Showing papers by "J. N. Reddy published in 2000"

Analysis of functionally graded plates

Abstract: Theoretical formulation, Navier's solutions of rectangular plates, and finite element models based on the third-order shear deformation plate theory are presented for the analysis of through-thickness functionally graded plates. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The formulation accounts for the thermomechanical coupling, time dependency, and the von Karman-type geometric non-linearity. Numerical results of the linear third-order theory and non-linear first-order theory are presented to show the effect of the material distribution on the deflections and stresses. Copyright © 2000 John Wiley & Sons, Ltd.

Shear deformable beams and plates: relationships with classical solutions

Abstract: Part and chapter headings: Preface. Introduction. Beams. Bending of Beams. Shear-Flexural Stiffness Matrix. Buckling of Columns. Tapered Beams. Plates. Theories of Plate Bending. Bending Relationships for Simply Supported Plates. Bending Relationships for Levy Solutions. Bending Relationships for Circular and Annular Plates. Bending Relationships for Sectorial Plates. Buckling Relationships. Free Vibration Relationships. Relationships for Inhomogeneous Plates. Subject index.

On vibration suppression of magnetostrictive beams

Abstract: Laminated composite beams containing magnetostrictive layers are modeled as distributed parameter systems and the magnetostrictive layers are used to control the vibration suppression. Velocity feedback with constant gain distributed controller is chosen to achieve vibration suppression. A general formulation of the problem based on classical and shear deformation (the first-order as well as the third-order) theories is presented, and analytical solutions of the equations are developed for simply supported boundary conditions. The effect of material properties, lamination scheme, and placement of the magnetostrictive layers on vibration suppression is investigated.

Displacement control of Timoshenko beams via induced strain actuators

Abstract: In this study, analytical solutions for the length and position of strain-induced patch actuators for the static adjustments of beam deflections are presented. To obtain precise deflection control, the Timoshenko beam theory has been adopted. The analytical solutions are derived conveniently by making use of exact relationships between the bending solutions of the Timoshenko beam theory and corresponding quantities of the Euler-Bernoulli beam theory. Examples of point deflection control for shear deformable beams subject to various loads are presented to illustrate the use of the analytical solutions derived. The significance of the contribution of transverse shear deformation effects on the control of beam deflection is discussed.

Relationship Between Vibration Frequencies of Reddy and Kirchhoff Polygonal Plates With Simply Supported Edges

Abstract: This paper presents an exact relationship between the natural frequencies of Reddy third-order plate theory and those of classical Kirchhoff plate theory for simply supported, polygonal isotropic plates, including rectangular plates. The relationship for the natural frequencies enables one to obtain the solutions of the third-order plate theory from the known Kirchhoff plate theory for the same problem. As examples, some vibration frequencies for rectangular and regular polygonal plates are determined using this relationship.

Numerical Simulation of Tubular Blown Film Processing

Abstract: A numerical simulation of the film blowing process was performed using the Runge-Kutta scheme. The kinematic and force balance equations governing the process are derived, and the constitutive model proposed by Cao and Campbell is utilized. The model accounts for liquidlike behavior at the freeze line; it alters the demarcation between liquidlike behavior and solidlike behavior from the suggested kinematicaly based constraint to a rheologically based constraint, the plastic-elastic transition (PET). The paper presents a detailed discussion on how the numerical models were developed and implemented. The numerical simulation was successful in duplicating Cao and Campbell's results. Recommendations are made to gain some insight into the problem.

Buckling of columns

Abstract: This chapter discusses an approach by means of an analogy for deriving the exact relationship between the elastic buckling loads of columns based on the Euler-Bemoulli beam theory, the Timoshenko beam theory, and the Reddy-Bickford beam theory. The exact relationship applies to axially loaded columns with boundary conditions that result in zero lateral force in the members. The resulting Reddy-Bickford buckling solutions are found to be higher than the Timoshenko buckling solutions. For the cases of pinned-pinned and fixed-free columns the buckling loads are practically the same for the two types of columns. However, in the case of fixed-fixed columns, the buckling loads are somewhat different, especially when the columns have relatively large values of the shear parameter Ω=D xx /(K s A xz L 2 ). The chapter emphasizes that the advantage of the Bickford-Reddy theory over the Timoshenko theory is that the former does not require a shear correction factor.

Substructure Simulation of Viscoelastic-Elastic Multibody Systems

Abstract: A substructure synthesis method is proposed for modeling the dynamic behavior of viscoelastic- elastic multibody system. The governing differential equations of motion are derived based on the Lagrange equations. Viscoelastic damping is incorporated into multibody systems to evaluate its effect on structural response. The viscoelastic damping proposed is based on layers of viscoelastic polymer directly attached to the systems. With the use of substructure synthesis method, the number of elastic coordinates needed in the approximate procedure is reduced. Numerical examples are presented to demonstrate the capabilities and efficiency of the proposed method. A comparison of the dynamic response has been presented for a two-link system with and without viscoelastic damping.