Showing papers by "J. N. Reddy published in 2003"

Moving least squares differential quadrature method and its application to the analysis of shear deformable plates

Abstract: A moving least squares differential quadrature (MLSDQ) method is developed and employed for the analysis of moderately thick plates based on the first-order shear deformation theory (FSDT). To carry out the analysis, the governing equations in terms of the generalized displacements (transverse deflection and two rotations) of the plate are formulated by employing the moving least squares approximation. The weighting coefficients used in the MLSDQ approximation are computed through a fast computation of shape functions and their derivatives. Numerical examples illustrating the accuracy, stability and convergence of the MLSDQ method are presented. Effects of support size, order of completeness and node irregularity on the numerical accuracy are investigated. Copyright © 2003 John Wiley & Sons, Ltd.

Frequency of Functionally Graded Plates with Three-Dimensional Asymptotic Approach

Abstract: The harmonic vibration problem of functionally graded plates is studied by means of a three-dimensional asymptotic theory formulated in terms of transfer matrix. Instead of using multiple time scales expansion, the frequency is determined in a much simpler way that renders the asymptotic method to be practically validated for finding any higher-order solutions. This is illustrated by applying the refined formulation to a functionally graded rectangular plate with simply supported edges. The locally effective material properties are estimated by the Mori–Tanaka scheme. Accurate natural frequencies associated with flexural, extensional, and thickness-stretching modes are provided.

Superelastic and Shape Memory Effects in Laminated Shape-Memory-Alloy Beams

Abstract: A simple shape-memory-alloy (SMA) model to simulate the superelastic behavior as well as the shape memory effect is proposed. It considers only the transformations from austenite to single-variant martensite and from single-variant martensite to austenite, taking into account the ine uence of the temperature in the constitutive relationship. The proposed SMA constitutive model is employed in a novel layerwise beam theory to develop new SMA beam e nite element models with suitable interpolation of the e eld variables involved. The e nite element models developed herein account for the time evolution SMA constitutive equations. In particular, the developed e nite elements treat the SMA material as reinforcement of elastic beams. Several applications are presented to assess the validity of the constitutive model and the proposed numerical procedure.

Green’s Functions for Infinite and Semi-infinite Anisotropic Thin Plates

Abstract: This paper presents fundamental solutions of an anisotropic elastic thin plate within the context of the Kirchhoff theory. The plate material is inhomogeneoous in the thickness direction. Two systems of problem's with non-self-equilibrated loads are solved. The first is concerned with in-plane concentrated forces and moments and in-plane discontinuous displacements and slopes, and the second with transverse concentrated forces. Exact closed-form Green's functions for infinite and semi-infinite plates are obtained using the recently established octet formalism by the authors for coupled stretching and bending deformations of a plate. The Green functions for an infinite plate and the surface Green functions for a semi-infinite plate are presented in a real form. The hoop stress resultants are also presented in a real form for a semi-infinite plate.

Dynamic Characteristics of Elastic Bonding in Composite Laminates: A Free Vibration Study

Abstract: In conventional analyses of composite laminates, the assumption of perfect bonding of adjoining layers is well accepted, although this is an oversimplification of the reality. It is possible that the bond strength may be less than that of the laminae. Thus, the study of weak bonding is an interesting focus area. In this study, an elastic bonding model based on three-dimensional theory of elasticity in a layerwise framework is used to study composite laminates. The differential quadrature (DQ) discretization is used to analyze the layerwise model. The present model enables the simulation of actual bonding stress states in laminated structures. The interfacial characteristics of transverse stress continuity as well as the kinematic continuity conditions are satisfied through the inclusion of the elastic bonding layer. The present model is employed to investigate the free vibration of thick rectangular cross-ply laminates of different boundary conditions and lamination schemes.

An asymptotic theory for vibrations of inhomogeneous/laminated piezoelectric plates

Abstract: An asymptotic theory for the vibration analysis of inhomogeneous monoclinic piezoelectric plates is developed by using small parameter expansion. The theory includes the important special case of a laminated plate in which each layer is homogeneous and orthotropic, but distinct from the other layers by having a different material or a different orientation. A hierarchy of two-dimensional equations of the same homogeneous operator for each order is reduced from the three-dimensional framework of linear piezoelectricity. The elasticity version of the leading-order equation is the same as that of the classical Kirchhoff inhomogeneous plate theory and, therefore, is easily solvable. By contrast, it is not straightforward to find solutions of the higher-order equations. The solvability condition is thus established for this purpose, by which higher-order frequency parameters are derived. The present theoretical formulation is examined by comparing the present asymptotic results with an exact three-dimensional solution for a piezoelectric bimorph strip, and excellent agreement is reached. Some new results are presented.

Computational procedures for the analysis of advanced materials and structures

Abstract: This paper deals with the development of a general finite element formulation of the layerwise theory that was proposed and advanced by the first author for laminated plate structures with piezoelectric materials (layers or patches). The formulation includes full electromechanical coupling. Several approximations are used for the primary variables of the theory in the thickness direction and different interpolation schemes are considered in the surface directions. A very good agreement is obtained for the models using cubic approximation in the thickness direction. The advantages of these models on the prediction of layer stresses are fully illustrated.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.