Showing papers by "J. N. Reddy published in 2004"
Book•
01 Jan 2004
TL;DR: In this article, the authors present an analysis of the properties of composite materials using the classical and first-order theories of Laminated Composite Plates and shells, as well as a detailed analysis of their properties.
Abstract: Equations of Anisotropic Elasticity, Virtual Work Principles, and Variational Methods Fiber-Reinforced Composite Materials Mathematical Preliminaries Equations of Anisotropic Entropy Virtual Work Principles Variational Methods Summary Introduction to Composite Materials Basic Concepts and Terminology Constitutive Equations of a Lamina Transformation of Stresses and Strains Plan Stress Constitutive Relations Classical and First-Order Theories of Laminated Composite Plates Introduction An Overview of Laminated Plate Theories The Classical Laminated Plate Theory The First-Order Laminated Plate Theory Laminate Stiffnesses for Selected Laminates One-Dimensional Analysis of Laminated Composite Plates Introduction Analysis of Laminated Beams Using CLPT Analysis of Laminated Beams Using FSDT Cylindrical Bending Using CLPT Cylindrical Bending Using FSDT Vibration Suppression in Beams Closing Remarks Analysis of Specially Orthotropic Laminates Using CLPT Introduction Bending of Simply Supported Rectangular Plates Bending of Plates with Two Opposite Edges Simply Supported Bending of Rectangular Plates with Various Boundary Conditions Buckling of Simply Supported Plates Under Compressive Loads Buckling of Rectangular Plates Under In-Plane Shear Load Vibration of Simply Supported Plates Buckling and Vibration of Plates with Two Parallel Edges Simply Supported Transient Analysis Closure Analytical Solutions of Rectangular Laminated Plates Using CLPT Governing Equations in Terms of Displacements Admissible Boundary Conditions for the Navier Solutions Navier Solutions of Antisymmetric Cross-Ply Laminates Navier Solutions of Antisymmetric Angle-Ply Laminates The Levy Solutions Analysis of Midplane Symmetric Laminates Transient Analysis Summary Analytical Solutions of Rectangular Laminated Plates Using FSDT Introduction Simply Supported Antisymmetric Cross-Ply Laminated Plates Simply Supported Antisymmetric Angle-Ply Laminated Plates Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported Transient Solutions Vibration Control of Laminated Plates Summary Theory and Analysis of Laminated Shells Introduction Governing Equations Theory of Doubly-Curved Shell Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Shells Linear Finite Element Analysis of Composite Plates and Shells Introduction Finite Element Models of the Classical Plate Theory (CLPT) Finite Element Models of Shear Deformation Plate Theory (FSDT) Finite Element Analysis of Shells Summary Nonlinear Analysis of Composite Plates and Shells Introduction Classical Plate Theory First-Order Shear Deformation Plate Theory Time Approximation and the Newton-Raphson Method Numerical Examples of Plates Functionally Graded Plates Finite Element Models of Laminated Shell Theory Continuum Shell Finite Element Postbuckling Response and Progressive Failure of Composite Panels in Compression Closure Third-Order Theory of Laminated Composite Plates and Shells Introduction A Third-Order Plate Theory Higher-Order Laminate Stiffness Characteristics The Navier Solutions Levy Solutions of Cross-Ply Laminates Finite Element Model of Plates Equations of Motion of the Third-Order Theory of Doubly-Curved Shells Layerwise Theory and Variable Kinematic Model Introduction Development of the Theory Finite Element Model Variable Kinematic Formulations Application to Adaptive Structures Layerwise Theory of Cylindrical Shell Closure Subject Index
3,457 citations
25 Mar 2004
TL;DR: The Finite Element Method: A Review 3. Heat Transfer and other Field Problems in One Dimension 4. Nonlinear Bending of Straight Beams 5. Bending Elastic Plates 7. Flows of Viscous Incompressible Fluids 8. Non-linear Analysis of Time-Dependent Problems 9. Finite Elements Formulations of Solids and Structures 10. Material Nonlinearities and Coupled Problems as mentioned in this paper
Abstract: 1. Introduction 2. The Finite Element Method: A Review 3. Heat Transfer and other Field Problems in One Dimension 4. Nonlinear Bending of Straight Beams 5. Heat Transfer and other Field Problems in Two Dimensions 6. Nonlinear Bending of Elastic Plates 7. Flows of Viscous Incompressible Fluids 8. Nonlinear Analysis of Time-Dependent Problems 9. Finite Element Formulations of Solids and Structures 10. Material Nonlinearities and Coupled Problems A1 Solution Procedures for Nonlinear Equations A2 Banded Symmetric and Unsymmetric Solvers
896 citations
Book•
15 Jun 2004
TL;DR: Exact solutions for buckling of structural members have been presented in this article, which can serve as benchmarks for checking the validity, convergence, and accuracy of numerical methods and solutions.
