Showing papers by "J. N. Reddy published in 1984"
TL;DR: In this paper, a higher-order shear deformation theory of laminated composite plates is developed, which accounts for parabolic distribution of the transverse shear strains through the thickness of the plate.
Abstract: A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.
3,504 citations
Book•
01 Jan 1984
TL;DR: Second-order Differential Equations in One Dimension: Finite Element Models (FEM) as discussed by the authors is a generalization of the second-order differential equation in two dimensions.
Abstract: 1 Introduction 2 Mathematical Preliminaries, Integral Formulations, and Variational Methods 3 Second-order Differential Equations in One Dimension: Finite Element Models 4 Second-order Differential Equations in One Dimension: Applications 5 Beams and Frames 6 Eigenvalue and Time-Dependent Problems 7 Computer Implementation 8 Single-Variable Problems in Two Dimensions 9 Interpolation Functions, Numerical Integration, and Modeling Considerations 10 Flows of Viscous Incompressible Fluids 11 Plane Elasticity 12 Bending of Elastic Plates 13 Computer Implementation of Two-Dimensional Problems 14 Prelude to Advanced Topics
3,043 citations
TL;DR: In this paper, a higher-order shear deformation theory of plates accounting for the von Karman strain was presented, which contains the same dependent unknowns as in the Hencky-Mindlin type first-order deformation theories and accounts for parabolic distribution of the transverse shear strains through the thickness of the plate.
695 citations
TL;DR: An extension of the Sanders shell theory for doubly curved shells to a shear deformation theory of laminated shells is presented in this paper, which accounts for transverse shear strains and rotation about the normal to the shell midsurface.
Abstract: An extension of the Sanders shell theory for doubly curved shells to a shear deformation theory of laminated shells is presented. The theory accounts for transverse shear strains and rotation about the normal to the shell midsurface. Exact solutions of the equations are presented for simply supported, doubly curved, cross‐ply laminated shells under sinusoidal, uniformly distributed, and concentrated point load at the center. Fundamental frequencies of cross‐ply laminated shells are also presented. The exact solutions presented herein for laminated composite shells should serve as bench mark solutions for future comparisons.
495 citations
Book•
01 Jan 1984
TL;DR: A review of the equations of MECHANICS can be found in this paper, where the Ritz Method and Weighted-Residual Methods are used to approximate the distance between two points.
Abstract: A REVIEW OF THE EQUATIONS OF MECHANICS. Introduction. Kinetics. Kinematics. Thermodynamic Principles. Constitutive Equations. Boundary--Value Problems of Mechanics. Equations of Bars, Beams, Torsion, and Plane Elasticity. ENERGY AND VARIATIONAL PRINCIPLES. Preliminary Concepts. Calculus of Variations. Virtual Work and Energy Principles. Stationary Variational Principles. Hamiltona s Principle. Energy Theorems of Structural Mechanics. VARIATIONAL METHODS OF APPROXIMATION. Some Preliminaries. The Ritz Method. Weighted--Residual Methods. The Finite--Element Method. THEORY AND ANALYSIS OF PLATES AND SHELLS. Classical Theory of Plates. Shear Deformation Theories of Plates. Laminated Composite Plates. Theory of Shells. Finite--Element Analysis of Plates and Shells. Bibliography. Answers to Selected Exercises. Index.
347 citations
TL;DR: In this article, a special three-dimensional element based on the total Lagrangian description of the motion of a layered anisotropic composite medium is developed, validated and employed to analyze laminated composite shells, which contains geometric nonlinearity, dynamic (transient) behavior and arbitrary lamination scheme and lamina properties.
Abstract: A special three-dimensional element based on the total Lagrangian description of the motion of a layered anisotropic composite medium is developed, validated and employed to analyze laminated anisotropic composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behavior and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration, and transient response are presented to illustrate the capabilities of the element.
99 citations
TL;DR: In this article, a description of the three-dimensional elasticity equations and the associated finite element model for natural vibrations of laminated rectangular plates are described and compared with those obtained by a shear deformable plate theory.
46 citations
TL;DR: In this paper, the results of a three-dimensional, geometrically nonlinear, finite-element analysis of the bending of cross-ply laminated anisotropic composite plates are presented.
32 citations
26 citations
TL;DR: In this paper, a mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated.
TL;DR: In this article, a materially nonlinear analysis of laminated composite plates is presented, based on the Reissner-Mindlin type plate theory and a fully three-dimensional elasticity theory, which is used to analyze the bending of plates under transverse loads.
01 Jan 1984
TL;DR: In this paper, an analysis of the free vibration and transient response of laminates using a mixed shear flexible element is presented based on a refined theory that accounts for a parabolic distribution of the transverse shear stresses through each lamina and requires no shear correction coefficients.
Abstract: An analysis of the free vibration and transient response of laminates using a mixed shear flexible element is presented. The element is based on a refined theory that accounts for a parabolic distribution of the transverse shear stresses through each lamina and requires no shear correction coefficients. The mixed formulation of the theory treats the five displacement functions and six stress resultants independently so that they are nodal degrees of freedom in the finite element model. Sample problems using the element are analyzed and the results of free vibration and transient response are presented. Compared to the existing shear deformation plate theory the present refined theory gives more accurate results for frequencies, displacements and stresses.
01 Jan 1984
TL;DR: In this paper, a displacement field based on a cubic function of the thicknes coordinate of the plate is proposed to account for the parabolic distribution of the transverse shear stresses.
Abstract: This paper deals with the dynamic analog of the higher-order shear deformation plate theory developed by the senior author. The theory is based on a displacement field in which the inplane displacements are expanded as cubic functions of the thicknes coordinate and the transverse deflection is assumed to be constant through the thickness. The additional dependent unkowns introduced with the quadratic and cubic terms of the thickness coordinate are eliminated by requiring the transverse shear stresses to vanish on the bounding planes of the plate. The theory accounts for the parabolic distribution of the transverse shear stresses, and hence no shear correction coefficients are required.
01 Jan 1984
TL;DR: In this paper, the authors used the unilateral contact approach to model the initial debonding and subsequent delamination of two-layer or multi-layer symmetric laminated plates under transverse loads.
Abstract: The unilateral contact approach is used to model the initial debonding and subsequent delamination of two-layer or multi-layer symmetric laminated plates under transverse loads. The mathematical formulation of the approach and associated finite element model are presented. The bond material (or adherent) is modelled as a continuum that has a uniaxial (in the transverse direction) elastic response. The flexural behavior of the plate is modelled by means of the Hencky-Mindlin type shear deformation theory. Two sample problems are presented. The relationship between the brittle fracture mechanics approach and the present approach is also discussed.