Showing papers by "J. N. Reddy published in 2001"

Three-dimensional thermomechanical deformations of functionally graded rectangular plates

Abstract: Three-dimensional thermomechanical deformations of simply supported, functionally graded rectangular plates are studied by using an asymptotic method. The locally effective material properties are estimated by the Mori–Tanaka scheme. The temperature, displacements and stresses of the plate are computed for different volume fractions of the ceramic and metallic constituents, and they could serve as benchmark results to assess two-dimensional approximate plate theories.

Three-Dimensional Solutions of Smart Functionally Graded Plates

Abstract: A smart functionally graded plate consists of a plate made of a functionally gradient material and actuators made of an active material. The active material, a layer or set of patches, is bonded on the metal-rich surface of the functionally graded plate. When the ceramic-rich surface of the substrate is subjected to thermomechanical loadings, displacements, and stresses may be controlled, and vibration amplitudes may be suppressed by the actuators with supplied electric power. In the attempt towards a basic understanding of the new type of smart structural system, this study considers a benchmark problem, namely, the bending of a functionally graded rectangular plate with an attached piezoelectric actuator. The transfer matrix and asymptotic expansion techniques are employed to obtain a three-dimensional asymptotic solution. In numerical computations, the locally effective material properties of the functionally gradient material are estimated by the Mori-Tanaka scheme, The three-dimensional distributions of displacements and stresses for different volume fractions of the ceramic and metallic constituents could serve as benchmark results to assess approximate theories and numerical methods.

Control of laminated composite plates using magnetostrictive layers

Abstract: In this paper, first-order shear deformation theory (FSDT) is employed to study vibration control of laminated composite plates. The magnetostrictive layers are used to control and enhance the vibration suppression via velocity feedback with a constant gain distributed control. Analytical solutions of the equations governing laminated plates with embedded magnetostrictive layers are obtained for simply-supported boundary conditions. The effects of material properties, lamination scheme, and placement of magnetostrictive layers with respect to laminate midplane on vibration suppression are studied in detail.

Generalized solutions of beams with jump discontinuities on elastic foundations

Abstract: The bending solutions of the Euler–Bernoulli and the Timoshenko beams with material and geometric discontinuities are developed in the space of generalized functions. Unlike the classical solutions of discontinuous beams, which are expressed in terms of multiple expressions that are valid in different regions of the beam, the generalized solutions are expressed in terms of a single expression on the entire domain. It is shown that the boundary-value problems describing the bending of beams with jump discontinuities on discontinuous elastic foundations have more compact forms in the space of generalized functions than they do in the space of classical functions. Also, fewer continuity conditions need to be satisfied if the problem is formulated in the space of generalized functions. It is demonstrated that using the theory of distributions (i.e. generalized functions) makes finding analytical solutions for this class of problems more efficient compared to the traditional methods, and, in some cases, the theory of distributions can lead to interesting qualitative results. Examples are presented to show the efficiency of using the theory of generalized functions.

ON p-VERSION HIERARCHICAL INTERPOLATION FUNCTIONS FOR HIGHER-ORDER CONTINUITY FINITE ELEMENT MODELS

Abstract: This paper presents a development of the p-version hierarchical interpolation functions in one, two three and higher dimensions. The interpolation functions may be used, for example, in obtaining strong solutions of differential equations. The concepts are presented first through the derivation of the Ci-functions in one dimension. Then the one-dimensional functions are used to derive the interpolation functions in two, three and higher dimensions. It is demonstrated that for rectangular finite elements the concepts presented herein allow the construction of any order hierarchical interpolation functions in one, two, three and higher dimensions. The necessary and sufficient conditions that must be satisfied by higher order continuity interpolation functions are presented. Theorems that insure that the proposed procedure of generating the higher order continuity interpolation functions are also presented. With this approach of constructing interpolations it is indeed possible to generate finite element interpolation functions with inter-element continuity in agreement with the strong solutions, which eliminate the need for the weak forms of differential equations.

Deformations of Piezothermoelastic Laminates with Internal Electrodes

Abstract: Deformations of multi-eleciroded laminates under thermoelectromechanical loads are studied. An asymptotic formulation is derived to reduce the three-dimensional problem to a hierarchy of two-dimensional equations and is examined by comparing the present results with an exact solution. New results are given by using the asymptotic scheme for ceramic multilayer actuators with interdigital electrodes.

Study of interlaminar stresses in composite laminates subjected to torsional loading

Abstract: A computational procedure for accurate determination of interlaminar stresses in thick and thin composite laminates subjected to torsional loading is presented. A multilevel, recursively defined preconditioner in conjunction with the preconditioned conjugate gradient (PCG) algorithm is constructed from a sequence of hierarchical vector spaces arising from the p-version of the finite element method. The computational procedure is used to model stress fields in thick and thin laminates in torsion using three-dimensional and quasi-three-dimensional models. Results indicate that the preconditioner developed here can be used to produce an efficient iterative solver for the determination of two- and three-dimensional stress fields in composite structures.

Vibration control of laminated composite plates using embedded smart layers

Abstract: Analytical solutions and finite element results of laminated composite plates with smart material layers embedded in them are presented in this study. The third-order plate theory of Reddy is used to study vibration suppression characteristics. The analytical solution for simply supported boundary conditions is based on the Navier solution procedure. The velocity feedback control is used. Parametric effects of the position of the smart material layers, material properties, and control parameters on the suppression time are investigated. It has been found that (a) the minimum vibration suppression time is achieved by placing the smart material layers farthest from the neutral axis, (b) using thinner smart material layers have better vibration attenuation characteristics, and, (c) the vibration suppression time is larger for a lower value of the feedback control coefficient.

Buckling and vibration of stepped, symmetric cross-ply laminated rectangular plates

Abstract: This paper presents the exact buckling loads and vibration frequencies of multi-stepped symmetric cross-ply laminated rectangular plates having two opposite edges simply supported while the other two edges may have any combination of free, simply supported, and clamped conditions. An analytical method that uses the Levy solution method and the domain decomposition technique is proposed to determine the buckling loads and natural frequencies of stepped laminated plates. Buckling and vibration solutions are obtained for symmetric cross-ply laminated rectangular plates having two-, three- and four-step thickness variations.

On the inelastic behavior of crystalline silicon at elevated temperatures

Abstract: The broad focus of this paper is on developing continuum models of inelastic response of crystalline materials that include the influence of microstructure, material symmetry, and dissipation of energy accompanying the changes in the microstructure. A framework has been developed, built on the idea of natural configurations of a material, that has provisions for explicit treatment of material microstructure (slip planes, dislocations, interfaces, etc.). It is demonstrated that the developed framework is applicable to diverse phenomena such as plasticity due to slip and twinning, and martensitic phase transformations. The developed framework is used to study the inelastic behavior of crystalline silicon at elevated temperatures.

A practical hybrid interior error estimator for localized h‐adaptive FEA

Abstract: A practical method for localized h ‐adaptive error estimation is presented based on interior estimates of the Galerkin solution. A previously published hybrid interior error estimator is revisited here and proper bounds are established. It is shown that in the present form of the estimator both the local accelerated convergence and the global superconvergence properties are maintained. The estimator is based on energy norms and all the computations are based on groups of connected elements. The resulting form of the estimator is shown to be simpler and more amenable to computational implementation than the previous one. Two plane elasticity problems are chosen as examples and both structured and h ‐adaptive global initial meshes are considered to compute the convergence characteristics of the solution in a few preselected zones. The solutions are benchmarked against conventional global h ‐adaptive superconvergent error estimators.