Abstract: The study of buckling loads, which often hinges on numerical methods, is key in designing structural elements. But the need for analytical solutions in addition to numerical methods is what drove the creation of Exact Solutions for Buckling of Structural Members. It allows readers to assess the reliability and accuracy of solutions obtained by numerical methods. The author has attempted to gather and present as many exact buckling solutions as possible in one single volume for engineers and researchers. These buckling solutions of columns, beams, arches, ring plates, and shells should serve as benchmarks for checking the validity, convergence, and accuracy of numerical methods and solutions. Catalog Copy.
354 citations
TL;DR: In this paper, a review of the shear deformation plate and shell theories is presented and a consistent third-order theory for composite shells is proposed, which has seven displacement functions satisfying the tangential traction-free conditions on the inner and outer surfaces of the shell.
Abstract: In this paper, a review of the shear deformation plate and shell theories is presented and a consistent third-order theory for composite shells is proposed. The discussion of plate and shell theories from Stavsky to the present is largely a review of various theories for modeling laminated shells, including shear effects and some analytical studies. Following this discussion, a finite element formulation of the proposed theory is developed. The formulation has seven displacement functions satisfying the tangential traction-free conditions on the inner and outer surfaces of the shell. Exact computations of stress resultants are carried out through numerical integration of material stiffness coefficients of the laminate. Numerical examples are presented for typical benchmark problems involving isotropic and composite plates, and cylindrical and spherical shells.
161 citations
TL;DR: In this paper, a partial mixed layerwise finite element model for adaptive plate structures is presented by considering a Reissner mixed variational principle, and the mixed functional is formulated using transverse stresses, displacement components and electric and magnetic potentials as primary variables.
148 citations
TL;DR: In this article, a new approach to conduct scratch tests on polymers is proposed, which includes the consideration of material parameters, use of microscopy for image analysis and the finite element method (FEM).
142 citations
TL;DR: In this article, the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space time decoupled formulation where a least square minimisation procedure is performed in space at each time step.
120 citations
TL;DR: In this article, a mesh-free radial basis function (RBF) method is employed for the buckling analysis of non-uniformly loaded thick plates, where the field variables are approximated using a set of scattered nodes in the problem domain.
105 citations
TL;DR: In this article, the transient response of laminated composite plates with embedded smart material layers is studied using a unified plate theory that includes the classical, first-order, and third-order plate theories.
77 citations
TL;DR: In this article, a finite element model has been derived to formulate the dynamics of the composite shells integrated with the patches of active constrained layer damping (ACLD) treatment, and the optimal size of the patches located at the optimal places has been determined on the basis of a frequency constraint.
Abstract: Active control of the vibration of laminated circular cylindrical composite shells has been demonstrated using optimally placed patches of active constrained layer damping (ACLD) treatment. A finite element model has been derived to formulate the dynamics of the composite shells integrated with the patches of ACLD treatment. Optimal placements of the patches are determined by employing a modal controllability criterion to control the first two modes of vibration. The optimal size of the patches located at the optimal places has been determined on the basis of a frequency constraint. The performance of these patches in enhancing the damping of the symmetric cross-ply and angle-ply laminated shells has been illustrated with frequency response functions of the shells.
