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Rectangular Plate (rectangular + plate)
Selected AbstractsThree-dimensional vibration analysis of rectangular thick plates on Pasternak foundationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2004D. Zhou Abstract The free-vibration characteristics of rectangular thick plates resting on elastic foundations have been studied, based on the three-dimensional, linear and small strain elasticity theory. The foundation is described by the Pasternak (two-parameter) model. The Ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation. The Chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction. The approach is suitable for rectangular plates with arbitrary boundary conditions. Convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions. It is shown that the present method has a rapid convergent rate, stable numerical operation and very high accuracy. Parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail, with respect to different thickness,span ratios and foundation parameters. Some results found for the first time have been given and some important conclusions have been drawn. Copyright © 2004 John Wiley & Sons, Ltd. [source] Application of a new differential quadrature methodology for free vibration analysis of platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2003G. Karami Abstract A new methodology is introduced in the differential quadrature (DQ) analysis of plate problems. The proposed approach is distinct from other DQ methods by employing the multiple boundary conditions in a different manner. For structural and plate problems, the methodology employs the displacement within the domain as the only degree of freedom, whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co-ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem. Employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently. In order to demonstrate the capability of the new methodology, all cases of free vibration analysis of rectangular isotropic plates, in which the conventional DQ methods have had some sort of difficulty to arrive at a converged or accurate solution, are carried out. Excellent convergence behaviour and accuracy in comparison with exact results and/or results obtained by other approximate methods were obtained. The analogous DQ formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised. It must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods. Copyright © 2002 John Wiley & Sons, Ltd. [source] Dynamic stability of a porous rectangular platePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Daniel Debowski The study is devoted to a axial compressed porous-cellular rectangular plate. Mechanical properties of the plate vary across is its thickness which is defined by the non-linear function with dimensionless variable and coefficient of porosity. The material model used in the current paper is as described by Magnucki, Stasiewicz papers. The middle plane of the plate is the symmetry plane. First of all, a displacement field of any cross section of the plane was defined. The geometric and physical (according to Hook's law) relationships are linear. Afterwards, the components of strain and stress states in the plate were found. The Hamilton's principle to the problem of dynamic stability is used. This principle was allowed to formulate a system of five differential equations of dynamic stability of the plate satisfying boundary conditions. This basic system of differential equations was approximately solved with the use of Galerkin's method. The forms of unknown functions were assumed and the system of equations was reduced to a single ordinary differential equation of motion. The critical load determined used numerically processed was solved. Results of solution shown in the Figures for a family of isotropic porous-cellular plates. The effect of porosity on the critical loads is presented. In the particular case of a rectangular plate made of an isotropic homogeneous material, the elasticity coefficients do not depend on the coordinate (thickness direction), giving a classical plate. The results obtained for porous plates are compared to a homogeneous isotropic rectangular plate. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Matched interface and boundary (MIB) method for the vibration analysis of platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2009S. N. Yu Abstract This paper proposes a novel approach, the matched interface and boundary (MIB) method, for the vibration analysis of rectangular plates with simply supported, clamped and free edges, and their arbitrary combinations. In previous work, the MIB method was developed for three-dimensional elliptic equations with arbitrarily complex material interfaces and geometric shapes. The present work generalizes the MIB method for eigenvalue problems in structural analysis with complex boundary conditions. The MIB method utilizes both uniform and non-uniform Cartesian grids. Fictitious values are utilized to facilitate the central finite difference schemes throughout the entire computational domain. Boundary conditions are enforced with fictitious values,a common practice used in the previous discrete singular convolution algorithm. An essential idea of the MIB method is to repeatedly use the boundary conditions to achieve arbitrarily high-order accuracy. A new feature in the proposed approach is the implementation of the cross derivatives in the free boundary conditions. The proposed method has a banded matrix. Nine different plates, particularly those with free edges and free corners, are employed to validate the proposed