A Three-Dimensional Inverse Problem of Estimating the Surface Thermal Behavior of the Working Roll in Rolling Process

1998 ◽  
Vol 122 (1) ◽  
pp. 76-82 ◽  
Author(s):  
Pao-Tung Hsu ◽  
Yue-Tzu Yang ◽  
Cha’o-Kuang Chen
Keyword(s):  
Boundary Conditions ◽  
Thermal Behavior ◽  
Measurement Errors ◽  
Inverse Analysis ◽  
Least Squares Method ◽  
Finite Difference Methods ◽  
Three Dimensional ◽  
Rolling Process ◽  
Initial Guess ◽  
The Matrix

A three-dimensional inverse analysis utilizes a different perspective to estimate the surface thermal behavior of the working roll in rolling process. The inverse analysis is based on the temperature reading taken inside the roll at several different locations. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary conditions. The present approach is to rearrange the matrix forms of the differential governing equations and estimate the surface unknown conditions of the working roll. Then, the linear least-squares method is adopted to find the solution. The advantages of this proposed inverse analysis method are that no prior information is needed regarding the functional form of the unknown quantities, no initial guess need be used and the numbers of iterations for calculation process is limited to one. The results show that only few measuring points are sufficient to estimate the boundary conditions when measurement errors are neglected. When measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions. [S1087-1357(00)70201-2]

Strengthening Effects of Single Particle with Different Mechanical Property on Ultra-Thin Rolling of AA1235 Aluminum Alloys

2017 ◽  
Vol 898 ◽  
pp. 1332-1339
Author(s):  
Cheng Wei Xia ◽  
Y.Z. Zhu ◽  
Ran Liu ◽  
Wei Long Fan ◽  
Xiao Hui Li
Keyword(s):  
Mechanical Property ◽  
Stress Concentration ◽  
Three Dimensional ◽  
Interaction Mechanism ◽  
Aluminum Foil ◽  
Rolling Process ◽  
3D Fem ◽  
Foil Rolling ◽  
The Matrix ◽  
Hardness Ratio

In aluminum foil rolling, the secondary particles may lead to stress concentration at the boundary between these particles and the matrix. Different types of particles would result in stress concentration at different levels. The three dimensional finite element modeling (3D-FEM) was used to simulate the effect of the particles with different hardness on mechanical properties of the matrix of AA1235 aluminum foils in its foil rolling process. The hardness ratio was used to evaluate the mechanical property of foils. It has been found that when the hardness ratio of the particle was similar to that of the matrix (R=1), the interaction mechanism of the dislocations with the particle was dislocation cutting way. When the hardness ratio of the particle to the matrix increased from 1 to 6, the interaction mechanism of the particle with the matrix changed from the dislocation cutting way to the Orowan dislocation bypass way. When the hardness ratio increased to as high as 6, dislocation interacted with the particle only by the Orowan dislocation bypass way.

An Inverse Method for Simultaneous Estimation of the Center and Surface Thermal Behavior of a Heated Cylinder Normal to a Turbulent Air Stream

2002 ◽  
Vol 124 (4) ◽  
pp. 601-608 ◽  
Author(s):  
Jiin-Hong Lin ◽  
Cha’o-Kuang Chen ◽  
Yue-Tzu Yang
Keyword(s):  
Boundary Conditions ◽  
Thermal Behavior ◽  
Measurement Errors ◽  
Boundary Behavior ◽  
Traditional Approach ◽  
Simultaneous Estimation ◽  
Unknown Boundary ◽  
Heated Cylinder ◽  
Air Stream ◽  
Unknown Boundary Conditions

A two-dimensional inverse analysis utilizes a different perspective to simultaneously estimate the center and surface thermal behavior of a heated cylinder normal to a turbulent air stream. A finite-difference method is used to discretize the governing equations and then a linear inverse model is constructed to identify the unknown boundary conditions. The present approach is to rearrange the matrix forms of the governing differential equations and estimate the unknown boundary conditions of the heated cylinder. Then, the linear least-squares-error method is adopted to find the solutions. The results show that only a few measuring points inside the cylinder are needed to estimate the unknown quantities of the thermal boundary behavior, even when measurement errors are considered. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown quantities, no initial guesses are required, no iterations in the calculating process are necessary, and the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can easily be identified.

