Showing papers by "J. N. Reddy published in 1992"

Finite Element Analysis of Composite Laminates

Abstract: The partial differential equations governing composite laminates (see Section 2.4) of arbitrary geometries and boundary conditions cannot be solved in closed form. Analytical solutions of plate theories are available (see Reddy [1–5]) mostly for rectangular plates with all edges simply supported (i.e., the Navier solutions) or with two opposite edges simply supported and the remaining edges having arbitrary boundary conditions (i.e., the Levy solutions). The Rayleigh-Ritz and Galerkin methods can also be used to determine approximate analytical solutions, but they too are limited to simple geometries because of the difficulty in constructing the approximation functions for complicated geometries. The use of numerical methods facilitates the solution of these equations for problems of practical importance. Among the numerical methods available for the solution of differential equations defined over arbitrary domains, the finite element method is the most effective method. A brief introduction to the finite element method is presented in Section 3.2.

A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates

Abstract: The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and is placements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and two-dimensional theories.

Postbuckling response and failure prediction of graphite-epoxy plates loaded in compression

Abstract: A shear deformable (three-dimensional) shell element is used to analyze the panels. Two panels without boles and one with a bole are studied, and the resulting responses and failure modes comelated well with the experimental results.

On vibration and buckling of symmetric laminated plates according to shear deformation theories

Abstract: The frequency and buckling equations of rectangular plates with various boundary conditions are developed within the third-order and the first-order shear deformation plate theories. The third-order theories account for a quadratic distribution of the transverse shear strains through the thickness of the plate. In the first part of this paper, Levinson's third-order theory, derived as a special case from Reddy's third-order theory, is used to study a plate laminated of transversely isotropic layers. The relationship between the original form of the governing equations and the interior and the edge-zone equations of the plate is closely examined and the physical insights from the latter equations are established. In the second part of the paper, the first-order shear deformation theory and the third-order theory of Reddy are studied for vibration and buckling.

Layer-wise shell theory for postbuckling of laminated circular cylindrical shells

Abstract: The layer-wise shell theory of Reddy is used to study the postbuckling response of circular cylindrical shells. The Rayleigh-Ritz method is used to solve the equations by assuming a double Fourier expansion of the displacements with trigonometric coordinate functions. Numerical results for postbuckling response of axially compressed multilayer cylinders with simply supported edge conditions are presented for different values of shell imperfections.

An assessment of four‐noded plate finite elements based on a generalized third‐order theory

Abstract: Plate finite elements based on the generalized third-order theory of Reddy and the first-order shear deformation theory are analyzed and compared on the basis of thick and thin plate modeling behavior, distortion sensitivity, overall accuracy, reliability, and efficiency. In particular, several four-noded Reddy-type elements and the nine-noded Lagrangian and heterosis (Mindlin-type) plate elements are analyzed to assess their behavior in bending, vibration, and stability of isotropic and laminated composite plates. A four-noded Reddy-type element is identified which is free of all spurious stiffness and zero energy modes, computationally efficient, and suitable for use in any general-purpose finite element program.

Penalty finite element analysis of incompressible flows using element by element solution algorithms

Abstract: Finite element analysis of complex three-dimensional flows requires solution of a large system of algebraic equations. These equations are most often solved using direct methods, i.e., Gauss elimination method. However, for complex problems, direct methods demand prohibitively large CPU times and storage, thus making it difficult to solve these equations economically even on supercomputers. Iterative methods, on the other hand, do not require large storage and CPU times because the global system of equations are not formulated and factorized. These advantages over direct methods have revived the interest in iterative solvers. The element by element solvers using conjugate gradient methods have been used successfully for the solution of problems in fluid and solid mechanics and were shown to be advantageous over direct methods. In this paper we present an element by element algorithm for solution of incompressible flow problems using a penalty finite element model. The iterative methods (conjugate gradient and generalized minimum residual method) are compared with the frontal equation solver for efficiency, and the iterative solvers are found to be economical when a large number of equations are to be solved.