method. The performance of the proposed method is compared with that of other established methods. Convergence and comparison studies indicate that the proposed MIB method works very well for the vibration analysis of plates. In particular, modal bending moments and shear forces predicted by the proposed method vanish at boundaries for free edges. Copyright © 2008 John Wiley & Sons, Ltd. [source] Solution of clamped rectangular plate problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2004Robert L. Taylor Abstract In this brief note, we present an efficient scheme for determining very accurate solutions to the clamped rectangular plate problem. The method is based upon the classical double cosine series expansion and an exploitation of the Sherman,Morrison,Woodbury formula. If the cosine expansion involves M terms and N terms in the two plate axes directions, then the classical method for this problem involves solving a system of (MN) × (MN) equations. Our proposal reduces the problem down to a system of well-conditioned N × N equations (or M × M when M < N). Numerical solutions for rectangular plates with various side ratios are presented and compared to the solution generated via Hencky's method. Corrections to classical results and additional digits for use in finite-element convergence studies are given. As an application example, these are used to show the rate of convergence for thin plate finite-element solutions computed using the Bogner,Fox,Schmit element. Copyright © 2004 John Wiley & Sons, Ltd. [source] Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2004D. Zhou Abstract The free-vibration characteristics of rectangular thick plates resting on elastic foundations have been studied, based on the three-dimensional, linear and small strain elasticity theory. The foundation is described by the Pasternak (two-parameter) model. The Ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation. The Chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction. The approach is suitable for rectangular plates with arbitrary boundary conditions. Convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions. It is shown that the present method has a rapid convergent rate, stable numerical operation and very high accuracy. Parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail, with respect to different thickness,span ratios and foundation parameters. Some results found for the first time have been given and some important conclusions have been drawn. Copyright © 2004 John Wiley & Sons, Ltd. [source] Organic Electro-optic Single- Crystalline Thin Films Grown Directly on Modified Amorphous Substrates,ADVANCED MATERIALS, Issue 3 2008O-P. Kwon High quality organic electro-optic single crystalline thin films are produced on amorphous C,N-modified glass substrates (see figure), which is a mimic surface of a crystal, by slow evaporation and capillary methods. The films have a suitable size (shaped as rectangular plates with side lengths in the range of 5,10 mm and regular thicknesses in the range of 1,40 ,m) for the fabrication of photonic devices. [source] Non-Asymptotic Modelling of Medium Thickness Plates with Plane Periodic StructurePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Eugeniusz BaronArticle first published online: 26 FEB 200 The main aim of this contribution are presented a certain selected problems (aspects) of non,asymptotic modelling of medium thickness (or Reissner,type) rectangular plates with a plane periodic in,homogeneous structure. In course of non,asymptotic modeling, by using tolerance averaging technique (TAT), apart from the known separation for biperiodic and uniperiodic plates, it is necessary to introduce extra partitions. The four non,asymptotic models of plates with plane periodic structure can be led out independently (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] New species of the diatom genus Fryxelliella (Bacillariophyta), Fryxelliella pacifica sp. nov., from the tropical Mexican PacificPHYCOLOGICAL RESEARCH, Issue 3 2008David U. Hernández-Becerril SUMMARY During phytoplankton monitoring of coasts off Salina Cruz, Oaxaca, in the tropical Mexican Pacific, a new species, Fryxelliella pacifica sp. nov., was found and is described in this paper. The species is solitary, with cells of medium size, discoid with three relatively large ocelli on the valve face, located close to the margins (3,5 areolae from the margins) and placed symmetrically. Significantly, it possesses the morphological characters that distinguish the genus Fryxelliella from related genera: the presence of the ,circumferential marginal tube' (siphon marginalis), the external subcircular or subtriangular apertures at the valve margins, and the ,juxtaposed rectangular plates' in the valve mantle. The species that appears to be the most closely related is Fryxelliella floridana Prasad, an extant species and the type of the genus. However Fryxelliella pacifica differs from it (i) the size and shape of the cell; (ii) the size, location and structure of the ocelli (which additionally are not elevated); (iii) the shape and density of the subcircular to subtriangular marginal apertures; (iv) the external morphology of the rimoportulae (short process, two concentric tubes with the outer tube tip as a crown); and (v) it is marine rather than brackish. Externally the rimoportulae have a rather complex structure of two concentric tubes: the exterior tube has a tip divided like a crown. In spite of the fact this species was found in plankton samples, it is considered to inhabit sandy sediments (epipsammic) or as tychoplanktonic. [source] | ||||||||||