Showing papers by "J. N. Reddy published in 1988"

Non-linear analysis of adhesively bonded joints

Abstract: An updated Lagrangian formulation is used to develop a 2-D finite element for the analysis of adhesively bonded joints. The finite element accounts for the geometric non-linearity. The present finite element results are in good agreement with those reported in the literature. The effect of boundary conditions and mesh on the stress distributions in lap joints is also investigated.

A Refined Small Strain and Moderate Rotation Theory of Elastic Anisotropic Shells

Abstract: A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-Love) shell theory, the Donnell-Mushtari-Vlasov shell theory, the Leonard-Koiter-Sanders moderate rotations shell theory, the von Karman type shear-deformation shell theory and the moderate-rotation shear-deformation plate theory developed by Reddy. The present theory is developed from an assumed displacement field, nonlinear strain-displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformations, which should alter the bending, stability, and post-buckling behavior of certain shell structures predicted using the presently available theories.

Finite‐element models of viscoelasticity and diffusion in adhesively bonded joints

Abstract: The paper contains a description of the finite-element model based on Schapery's non-linear viscoelastic constitutive equation for the adhesive, a non-linear generalized Fickean diffusion model and an updated Lagrangian formulation of a two-dimensional stress state, to analyse adhesively bonded joints. The finite-element analysis program, called NOVA, is used to analyse a number of adhesive joints, and the results are compared with existing experimental results and analytical solutions.

A solid-shell transition element for geometrically non-linear analysis of laminated composite structures

Abstract: Using the incremental equations of motion of a continuous medium and the total Lagrangian description, three different elements, i.e. degenerated shell element, 3-D continuum element and solid-shell transition element, are developed for the geometrically non-linear analysis of laminated composite structures. Compatibility and completeness requirements are stressed in modelling shell-type structures in order to assure the convergence of the finite element analysis. A number of laminated plate and shell examples are presented to demonstrate the validity and efficiency of various elements.

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

Comparison of Flow Birefringence Data with a Numerical Simulation of the Hole Pressure

Abstract: The penalty‐Galerkin finite‐element method is used to simulate the flow of a polystyrene melt over a rectangular slot placed perpendicular to the flow direction. The White‐Metzner constitutive equation is used with a Carreau model viscosity function and a shear rate‐dependent relaxation time defined so that the primary normal stress difference is exactly reproduced by the model in simple shear flow. Values of the stress field predicted by the simulation are compared with those obtained experimentally by means of flow birefringence. As observed by others, the limiting elasticity value as determined by the Weissenberg number (We) for convergence of the algorithm decreased with increased refinement of the mesh. However, good agreement is still found between predicted values of stress using the coarse mesh and those measured by means of flow birefringence. This work suggests that there may be an optimum mesh for a given flow and constitutive equation which will still give physically realistic results. The Wei...

Nonlinear Viscoelastic Finite Element Analysis of Adhesive Joints

Abstract: A good understanding of the process of adhesion from the mechanics viewpoint and the predictive capability for structural failures associated with adhesively bonded joints require a realistic modeling (both constitutive and kinematic) of the constituent materials. The present investigation deals with the development of an Updated Lagrangian formulation and the associated finite element analysis of adhesively bonded joints. The formulation accounts for the geometric nonlinearity of the adherends and the nonlinear viscoelastic behavior of the adhesive. Sample numerical problems are presented to show the stress and strain distributions in bonded joints.

Friction Phenomenon in Contact Stress Problems

Abstract: : Numerical, experimental, and hybrid combinations of these methods, were used to study plane contact problems. The experimental program used moire interferometry to determine in-plane displacement fields near the contact boundaries of pin-loaded aluminum and graphite-epoxy plates. The experiments closely modeled two dimensional behavior and introduced zero-thickness gratings (for the aluminum plate). The experimental data were reduced by means of a localized hybrid analysis which used the experimental displacement data as input to a finite element analysis of selected zones of interest. The stress distributions obtained were generally consistent with those of published analytical and experimental studies but the detailed frictional phenomena were found to be very localized and somewhat irregular. The composite plate program featured a failure analysis based upon the experimentally determined stress distributions. These distributions were combined with a maximum stress failure criterion to predict the mode and location of the failure. The results of an earlier experiment were used to assess the accuracy of a general finite element algorithm for plane elastic problems. On the basis of this comparison refinements to the solution methodology were made. Keywords: Matrix cracking, Composite plates, Aluminum, Contact, Moire interferometry, Fringe patterns, Hybrid techniques elasto-plastic analysis, Eulerian-Lagrangian formulation, Finite element analysis.