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Equivalent Problem (equivalent + problem)

Distribution by Scientific Domains

Engineering	100%

Selected Abstracts

On the discretization of problems involving periodic planar tilings

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2001
André Bénard
Abstract Features related to the discretization of problems characterized by simple periodic tilings using cells of various shapes are discussed. Various cell geometries that tile the plane periodically are considered. Equivalent problems are identified, where the discretization can take place on a parallelogram, regardless of the shape of the original cell. These equivalent problems also suggest a numbering of the equations that results in matrices with interesting and useful properties. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Designing materials with prescribed elastic properties using polygonal cells

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2003
Alejandro R. Diaz
Abstract An extension of the material design problem is presented in which the base cell that characterizes the material microgeometry is polygonal. The setting is the familiar inverse homogenization problem as introduced by Sigmund. Using basic concepts in periodic planar tiling it is shown that base cells of very general geometries can be analysed within the standard topology optimization setting with little additional effort. In particular, the periodic homogenization problem defined on polygonal base cells that tile the plane can be replaced and analysed more efficiently by an equivalent problem that uses simple parallelograms as base cells. Different material layouts can be obtained by varying just two parameters that affect the geometry of the parallelogram, namely, the ratio of the lengths of the sides and the internal angle. This is an efficient way to organize the search of the design space for all possible single-scale material arrangements and could result in solutions that may be unreachable using a square or rectangular base cell. Examples illustrate the results. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Some results in nonlinear QFT

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2001
A. Baños
Abstract Nonlinear QFT (quantitative feedback theory) is a technique for solving the problem of robust control of an uncertain nonlinear plant by replacing the uncertain nonlinear plant with an ,equivalent' family of linear plants. The problem is then finding a linear QFT controller for this family of linear plants. While this approach is clearly limited, it follows in a long tradition of linearization approaches to nonlinear control (describing functions, extended linearization, etc.) which have been found to be quite effective in a wide range of applications. In recent work, the authors have developed an alternative function space method for the derivation and validation of nonlinear QFT that has clarified and simplified several important features of this approach. In particular, single validation conditions are identified for evaluating the linear equivalent family, and as a result, the nonlinear QFT problem is reduced to a linear equivalent problem decoupled from the linear QFT formalism. In this paper, we review this earlier work and use it in the development of (1) new results on the existence of nonlinear QFT solutions to robust control problems, and (2) new techniques for the circumvention of problems encountered in the application of this approach. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Electromagnetic scattering from perfectly conducting periodic surfaces by transforming into equivalent boundary condition

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 8 2008
Necmi Serkan TezelArticle first published online: 28 MAY 200
Abstract In this study, electromagnetic scattering from perfectly conducting periodic surface have been solved by means of transformation of problem into equivalent problem, that is scattering from plane represented by high order inhomogeneous impedance boundary condition (IBC). High order impedance functions are determined by function of the roughness of the surface. Then, transformed equivalent problem is solved by means of series expansion method using Floquet modes. This transformation makes the problem simple formulation and computational effectively without involving calculation of slowly converging periodic Green's function. Results and computational times obtained by transform method and those obtained by Method of Moment (MoM) technique are compared. Good agreements are observed in results. It is also observed that transform method needs much less computational time than MoM method. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1997,2000, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23567 [source]