65 citations
TL;DR: In this paper, a Reissner mixed variational principle is used to formulate the finite element model for piezolaminated plate structures and the mixed functional is formulated using transverse stresses, transverse electrical displacement (if continuity, across the thickness, is required), displacement components and electrical potential as primary variables.
TL;DR: In this paper, the third-order shear deformation theories of laminated composite shells are developed using the strain-displacement relations of Donnell and Sanders theories, which also account for geometric nonlinearity in the von Karman sense.
Abstract: Third-order shear deformation theories of laminated composite shells are developed using the strain–displacement relations of Donnell and Sanders theories. These theories also account for geometric nonlinearity in the von Karman sense. Analytical (Navier) solutions for vibration suppression in cross-ply laminated composite shells with surface mounted smart material layers are developed using the linear versions of the two shell theories and for simply supported boundary conditions. Numerical results are presented to bring out the parametric effects of shell types (cylindrical, spherical, and doubly curved shells) and material properties on vibration suppression. A simple negative velocity feedback control in a closed loop is used.
TL;DR: The mesh-free moving least-squares differential quadrature (MLSDQ) method as mentioned in this paper was proposed for solving the fourth-order, partial differential equation governing the bending of thin plates according to classical plate theory.
TL;DR: In this paper, a micropump actuated by electrostatic forces is dynamically analyzed using the boundary element method to solve the quasi-3D Laplace equation that the potential difference satisfies in order to obtain the surface charge density and corresponding electrostatic force.
TL;DR: It is demonstrated that when the boundary value problems are described by non-linear differential operators, Galerkin processes and weak forms can never be variationally consistent and hence result in degenerate computational processes and suffer from same problems as in the case of non-self-adjoint operators.
Abstract: In the companion papers [1,2], authors introduced the concepts of k-version of finite element method and k, hk, pk, hkp-processes of the finite element method for boundary value problems described by self-adjoint and non-self adjoint operators using Ĥk,p(Ω) spaces with specific details including numerical studies for weak forms and least square processes. It was demonstrated that a variationally consistent (VC) weak form is possible when the differential operator is self-adjoint, however, in case of non-self-adjoint operators the weak forms are variationally inconsistent (VIC) which lead to degenerate computational processes that can produce spurious oscillations in the computed solutions. In this paper we demonstrate that when the boundary value problems are described by non-linear differential operators, Galerkin processes and weak forms can never be variationally consistent and hence result in degenerate computational processes and suffer from same problems as in the case of non-self-adjoint operators ...
TL;DR: The most significant finding of this study is that the deflection response does not fall intermediate to those of the metal or ceramic plates, due to the nonlinear coupling of mechanical and thermal contributions.
Abstract: Linear and nonlinear thermomechanical response of the functionally graded (metal-ceramic) plates subjected to static and dynamic loads is studied. The third-order plate theory of Reddy with the von Karman geometric nonlinearity is used for the kinematic and kinetic descriptions, and two constitutent power-law distribution through the plate thickness is employed. A displacement finite element model is developed with the Newmark time integration scheme, and the Newton-Raphson iterative procedure is used for the solution of nonlinear algebraic equations. While the model is general enough to be used for any boundary conditions, the simply supported and clamped boundary conditions are used to study the parametric effect of the power-law index and surface temperatures and mechanical loads on the thermomechanical response. The most significant finding of this study is that the deflection response does not fall intermediate to those of the metal or ceramic plates. This is due to the nonlinear coupling of mechanical and thermal contributions.
TL;DR: In this article, a general finite element formulation using the layerwise theory is developed for the analysis of laminated plate structures with piezoelectric layers or patches, and a very good agreement is obtained for the models using cubic approximation in the thickness direction.
TL;DR: In this paper, a finite element formulation for the bending of thin and thick plates based on least-squares variational principles is presented, where high-order nodal expansions are used to construct the discrete finite element model based on the least square formulation.
