Showing papers by "J. N. Reddy published in 2005"

A corotational finite element formulation for the analysis of planar beams

Abstract: An efficient and accurate locking-free corotational beam finite element for the analysis of large displacements and small-strain problems is developed in this paper. Three different finite element models based on three different beam theories, namely, the Euler–Bernoulli, Timoshenko, and simplified Reddy theories are presented. In order to develop a single corotational finite element that incorporates the kinematics of all three theories, the unified linear finite element model of beams developed by Reddy (Comm. Numer. Meth. Eng. 1997; 13:495–510) is included in the formulation. An incremental iterative technique based on the Newton–Raphson method is employed for the solution of the non-linear equilibrium equations. Numerical examples that demonstrate the efficiency and large rotation capability of the corotational formulation are presented. The element is validated by comparisons with exact and/or approximate solutions available in the literature. Very good agreement is found in all cases. Copyright © 2005 John Wiley & Sons, Ltd.

Non-linear response of laminated composite plates under thermomechanical loading

Abstract: The non-linear response of laminated composite plates under thermomechanical loading is studied using the third-order shear deformation theory (TSDT) that includes classical and first-order shear deformation theories (CLPT and FSDT) as special cases. Geometric non-linearity in the von Karman sense is considered. The temperature field is assumed to be uniform in the plate. Layers of magnetostrictive material, Terfenol-D, are used to actively control the center deflection. The negative velocity feedback control is used with the constant gain value. The effects of lamination scheme, magnitude of loading, layer material properties, and boundary conditions are studied under thermomechanical loading.

Least-squares finite element formulations for one-dimensional radiative transfer

Abstract: We present least-squares-based finite element formulations for the numerical solution of the radiative transfer equation in its first-order primitive variable form. The use of least-squares principles leads to a variational unconstrained minimization problem in a setting of residual minimization. In addition, the resulting linear algebraic problem will always have a symmetric positive definite coefficient matrix, allowing the use of robust and fast iterative methods for its solution. We consider space-angle coupled and decoupled formulations. In the coupled formulation, the space-angle dependency is represented by two-dimensional finite element expansions and the least-squares functional minimized in the continuous space-angle domain. In the decoupled formulation the angular domain is represented by discrete ordinates, the spatial dependence represented by one-dimensional finite element expansions, and the least-squares functional minimized continuously in space domain and at discrete locations in the angle domain. Numerical examples are presented to demonstrate the merits of the formulations in slab geometry, for absorbing, emitting, anisotropically scattering mediums, allowing for spatially varying absorption and scattering coefficients. For smooth solutions in space-angle domain, exponentially fast decay of error measures is demonstrated as the p-level of the finite element expansions is increased. The formulations represent attractive alternatives to weak form Galerkin finite element formulations, typically applied to the more complicated second-order even- and odd-parity forms of the radiative transfer equation.

Consistent Third-Order Shell Theory with Application to Composite Cylindrical Cylinders

Abstract: A consistent third-order shell theory with applications to composite circular cylinders is presented and its finite element formulation is developed. The formulation has seven displacement functions and requires C 0 continuity in the displacement field. The exact computation of stress resultants is carried out through numerical integration of material stiffness coefficients of the laminate. A displacement finite element model is developed using Lagrange elements with higher-order interpolation polynomials. These elements preclude any effect of shear and membranes locking. Comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and composite cylindrical shells are found to be excellent and show the validity of the developed shell theory and its implementation into a finite element code.

Numerical simulation of thermomechanical behaviours of shape memory alloys via a non-linear mesh-free Galerkin formulation

Abstract: A new computational approach is developed based on the mesh-free method for the numerical simulation of shape memory alloys. A thermomechanical constitutive model is used to describe the complex material response. The incremental displacement-based mesh-free formulation is constructed in a total Lagrangian description by employing the moving least square shape function and rate form of the shape memory alloy constitutive model in the variational equations. This mesh-free formulation is not only applicable to large deformation problems, but also accounts for both stress and thermally induced phase transformation. Moreover, the newly developed mesh-free codes can deal with complex loading paths and multiple temperature cycles in numerical simulation. The performance of the proposed mesh-free scheme for the simulation of shape memory alloys is demonstrated in several numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.

