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Showing papers by "J. N. Reddy published in 1995"


Journal ArticleDOI
TL;DR: In this article, a refined theory of laminated composite plates with piezoelectric laminae is developed using an energy principle, which includes coupling between mechanical deformations and the charge equations of electrostatics.

360 citations


Book
01 Jan 1995
TL;DR: Theoretical Background The Effect of Stress Concentration Examples Correlation of Theory and Experiment References for Additional Reading CRASH ANALYSIS Introduction Theoretical Formulation Cor correlation of theory and experiment References for additional Reading
Abstract: INTRODUCTION AND PRELIMINARIES Introduction Present Study Mathematical Preliminaries Exercise Problems References for Additional Reading REVIEW OF GOVERNING EQUATIONS Classification of Equations Kinematics Kinetics Constitutive Equations Summary Exercise Problems References for Additional Reading MECHANICAL BEHAVIOR OF COMPOSITE MATERIALS Terminology and Definitions Lamina Constitutive Equations Transformation of Stresses and Strains Constitutive Relations for Plane Stress Exercise Problems References for Additional Reading THEORIES OF LAMINATED PLATES Introduction Classical Laminated Plate Theory The First-Order Shear Deformation Theory Stiffness Characteristics of Selected Lamination Schemes Exercise Problems References for Additional Reading ANALYSIS OF RECTANGULAR PLATES Introduction The Navier Solutions The Levy Solutions Finite Element Models Computation of Stresses and Strains Example Problems References for Additional Reading FAILURES IN COMPOSITE LAMINATES Introduction Matrix Cracks Delaminations Fiber Pull/Push Out Failure Criteria References for Additional Reading VARIABLE THICKNESS STRUCTURES Introduction Theoretical Background The Effect of Stress Concentration Examples Correlation of Theory and Experiment References for Additional Reading CRASH ANALYSIS Introduction Theoretical Formulation Correlation of Theory and Experiment References for Additional Reading ANALYSIS OF LARGE STRUCTURES Introduction The Substructuring Technique Analysis Considerations The Design of a Bus Structure References for Additional Reading PRACTICAL ANALYSIS WITH DAC Introduction DAC Software DAC Plates/Sandwich Program DAC Reinforced Sandwiches Program Sample Applications Closure References for Additional Reading SUBJECT INDEX

101 citations


Journal ArticleDOI
TL;DR: In this paper, the authors presented results of the stress analysis of multilayered plates subject to thermal and mechanical loads in the context of the three-dimensional quasi-static theory of thermoelasticity.

95 citations


Journal ArticleDOI
TL;DR: In this article, a progressive failure algorithm is developed where the Generalized Layerwise Plate Theory (GLPT) of Reddy is used for the kinematic description and the material is modeled as a stable progressively fracturing solid.
Abstract: A progressive failure algorithm is developed where the Generalized Layerwise Plate Theory (GLPT) of Reddy is used for the kinematic description and the material is modeled as a stable progressively fracturing solid. The geometric non-linearity is taken into account in the von Karman sense, and the extensibility of transverse normals is included in the finite element formulation. The progressive failure algorithm is used to study the effect of the geometric non-linearity, span-to-depth ratio, lamination sequence and the boundary conditions at the supports on the first-ply and the ultimate failure loads of composite laminates in bending. In addition, a new stiffness reduction scheme is proposed, in which stiffness properties of the failed element is reduced gradually, resulting in partial unloading depending on the amount of damage it accumulates.

73 citations


Journal ArticleDOI
TL;DR: In this article, a power series solution is presented for the static equilibrium equations of an axisymmetric composite cylinder under loadings due to surface mounted or embedded piezoelectric laminae.
Abstract: A power series solution is presented for the static equilibrium equations of an axisymmetric composite cylinder under loadings due to surface mounted or embedded piezoelectric laminae. Both uniform and nonuniform distributions of the piezoelectric effect are studied and results are verified using a finite element model based on axisymmetric two-dimensional elasticity theory equations. A cylindrical truss element actuator is developed which may be used for damping vibrations of truss-type structures. Finally, the effects of a piezoelectric patch have been investigated. The axial forces generated at the fixed ends of a cylinder are found to be proportional to the length of the patch.