On boundary layer and interior equations for higher-order theories of plates

Abstract: Several shear-deformation plate theories of symmetric laminated plates with transversely isotropic layers are reviewed and the governing equations of these theories are then recast into two equations: one for the interior of the domain and the other for the edge-zone or the boundary layer. For the first time it si shown that the governing equations of the third-order shear-deformation theory of Reddy result in a sixth-order interior equation and a second-order edge-zone equations. It is also demonstrated that in bending and stability problems, and under certain conditions in dynamic problems, the contribution of the edge-zone equation is identically zero for a simply-supported plate. The pure-shear frequencies of a plate according to different theories are determined and compared. Verschiedene Schubdeformations-Plattentheorien von symmetrisch geschichteten Platten mit transversal-isotropen Schichten werden erneut vorgestellt, und die Grundgleichungen dieser Theorien werden dann in zwei Gleichungen umgeformt: eine fur das Innere des Gebietes, und die andere fur das Randgebiet oder die Grenzschicht. Zunachst wird gezeigt, das die Grundgleichungen der Schubdeformationstheorie 3. Ordnung von Reddy in eine innere Gleichung 6. Ordnung und eine Randgebietsgleichung 2. Ordnung ubergehen. Es wird auch gezeigt, das fur Biege- und Stabilitatsprobleme und unter bestimmten Bedingungen fur dynamische Probleme der Beitrag der Randgebietsgleichung fur eine frei aufliegende Platte identisch Null ist. Die reinen Schubfrequenzen einer Platte werden nach verschiedenen Theorien bestimmt und miteinander verglichen.

On first‐ and second‐order moderate rotation theories of laminated plates

Abstract: The first- and second-order, small strain and moderate rotation, theories of anisotropic laminated plates are developed and numerically evaluated. Beginning with an assumed displacement field and introducing various order-of-magnitude assumptions, the governing equilibrium equations of laminated plates are derived from the principle of virtual displacements. The finite-element formulation for the second-order moderate rotation theory is developed, and numerical results are presented to evaluate the new plate theories in comparison with the von Karman plate theory with shear deformation. For comparison purposes, the 2-D elasticity theory with full non-linearity is also analysed using the finite element method. It is found that the second-order theory with moderate rotations is closest to the 2-D finite elasticity theory.

Finite-element analysis of flows of non-Newtonian fluids in three-dimensional enclosures

Abstract: A finite-element model based on the penalty function formulation of the Navier-Stokes equations governing flows of unsteady, incompressible, non-isothermal, non-Newtonian fluids in three-dimensional enclosures is presented. Power-law and Carreau constitutive relations are used, and the viscosity is assumed to be temperature dependent. The resulting non-linear equations are solved by Picard's method (i.e. direct iteration). The finite-element model is used to analyze several problems, such as flows through circular pipe, cubical cavity, and tubular and square contractions. Wherever possible, comparisons are made between present numerical solutions and available analytical or numerical solutions. The present results are in good agreement with other solutions. The finite-element model developed here can be modified to accommodate other forms of constitutive relations.

Numerical simulation of forming processes using a coupled fluid flow and heat transfer model

Abstract: Numerical simulation of forming processes is studied using the Navier-Stokes equations and the energy equation governing viscous, incompressible fluids. A review of various important aspects of forming processes is also reviewed for completeness. A penalty finite element model of the equations is developed. The finite element model is used to study the effectiveness of various constitutive models developed for metal forming and polymer processing. The element-by-element (EBE) data structure with efficient iterative solution methods is used to solve the large systems of equations that arise in the analysis of complex 3-D problems. Numerical results for problems representative of various forming processes (e.g. extrusion and solidification) are presented.