scholarly journals DIFFERENCE METHODS TO ONE AND MULTIDIMENSIONAL INTERDIFFUSION MODELS WITH VEGARD RULE

2019 ◽  
Vol 24 (2) ◽  
pp. 276-296 ◽  
Author(s):  
Lucjan Sapa ◽  
Bogusław Bożek ◽  
Marek Danielewski
Keyword(s):  
Boundary Conditions ◽  
Finite Difference Methods ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Uniqueness Of Solutions ◽  
Strongly Coupled ◽  
Implicit Difference Schemes ◽  
Coupled Boundary Conditions ◽  
Difference Methods ◽  
The One

In this work we consider the one and multidimensional diffusional transport in an s-component solid solution. The new model is expressed by the nonlinear parabolic-elliptic system of strongly coupled differential equations with the initial and the nonlinear coupled boundary conditions. It is obtained from the local mass conservation law for fluxes which are a sum of the diffusional and Darken drift terms, together with the Vegard rule. The considered boundary conditions allow the physical system to be not only closed but also open. We construct the implicit finite difference methods (FDM) generated by some linearization idea, in the one and two-dimensional cases. The theorems on existence and uniqueness of solutions of the implicit difference schemes, and the theorems concerned convergence and stability are proved. We present the approximate concentrations, drift and its potential for a ternary mixture of nickel, copper and iron. Such difference methods can be also generalized on the three-dimensional case. The agreement between the theoretical results, numerical simulations and experimental data is shown.

Thermal Behavior of Rectangular Flux Channels With Discretely Specified Contact Flux and Temperature

2015 ◽  
Author(s):  
Masood Razavi ◽  
Yuri S. Muzychka ◽  
Serpil Kocabiyik
Keyword(s):  
Boundary Conditions ◽  
Thermal Behavior ◽  
Least Squares Method ◽  
Separation Of Variables ◽  
Heat Fluxes ◽  
Fourier Series Expansion ◽  
The Finite Element Method ◽  
Commercial Software Package ◽  
Good Agreement

In this paper, an analytical solution for the thermal behavior of rectangular flux channels with discretely specified boundary conditions is presented. The boundary conditions along the source plane can be a combination of contact temperatures, heat fluxes, and/or adiabatic. Convective cooling is applied along the sink plane, and the edges of the channel are assumed adiabatic. The governing equation of the system is the Laplace equation which is solved using the method of separation of variables and the least squares method. The solution is presented in the form of Fourier series expansion. As a case study, a symmetrical flux channel with a combination of five discretely specified boundary conditions, including temperature, heat flux and adiabatic conditions is considered. Temperature profile along the channel is calculated and compared with the Finite Element Method (FEM) using COMSOL commercial software package [1]. A good agreement is observed between the analytical and FEM results.

scholarly journals Cell-generated traction forces and the resulting matrix deformation modulate microvascular alignment and growth during angiogenesis

2014 ◽  
Vol 307 (2) ◽  
pp. H152-H164 ◽  
Author(s):  
Clayton J. Underwood ◽  
Lowell T. Edgar ◽  
James B. Hoying ◽  
Jeffrey A. Weiss
Keyword(s):  
Boundary Conditions ◽  
Compressive Strain ◽  
Three Dimensional ◽  
Image Data ◽  
Local Strain ◽  
Traction Forces ◽  
Various Boundary Conditions ◽  
The Matrix ◽  
Vitro Model

The details of the mechanical factors that modulate angiogenesis remain poorly understood. Previous in vitro studies of angiogenesis using microvessel fragments cultured within collagen constructs demonstrated that neovessel alignment can be induced via mechanical constraint of the boundaries (i.e., boundary conditions). The objective of this study was to investigate the role of mechanical boundary conditions in the regulation of angiogenic alignment and growth in an in vitro model of angiogenesis. Angiogenic microvessels within three-dimensional constructs were subjected to different boundary conditions, thus producing different stress and strain fields during growth. Neovessel outgrowth and orientation were quantified from confocal image data after 6 days. Vascularity and branching decreased as the amount of constraint imposed on the culture increased. In long-axis constrained hexahedral constructs, microvessels aligned parallel to the constrained axis. In contrast, constructs that were constrained along the short axis had random microvessel orientation. Finite element models were used to simulate the contraction of gels under the various boundary conditions and to predict the local strain field experienced by microvessels. Results from the experiments and simulations demonstrated that microvessels aligned perpendicular to directions of compressive strain. Alignment was due to anisotropic deformation of the matrix from cell-generated traction forces interacting with the mechanical boundary conditions. These findings demonstrate that boundary conditions and thus the effective stiffness of the matrix regulate angiogenesis. This study offers a potential explanation for the oriented vascular beds that occur in native tissues and provides the basis for improved control of tissue vascularization in both native tissues and tissue-engineered constructs.