Abstract: A finite element formulation for the bending of thin and thick plates based on least-squares variational principles is presented. Finite element models for both the classical plate theory and the first-order shear deformation plate theory (also known as the Kirchhoff and Mindlin plate theories, respectively) are considered. High-order nodal expansions are used to construct the discrete finite element model based on the least-squares formulation. Exponentially fast decay of the least-squares functional, which is constructed using the L2 norms of the equations residuals, is verified for increasing order of the nodal expansions. Numerical examples for the bending of circular, rectangular and skew plates with various boundary conditions and plate thickness are presented to demonstrate the predictive capability and robustness of the new plate bending elements. Plate bending elements based on this formulation are shown to be insensitive to both shear-locking and geometric distortions. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this paper, a mixed layerwise finite element model for adaptive plate structures is presented, in contrast with the standard layerwise displacement finite element (LDFE) model, which fulfils the continuity of all primary variables across the interface between adjacent layers.
TL;DR: In this article, the buckling and postbuckling behavior of laminated cylindrical shells under axial compression and lateral pressure loading are investigated and a nonlinear theory for thin cylinders incorporating the effects of transverse shear deformation is employed.
Abstract: In the present work the buckling and postbuckling behavior of laminated cylindrical shells under axial compression and lateral pressure loading are investigated. A nonlinear theory for thin cylinders incorporating the effects of transverse shear deformation is employed. A modal solution based on the Koiter theory is utilized to derive the nonlinear equilibrium equations for the postcritical behavior of the shell. The Rayleigh–Ritz method is used to obtain analytical solutions for the critical load through algebraic routines written in Maple. Prebuckling and postbuckling equations are also solved by using symbolic computation. The influence played by geometrical parameters of the cylinder and physical parameters of the laminate (i.e. fiber orientation of each lamina, material properties and number of layers) on the critical and postcritical behavior of the shell is examined. It is noticed that the stability of shells is highly dependent on laminate characteristics and, from these observations, it is concluded that specific configurations of laminates should be designed for each kind of application.
TL;DR: In this article, an exact closed-form solution for coupled stretching and bending deformations of the plate subjected to remote uniform membrane stress resultants and bending moments is obtained, which is consistent with the uniformity property of the Eshelby inclusion solution in 3D elasticity.
TL;DR: In this paper, a two-dimensional finite-element formulation and solution of a set of transient coupled heat and diffusive moisture transfer equations is presented for stepwise convective drying of banana slices.
Abstract: A two-dimensional finite-element formulation and solution of a set of transient coupled heat and diffusive moisture transfer equations is presented. The solution procedure developed uses an alpha family of approximation for stepping in time for the solution of the coupled set of equations applied to simulate the stepwise convective drying behavior of banana slices. The model tested was validated with experimental data from different sources for stepwise drying of banana using a heat pump dryer (HPD) as well as continuous batch drying in both Cartesian and cylindrical coordinate systems. The maximum deviation of moisture content between experimental and simulation results was 0.05% wet basis (% w.b.). Good agreement of the simulated results with experimental data for stepwise as well as continuous convective drying of banana samples indicates the validity of the procedure and its incorporation in the optimization of drying processes.
TL;DR: In this paper, the authors present numerical simulation results for the compressible Euler equations and compressible Navier-Stokes equations using least-squares finite element models for the high and low-speed compressible flow regime.
TL;DR: In this article, the first-order shear deformation shell theory (FSDT) is used to represent the shell kinematics and equations of motion, and the exact solution for symmetric laminated shells with embedded actuating layers under simply supported boundary conditions is obtained using the Navier solution procedure.
Abstract: Analytical solutions of laminated composite shells with embedded actuating layers are presented in this study. The magnetostrictive actuating layers are used to control natural vibration of laminated composite shell panels. The first-order shear deformation shell theory (FSDT) is used to represent the shell kinematics and equations of motion. The exact solution for symmetric laminated shells with embedded actuating layers under simply supported boundary conditions is obtained using the Navier solution procedure. Negative velocity feedback control is used. The parametric effects of the position of the magnetostrictive layers, material properties and control parameters on the vibration suppression are investigated in detail.
