METHOD

2011 ◽  
Vol 08 (03) ◽  
pp. 493-512 ◽  
Author(s):  
DAVID FRANKE ◽  
ERNST RANK ◽  
ALEXANDER DÜSTER
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
The Finite Element Method ◽  
Problem Size ◽  
Element Mesh ◽  
Polynomial Degree ◽  
Adaptive Discretization ◽  
Loss Of Regularity ◽  
Element Method

In this paper we present an rp-adaptive discretization strategy to perform unilateral two-dimensional (2D) mechanical contact simulations by combining the r- and p-versions of the finite element method (FEM). The p-version leaves the finite element mesh unchanged and increases the shape function's polynomial degree in order to obtain convergence toward the exact solution of the underlying mathematical model. The r-method relocates nodes of an existing FE-mesh to improve the discretization of a given problem without introducing additional degrees of freedom, therefore, keeping the problem size fixed. The rp-version, which is a combination of the two aforementioned methods, is used in our study to move a node of the FE-mesh to the end of the contact zone to account for the loss of regularity that arises due to the change from contact to noncontact along the edge. It will be shown that highly accurate results can be obtained by using high-order (p) finite elements in combination with the penalty method and a relocation (r) of element nodes.

Rotordynamics analysis of a quill-shaft coupling-rotor-bearing system

2014 ◽  
Vol 229 (8) ◽  
pp. 1385-1398 ◽  
Author(s):  
S Feng ◽  
HP Geng ◽  
L Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequency ◽  
Stiffness Matrix ◽  
Equation Of Motion ◽  
Numerical Results ◽  
The Finite Element Method ◽  
Rotor Bearing ◽  
Bearing System ◽  
Element Method

A quill-shaft coupling-rotor-bearing system is modeled and reported in this paper. The system consists of two rotors connected by a quill-shaft coupling in which each rotor is supported by two bearings. The stiffness matrix of the quill-shaft coupling is deduced and the equation of motion of the system is obtained by using the finite element method. Finally, the rotordynamics analysis of the system is conducted. The numerical results show that more frequency veering points occur for the quill-shaft coupling-rotor-bearing system compared with those of single rotor. In addition, the stiffness of the flexural element has significant effects on the first bending natural frequency of the quill shaft when the length of the quill shaft becomes shorter.

scholarly journals Simulation, Modeling and Experimental Research on the Thermal Effect of the Motion Error of Hydrostatic Guideways

Micromachines ◽  
2021 ◽  
Vol 12 (12) ◽  
pp. 1445
Author(s):  
Pengli Lei ◽  
Zhenzhong Wang ◽  
Chenchun Shi ◽  
Yunfeng Peng ◽  
Feng Lu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thermal Effect ◽  
Degrees Of Freedom ◽  
Machining Accuracy ◽  
The Finite Element Method ◽  
Initial State ◽  
Motion Error ◽  
Kinematics Model ◽  
Element Method

Hydrostatic guideways are widely applied in ultra-precision machine tools, and motion errors undermine the machining accuracy. Among all the influence factors, the thermal effect distributes most to motion errors. Based on the kinematic theory and the finite element method, a 3-degrees-of-freedom quasi-static kinematics model for motion errors containing the thermal effect was established. In this model, the initial state of the closed rail as a “black box” is regarded, and a self-consistent setting method for the initial state of the guide rails is proposed. Experiments were carried out to verify the thermal motion errors simulated by the finite element method and our kinematics model. The deviation of the measured thermal vertical straightness error from the theoretical value is less than 1 μm, which ensured the effectiveness of the model we developed.

Stability Analysis of Composite Perforated Annular Sector Plates Under Thermomechanical Loading by Finite Element Method

2018 ◽  
Vol 18 (07) ◽  
pp. 1850100 ◽  
Author(s):  
Alireza Shaterzadeh ◽  
Hamed Behzad ◽  
Mohammad Shariyat
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Mechanical Load ◽  
Perforated Plate ◽  
Curvilinear Coordinates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
The Stability ◽  
Element Method

This paper presents the stability analysis of a perforated plate with sector geometry made of composite materials. The sector of concern is a compound of graphite-epoxy and glass-epoxy with identical ply thickness but different fiber angles for each layer. The mechanical load conditions considered include uniform axial, circumferential, and biaxial pressure, while the thermal loading is specified to be uniform temperature increase over the whole sector. The existence of one or two circular holes has increased the complexity of analysis. To obtain solutions of high accuracy, the three-dimensional elasticity theory relations have been employed. Using the finite element method along with the stability condition of Trefftz, the buckling equation of the structure is derived. Green nonlinear strain-displacement relations are used to form the geometrical stiffness matrix. Unlike the finite element method used by other researches, a novel curved 3D B-Splined element is used to more accurately trace the displacement and stress variations of the structure. This element can be used in solution domains with geometric discontinuities, such as perforated plates and also meshed in the thickness direction. Moreover, instead of using the common von Karman assumptions, the most general form of the strain tensors in the curvilinear coordinates is adopted. The buckling load is obtained by extremizing the second variations of the total potential energy. The finite element formulation is coded in the MATLAB software. The effects of various parameters such as sector dimensions, dimensions of the hole, mechanical load directions, and fiber angles of each layer on the thermomechanical buckling is investigated.

Load-induced stiffness matrix of plates

2002 ◽  
Vol 29 (1) ◽  
pp. 181-184 ◽  
Author(s):  
Shi-Jun Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Closed Form Solutions ◽  
Stiffness Matrices ◽  
Support Conditions ◽  
Stiffening Effect ◽  
Element Method

In this paper, a rectangular plate element for the finite-element method, which takes into consideration the stiffening effect of dead loads, is proposed. The element stiffness matrices that include the effect of dead loads are derived. The effect of dead loads on dynamic behaviors of plates is analyzed using the finite-element method. It is shown that the stiffness of plates increases when the effect of dead loads is included in the calculation and that the effect is more significant for plates with a smaller stiffness. The validity of the proposed procedure is confirmed by numerical examples. Although the finite-element results obtained are in agreement with the approximate closed-form solutions, the proposed method based on a finite-element formulation is more easily applied to practical structures under various support conditions and various types of dead loads.Key words: load-induced stiffness matrix of plate, stiffening effect of dead loads.

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