Showing papers by "J. N. Reddy published in 1989"

On refined computational models of composite laminates

Abstract: Finite element models of the continuum-based theories and two-dimensional plate/shell theories used in the analysis of composite laminates are reviewed. The classical and shear deformation theories up to the third-order are presented in a single theory. Results of linear and non-linear bending, natural vibration and stability of composite laminates are presented for various boundary conditions and lamination schemes. Computational modelling issues related to composite laminates, such as locking, symmetry considerations, boundary conditions, and geometric non-linearity effects on displacements, buckling loads and frequencies are discussed. It is shown that the use of quarter plate models can introduce significant errors into the solution of certain laminates, the non-linear effects are important even at small ratio of the transverse deflection to the thickness of antisymmetric laminates with pinned edges, and that the conventional eigenvalue approach for the determination of buckling loads of composite laminates can be overly conservative.

Buckling and vibration of laminated composite plates using various plate theories

Abstract: Analytical and finite-element solutions of the classical, first-order, and third-order laminate theories are developed to study the buckling and free-vibration behavior of cross-ply rectangular composite laminates under various boundary conditions

A plate bending element based on a generalized laminate plate theory

Abstract: .( SUMMARY A plate bending element based on the generalized laminate plate theory (GLPT) developed by the senior author is described and its accuracy is investigated by comparison with the exact solutions ofthe generalized plate theory and the 3D-elasticity theory. The element accounts for transverse shear deformation and layer­ wise description of the inplane displacements of the laminate. The element has improved description of the inplane as well as the transverse deformation response. A method for the computation of interlaminar (transverse) stresses is also presented. 1. BACKGROUND Laminated composite plates are often modelled using the classical laminate plate theory (CLPT) or the first-order shear deformation plate theory (FSDT). In both cases the laminate is treated as a single-layer plate with equivalent stiffnesses, and the displacements are assumed to vary through the thickness according to a single expression (see Reddy 1 ), not allowing for possible discontinuities in strains at an interface of dissimilar material layers. Recently, Reddy2 presented a general laminate plate theory that allows layer-wise representation of inplane displacements, and an improved response of inplane and transverse shear deformations is predicted. Similar but different theories have appeared in the literature. 3-6 In the generalized laminate plate theory (0LPT) the equations of three-dimensional elasticity are reduced to differential equations in terms of unknown functions in two dimensions by assuming layer-wise approximation of the displacements through the thickness. Consequently, the strains are different in different layers. Exact analytical solutions of the theory were developed by the authors 7 ,8 to evaluate the accuracy ofthe theory compared to the 3D-elasticity theory. The results indicated that the generalized laminate plate theory allows accurate determination ofinterlaminar stresses. The present study deals with the finite-element formulation of the theory and its application to laminated composite plates. In the interest of brevity only the main equations of the theory are reviewed and the major steps of the formulation are presented. The accuracy of the numerical

On the Generalization of Displacement-Based Laminate Theories

Abstract: A review and generalization of the displacement-based two-dimensional plate theories is presented. The classical and shear deformation single-layer theories up to the third-order are presented in a single theory through tracers. The layer-wise laminate theory developed by the author is reviewed. Numerical results are presented to illustrate the accuracy of the layer-wise theory by comparison with the analytical solution of the 3-D elasticity theory.

Continuum-based stiffened composite shell element for geometrically nonlinear analysis