TL;DR: In this paper, the effects of shear deformation and geometric nonlinearity on the bending and transient response are investigated using the finite element method, where magnetostrictive material, Terfenol-D, layers are used to actively control the deflection via simple negative velocity feedback control in a closed loop.
Abstract: In this paper, the third-order shear deformation theory is employed to study static and dynamic deflection control of laminated composite plates. The effects of shear deformation and geometric nonlinearity (in the von Karman sense) on the bending and transient response are investigated using the finite element method. Magnetostrictive material, Terfenol-D, layers are used to actively control the deflection via simple negative velocity feedback control in a closed loop. The effects of the lamination scheme, types of load, and boundary conditions on the deflection are investigated.
TL;DR: In this article, the surface Green functions for an infinite anisotropic elastic thin plate with a Griffith crack or an anticrack (rigid line inclusion) were studied and the intensity factor of membrane stress resultants and bending moments were obtained in a real form for the Griffith crack subjected to concentrated loads.
TL;DR: A finite element model is developed for the laminated composite plates integrated with the patches of ACLD treatment to describe the coupled structural-acoustic behavior of the plates enclosing an acoustic cavity.
Abstract: This paper deals with the active structural acoustic control of thin laminated composite plates using piezoelectric fiber-reinforced composite (PFRC) material for the constraining layer of active constrained layer damping (ACLD) treatment. A finite element model is developed for the laminated composite plates integrated with the patches of ACLD treatment to describe the coupled structural-acoustic behavior of the plates enclosing an acoustic cavity. The performance of the PFRC layers of the patches has been investigated for active control of sound radiated from thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite plates into the acoustic cavity. The significant effect of variation of piezoelectric fiber orientation in the PFRC layer on controlling the structure-borne sound radiated from thin laminated plates has been investigated to determine the fiber angle in the PFRC layer for which the structural-acoustic control authority of the patches becomes maximum.
TL;DR: In this paper, a finite element model has been derived to formulate the dynamics of the composite beams integrated with a patch of ACLD treatment and a piece of piezoelectric film acting as a distributed sensor with and without the presence of delamination.
Abstract: An ove lw ork demonstrates the effect of delamination in smart laminated composite beams on the performance of active constrained layer damping (ACLD) treatment. A finite element model has been derived to formulate the dynamics of the composite beams integrated with a patch of ACLD treatment and a patch of piezoelectric film acting as a distributed sensor with and without the presence of delamination at different locations. Frequency response functions of the beams have been examined to observe the effect of delamination on the performance of ACLD treatment. It has been observed that the ACLD treatment improves the active damping characteristics of the beams, even in the presence of delamination, and that the responses of the beams are sensitive to the variation of the location of delamination. The responses due to active constrained layer damping presented may provide a useful guide to detect the presence of delamination in smart composite beams by the use of the existing numerical techniques.
TL;DR: In this article, a flexible computational procedure for solving 3D linear elastic structural mechanics problems is presented that currently uses three forms of approximation function (natural neighbour, moving least squares, and Lagrange polynomial) and three types of integration grids to reproduce the natural element method and the finite element method.
Abstract: A flexible computational procedure for solving 3D linear elastic structural mechanics problems is presented that currently uses three forms of approximation function (natural neighbour, moving least squares—using a new nearest neighbour weight function—and Lagrange polynomial) and three types of integration grids to reproduce the natural element method and the finite element method. The addition of more approximation functions, which is not difficult given the structure of the code, will allow reproduction of other popular meshless methods. Results are presented that demonstrate the ability of the first-order meshless approximations to capture solutions more accurately than first-order finite elements. Also, the quality of integration for the three types of integration grids is compared. The concept of a region is introduced, which allows the splitting of a domain into different sections, each with its own type of approximation function and spatial integration scheme. Copyright © 2004 John Wiley & Sons, Ltd.