Determination of Temperatures and Heat Fluxes on Surfaces and Interfaces of Multi-Domain Three-Dimensional Electronic Components

2003 ◽  
Author(s):  
Brian H. Dennis ◽  
Zhen-Xue Han ◽  
George S. Dulikravich
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Measurement Errors ◽  
Sparse Matrix ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Junction Temperature ◽  
Element Formulation ◽  
Finite Element Program ◽  
Element Program

A finite element method (FEM) formulation for the prediction of unknown steady boundary conditions in heat conduction for multi-domain three-dimensional solid objects is presented. The FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown, provided such quantities are sufficiently over-specified on other boundaries. An inverse finite element program has been previously developed and successfully tested on 3-D simple geometries. The finite element code uses an efficient sparse matrix storage scheme that allows treatment of realistic three-dimensional problems on personal computer. The finite element formulation also allows for very straight-forward treatment of geometries composed of many different materials. The inverse FEM formulation was applied to the prediction of die junction temperature distribution in a simple ball grid array (BGA) electronic package. Examples are presented with simulated measurement that include random measurement errors. Regularization was applied to control numerical error when large measurement errors were added to the over-specified boundary conditions.

Determination of Temperatures and Heat Fluxes on Surfaces and Interfaces of Multidomain Three-Dimensional Electronic Components

2004 ◽  
Vol 126 (4) ◽  
pp. 457-464 ◽  
Author(s):  
Brian H. Dennis ◽  
Zhen-xue Han ◽  
George S. Dulikravich
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Measurement Errors ◽  
Sparse Matrix ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Junction Temperature ◽  
Element Formulation ◽  
Finite Element Program ◽  
Element Program

A finite element method (FEM) formulation for the prediction of unknown steady boundary conditions in heat conduction for multidomain three-dimensional (3D) solid objects is presented. The FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown, provided such quantities are sufficiently overspecified on other boundaries. An inverse finite element program has been previously developed and successfully tested on 3D simple geometries. The finite element code uses an efficient sparse matrix storage scheme that allows treatment of realistic 3D problems on personal computer. The finite element formulation also allows for very straightforward treatment of geometries composed of many different materials. The inverse FEM formulation was applied to the prediction of die-junction temperature distribution in a simple ball grid array electronic package. Examples are presented with simulated measurements, which include random measurement errors. Regularization was applied to control numerical error when large measurement errors were added to the overspecified boundary conditions.

Designing TIMP (tissue inhibitor of metalloproteinases) variants that are selective metalloproteinase inhibitors

2003 ◽  
Vol 70 ◽  
pp. 201-212 ◽  
Author(s):  
Hideaki Nagase ◽  
Keith Brew
Keyword(s):  
Three Dimensional ◽  
Therapeutic Interventions ◽  
Tissue Inhibitors Of Metalloproteinases ◽  
Structural Basis ◽  
Structural Elements ◽  
Ridge Structure ◽  
Extracellular Matrix Components ◽  
Metalloproteinase Inhibitors ◽  
The Matrix ◽  
A Disintegrin And Metalloproteinase

The tissue inhibitors of metalloproteinases (TIMPs) are endogenous inhibitors of the matrix metalloproteinases (MMPs), enzymes that play central roles in the degradation of extracellular matrix components. The balance between MMPs and TIMPs is important in the maintenance of tissues, and its disruption affects tissue homoeostasis. Four related TIMPs (TIMP-1 to TIMP-4) can each form a complex with MMPs in a 1:1 stoichiometry with high affinity, but their inhibitory activities towards different MMPs are not particularly selective. The three-dimensional structures of TIMP-MMP complexes reveal that TIMPs have an extended ridge structure that slots into the active site of MMPs. Mutation of three separate residues in the ridge, at positions 2, 4 and 68 in the amino acid sequence of the N-terminal inhibitory domain of TIMP-1 (N-TIMP-1), separately and in combination has produced N-TIMP-1 variants with higher binding affinity and specificity for individual MMPs. TIMP-3 is unique in that it inhibits not only MMPs, but also several ADAM (a disintegrin and metalloproteinase) and ADAMTS (ADAM with thrombospondin motifs) metalloproteinases. Inhibition of the latter groups of metalloproteinases, as exemplified with ADAMTS-4 (aggrecanase 1), requires additional structural elements in TIMP-3 that have not yet been identified. Knowledge of the structural basis of the inhibitory action of TIMPs will facilitate the design of selective TIMP variants for investigating the biological roles of specific MMPs and for developing therapeutic interventions for MMP-associated diseases.

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