Non-linear analysis of free-edge effects in composite laminates subjected to axial loads

Abstract: A finite-element model based on the quasi-three-dimensional elasticity theory of Pipes and Pagano with the non-linear strain-displacement equations is used to study the effect of geometric non-linearity on free-edge stress fields in composite laminates subjected to in-plane loads. The results obtained for transverse normal and shear stresses indicate that the qualitative nature of the stresses remains the same as those obtained in the linear analysis, but the non-linear stresses are larger in magnitude by 5–40%, depending on the laminate. However, in most cases the difference is found to be about 10%.

Composite Structures: Testing, Analysis and Design

Abstract: The use of composite materials has increased steadily during the past two decades, particularly in aerospace, hydrospace and automotive structures. This increase is mainly because many composite materials exhibit high strength-to-weight and stiffness-to-weight ratios, which make them ideally suited for use in weight-sensitive structures. In addition, many of these materials are more corrosion resistant and more thermally stable than metals. The contributors to this volume provide an overview of recent advances related to the development of novel composite systems, thermomechanical models, computational schemes, design methodologies and manufacturing aspects for advanced composite materials for aerospace applications.

Local Mechanics Concepts for Composite Material Systems: Iutam Symposium, Blacksburg, Va, 1991

Abstract: Axisymmetric Micromechanical Stress Fields in Composites.- Analytical Modeling of Micromechanical Stress Variations in Continuous Fiber-Reinforced Composites.- Some Aspects of Continuum Damage Mechanics Applied to Polymer and Ceramic Matrix Composites.- Micromechanics as a Basis for Damage Mechanics.- Micromechanics for Performance Simulation.- On Statistical Micromechanical Theories for Brittle Solids with Interacting Microcracks.- Fibre Composites: Mesomechanics and Mesostructures.- Matrix Cracking and Interphase Failure in Fiber Composites.- An Experimental Element Technique for Transverse Fracture in CFRP and GFRP.- Interaction of Fatigue Mechanisms During Crack Growth in Arall.- Deformation of a Metal-Ceramic Composite with a Crystal Matrix: Reinforcement Distribution Effects.- An Energy Based Model for the Influence of the Fibre-Matrix Interface Strength on the Interlaminar Fracture Toughness of UD-Composite Laminates.- Analysis of Local Buckling in Viscoelastic Composites.- Analytical Models of Stress Transfer in Unidirectional Composites and Cross-Ply Laminates, and Their Application to the Prediction of Matrix/Transverse Cracking.- Local Stresses and Thermoelastic Properties of Composite Laminates Containing Micro Cracks.- Analysis of Interlaminar Stresses and Failures Using a Layer-Wise Laminate Theory.- Green's Function Method for Calculation of Stress Fields in Composite Materials.- Spline Function Aided Analysis of Inhomogeneous Materials and Structures.- Symbolic Algebra Approach to Composite Materials Analysis.- Scanning Acoustic Microscope Simulation for Determining Interphase Structure.

Mechanics of Composite Laminates

Abstract: Analysis of structures made of composite materials requires a knowledge of anisotropic elasticity, an appropriate structural theory that accounts for desired kinematics, failure criteria to determine if the structure has failed, and a numerical method to solve the boundary-value problem associated with the structure. The study of anisotropic elasticity and structural theories used to analyze composite laminates constitute the topics for this chapter.

Analysis of Interlaminar Stresses and Failures Using a Layer-Wise Laminate Theory

Abstract: The layer—wise laminate theory of Reddy [1] is used to study interlaminar stress fields and carry out progressive failure analysis of composite laminates. The layer-wise theory not only predicts accurate interlaminar stress fields but it also provides a convenient format for modeling multiple delaminations. The computational model based on the layer—wise theory is capable of modeling free edge effects and energy release rates with the same accuracy as a conventional 3-D finite element model. The progressive failure analysis is based on an algorithm in which the damage is accounted through phenomenalogical failure criteria and a stiffness reduction coefficient. The stiffness reduction coefficient is used to define the equivalent material properties, which are used to update the stiffness matrix. It is demonstrated through an example problem that three-dimensional stress analysis is a necessary requirement but not sufficient to predict the failure behavior of composites laminate accurately.