43 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the vibrations of inflatable dams and applied the finite element method to determine the equilibrium shape of the dam and then analyzed small vibrations about that configuration.
Abstract: Inflatable dams are used for various purposes, such as controlling flood-waters, diverting water for irrigation, impounding water for recreation, raising the height of existing spillways, and preventing beach erosion. They are flexible, cylindrical structures attached to a rigid, horizontal base. The vibrations of such dams are investigated in this paper. The dam is modelled as an elastic shell inflated with air and anchored along two of its generators. Both infinitely—long dams and dams of finite length are considered. Previous analyses have only considered two-dimensional vibrations and have assumed that the dam is an inextensible membrane. The finite element method is applied, first to determine the equilibrium shape of the dam and then to analyze small vibrations about that configuration. For the numerical examples, the lowest six vibration frequencies and corresponding mode shapes are obtained. The results are compared to those when no external water is present.

28 citations


Journal ArticleDOI
TL;DR: In this article, geometrically nonlinear theories of laminated composite plates with piezoelectric laminae are developed and the coupling between mechanical deformations, temperature changes, and electric displacements is investigated.
Abstract: In this paper geometrically nonlinear theories of laminated composite plates with piezoelectric laminae are developed The formulations are based on thermopiezoelectricity, and include the coupling between mechanical deformations, temperature changes, and electric displacements Two different theories are presented: one based on an equivalent-single-layer third-order theory and the other based on the layerwise theory, both of which were developed by the senior author for composite laminates without piezoelectric laminae In the present study, they are extended to include piezoelectric laminae In both theories, the electric field is expanded layerwise through the laminate thickness The dynamic version of the principle of virtual displacements (or Hamilton’s principle) is used to derive the equations of motion and associated boundary conditions of the two theories These theories may be used to accurately determine the response of laminated plate structures with piezoelectric laminae and subjected to thermomechanical loadings

24 citations


Book ChapterDOI
01 Jan 1995
TL;DR: In this article, an upper bound on the reduced stiffness of cross-ply laminates with transverse matrix cracks is derived, complementary to Hashin's lower bound, for a given density of matrix cracks, and the associated elasticity problem is solved using the Layerwise Laminate Theory of Reddy.
Abstract: Cross-ply laminates with transverse matrix cracks are studied using the variational approach. An upper bound on the reduced stiffness has been derived, complementary to Hashin’s lower bound, for a given density of matrix cracks. Staggerring in crack patterns is also considered. The associated elasticity problem is solved using the Layerwise Laminate Theory of Reddy. The effect of crack density on the crack opening displacements and stress transfer is examined.

5 citations


Journal ArticleDOI
TL;DR: In this article, a hybrid boundary element model is proposed for the analysis of layers, plates, and multilayered systems consisting of isotropic and linear elastic materials, based on the layerwise laminate theory of Reddy, which assumes piecewise continuous distribution of the displacement components through the system's thickness.
Abstract: A hybrid method is presented for the analysis of layers, plates, and multilayered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multilayered system using a total potential energy formulation. The layerwise laminate theory of Reddy is employed to develop a layerwise, two-dimensional, displacement-based, hybrid boundary element model that assumes piecewise continuous distribution of the displacement components through the system's thickness. A one-dimensional finite element model is used for the analysis of the multilayered system through its thickness, and integral Fourier transforms are used to obtain the exact solution for the in-plane problem. Explicit expressions are obtained for the fundamental solution of a typical infinite layer (element) assuming linear displacement distribution through its thickness. This fundamental solution is given in a closed form in the cartesian space, and it can be applied in the two-dimensional boundary integral equation model to analyze layered structures with finite dimensions. The proposed method provides a simple, efficient, and versatile model for a three-dimensional analysis of thick plates or multilayered systems.