Abstract: A continuum-based, laminated, stiffened shell element is used to investigate the static, geometrically nonlinear response of composite shells. The element is developed from a three-dimensional continuum element based on the incremental, total Lagrangian formulation. The Newton-Raphson method or modified Riks method is used to trace the nonlinear equilibrium path. A number of sample problems of unstiffened and stiffened shells are presented to show the accuracy of the present element and to investigate the nonlinear response of laminated composite plates and shells. INITE-ELEMENT analyses of the large displacement the- ories are based on the principle of virtual work or the associated principle of stationary potential energy. Horrigmoe and Bergan1 presented classical variational principles for non- linear problems by considering incremental deformations of a continuum. A survey of various principles in incremental form in different reference configurations, such as the total Lagran- gian and updated Lagrangian formulations, is presented by Wiinderlich.2 In the total Lagrangian description, all static and kinematic variables are referred to the initial configura- tion. Finite-element models based on such formulations have been used in the analysis of arch and shell instability prob- lems.3'6 A special numerical technique must be adopted to trace the path of the load-deflection curve near the limit point (i.e., critical buckling load) and in the postbuckling region, because the stiffness matrix in the vicinity of the limit point is nearly singular, and the descending branch of the load-deflec- tion curve in the postbuckling region is characterized by a negative-definite stiffness matrix. Many methods have been proposed to solve limit-point problems. Among these are the simple methods of suppressing equilibrium iterations,7'8 the introduction of artificial spring,3 the displacement control method,7'8 and the "constant-arc-length method" of Riks. 11-12 Reviews of these most commonly used techniques are con- tained in Refs. 13 and 14. Among these methods, the modified Riks method appears to be the most effective in conjunction with the finite-element method. Many investigators11'15 have used this method in its original or modified form to determine the pre- and postbuckling behavior of various types of struc- tures such as arches, shells, and domes. In most of these works, only isotropic material was considered. Very few works of the nonlinear buckling analysis of laminated com- posite structures are reported in the literature.16 When solving the problems of shells with stiffeners by the finite-element method, a beam element whose displacement pattern is compatible with that of the shell is required. In analyzing eccentrically stiffened cylindrical shell, Kohnke and Schnobrich17 proposed a 16-deg-of-free dom (DOF) isotropic beam finite element that has displacements compatible with

Dynamic response of cross‐ply laminated shallow shells according to a refined shear deformation theory

Abstract: The dynamic response of cross‐ply laminated shallow shells is investigated using the third‐order shear deformation shell theory of Reddy [J. Appl. Mech. 41, 47 (1984)]. The theory accounts for cubic variation of the in‐plane displacements through the thickness and does not require shear correction coefficients. The state‐space approach is used to develop the analytical solutions of simply supported, cross‐ply shells using the classical, first‐order, and higher‐order theories. The use of the separation of variables technique for the higher‐order theory is also presented. Numerical results of the higher‐order theory for center deflection and normal stresses of spherical shells under various loadings are compared with those obtained using the classical and first‐order [or Sanders, Q. Appl. Math. 21, 21–36 (1963)] shell theories.

A Model for the Diffusion of Moisture in Adhesive Joints. Part III: Numerical Simulations

Abstract: The coupling mechanisms between the diffusion process and the viscoelastic response of an adhesive are explained. A numerical scheme for fully-coupled solutions is proposed and implemented in a two-dimensional finite element code. A number of numerical simulations are presented in order to illustrate the importance of the following features: (1) the bulk viscoelastic behavior, (2) penetrant size, (3) physical aging, (4) the strain dependence of the diffusion coefficient, (5) the concentration dependence of the diffusion coefficient and (6) differential, swelling. The effect of moisture intrusion on the stress (strain) distribution across a butt joint is also presented.

Penalty finite element analysis of free surface flows of power-law fluids

Abstract: The penalty function method is used to formulate the finite element model of the free surface flows of incompressible, viscous, power-law fluids in plane and axisymmetric situations. Two different procedures of obtaining the free surface are presented, and application of the present finite element model to die-swell problems is discussed. The numerical results are compared with available experimental data and numerical results obtained by others.

On computational schemes for global-local stress analysis

Abstract: An overview is given of global-local stress analysis methods and associated difficulties and recommendations for future research. The phrase global-local analysis is understood to be an analysis in which some parts of the domain or structure are identified, for reasons of accurate determination of stresses and displacements or for more refined analysis than in the remaining parts. The parts of refined analysis are termed local and the remaining parts are called global. Typically local regions are small in size compared to global regions, while the computational effort can be larger in local regions than in global regions.