4 citations


31 Dec 1995
TL;DR: In this article, the authors describe the finite element formulation and implementation of a micromechanics based constitutive model of pseudoelasticity, which accounts for behavior similar to isotropic and kinematic hardening of elastoplasticity.
Abstract: In this paper, we describe the finite element formulation and implementation of a micromechanics based constitutive model of pseudoelasticity. The constitutive model describes the behavior of SMA`s through a constitutive element (CE) consisting of several grains. A volume average over the CE provides the macroscopic continuum response. The remarkable feature of this model is its strong similarity to the incremental stress strain relations of elastoplasticity and the internal variable approach. The martensitic transformations are described through the evolution of martensite volume fraction over the CE. The model accounts for behavior similar to isotropic and kinematic hardening of elastoplasticity. The finite element formulation involves the linearization of the weak form, computation of the tangent stiffness, and a stress update based on the operator split method. A numerical result is presented to illustrate the accuracy of the finite element formulation with respect to the theoretical model.

2 citations


Journal ArticleDOI
TL;DR: In this paper, the Navier's equations of elasticity for compressible solids and the penalty function formulation of viscous incompressible fluids are utilized in a boundary element model to analyze problems in two dimensions.


Proceedings ArticleDOI
05 May 1995
TL;DR: In this article, a hybrid theory of laminated composite plates with piezoelectric laminae is presented, where an equivalentsingle layer theory is used for the mechanical displacement field whereas the potential function for piezo-electric lamine is modeled using a layerwise discretization in the thickness direction.
Abstract: A refined theory of laminated composite plates with piezoelectric laminae is presented. The formula-tion is based on linear piezoelectricity, and includes the coupling between mechanical deformations and thecharge equations of electrostatics. The theory developed herein is hybrid in the sense that an equivalentsingle layer theory is used for the mechanical displacement field whereas the potential function for piezo-electric laminae is modeled using a layerwise discretization in the thickness direction. For the equivalentsingle layer, the third—order shear deformation theory of Reddy is used. This hybrid feature is good inthat it demonstrates a way in which multilayered smart skin piezolectric structures may be analyzed toaccommodate multiple voltage inputs and/or sensor outputs.Keywords: analytical solutions, hybrid theory, composite laminates, piezoelectric laminae, shear defor-mation laminate theory, layerwise laminate theory. 1. INTRODUCTION The study of embedded or surface mounted piezoelectric materials in structures has received consid-erable attention in recent years. One reason for this is that it may be possible to create certain types ofstructures and systems capable of adapting to or correcting for changing operating conditions. The advan-tage of incorporating these special types of materials into the structure is that the sensing and actuatingmechanism becomes part of the structure by sensing and actuating strains directly.In order to utilize the strain sensing and actuating (SSA) properties of piezoelectric materials, theinteraction between the structure and the SSA material must be well understood. Mechanical models forstudying the interaction of piezoelectric patches surface mounted to beams have been developed by Crawleyand de Luis (1987) and Chandra and Chopra (1993). The study presented here is different from these in thatwe study laminated plates containing piezoelectric laminae. The SSA lamina can offer both a discrete effectsimilar to patches as well as a distributed effect. Lee (1990) derived a theory for laminated piezoelectricplates based upon classical plate theory where the linear piezoelectric constitutive equations were the onlysource of coupling between the electric field and the mechanical displacement field. Tiersten (1969) modeledsingle—layer piezoelectric plates, including the charge equations, but did not study laminates. Tzou andZhong (1993) derived governing equations for piezoelectric shells using the first—order shear deformationtheory and included the charge equations of electrostatics. From these equations, classical, and first—ordershear deformation plate theories were derived for single layer piezoelectric laminae.