A local-analytic-based discretization procedure for the numerical solution of incompressible flows

Abstract: An Erratum has been published for this article in International Journal for Numerical Methods in Fluids 2005, 49(8): 933. We present a local-analytic-based discretization procedure for the numerical solution of viscous fluid flows governed by the incompressible Navier–Stokes equations. The general procedure consists of building local interpolants obtained from local analytic solutions of the linear multi-dimensional advection–diffusion equation, prototypical of the linearized momentum equations. In view of the local analytic behaviour, the resulting computational stencil and coefficient values are functions of the local flow conditions. The velocity–pressure coupling is achieved by a discrete projection method. Numerical examples in the form of well-established verification and validation benchmarks are presented to demonstrate the capabilities of the formulation. The discretization procedure is implemented alongside the ability to treat embedded and non-matching grids with relative motion. Of interest are flows at high Reynolds number, (105)–(107), for which the formulation is found to be robust. Applications include flow past a circular cylinder undergoing vortex-induced vibrations (VIV) at high Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd.

An integrated approach towards the study of scratch damage of polymer

Abstract: To seek a better understanding of the scratch damage of polymers, an integrated analysis approach is proposed in this article. This integrated approach essentially involves (a) the use of a new scratch test device for testing, (b) employing microscopy techniques and image an analysis tool, VIEEW®, for studying material damage and scratch visibility, and finally (c) performing finite element (FE) modeling to examine the mechanical response of the polymeric substrate involved during the scratch process. Applying this approach to five model material systems and employing linearly increasing load tests, the findings of the fundamental material science study of the scratch damage of these materials are presented. From the three-dimensional FE analysis, the numerical results generated were able to reasonably predict the scratch damage and provide corresponding mechanistic interpretation. The essential link between material science and mechanics outlines the uniqueness of this approach for studying the scratch damage of polymers.

Layerwise modeling of progressive damagein fiber-reinforced composite laminates

Abstract: This paper investigates the effects of discrete layer transverse shear strain and discrete layer transverse normal strain on the predicted progressive damage response and global failure of fiber-reinforced composite laminates. These effects are isolated using a hierarchical, displacement-based 2-D finite element model that includes the first-order shear deformation model (FSD), type-I layerwise models (LW1) and type-II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C 0 continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C 0 continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics (CDM) model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the homogenized composite material ply. In modeling laminates that exhibit either widespread or localized transverse shear deformation, the results obtained in this study clearly show that the inclusion of discrete layer kinematics significantly increases the rate of local damage accumulation and significantly reduces the predicted global failure load compared to solutions obtained from first-order shear deformable models. The source of this effect can be traced to the improved resolution of local interlaminar shear stress concentrations, which results in faster local damage evolution and earlier cascading of localized failures into widespread global failure.

An Efficient Continuum Damage Model and its Application to Shear Deformable Laminated Plates

Abstract: In this article an efficient 3-D continuum damage mechanics formulation for composite laminates and its implementation into a finite element model that is based on the first order shear deformation theory of laminates are described. In the damage formulation each composite ply is treated as a homogeneous orthotropic material that can exhibit orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. This type of damage is efficiently described by a symmetric second order tensor field that serves as an evolving internal variable within the framework of irreversible thermodynamics. The damage tensor is continuous within each material ply of a given element, but can be discontinuous across material layer boundaries and inter-element boundaries. The resulting finite element formulation is shown to be robust, stable and efficient for the simulation of progressive damage and global failures in large-scale composite laminate problems. Numerical ex...

Structure and properties of the fundamental elastic plate matrix

Abstract: This work presents further development of the octet formalism established by the authors for the classical Kirchhoff anisotropic plate theory. The structure of the fundamental elastic plate matrix is fully explored and the explicit expression is provided. The matrices N 2 and -N 3 are proved to be positive semi-definite. Thus, H and L are positive definite. Further studies are concerned with a rotated coordinate system. The transform relation between the eigenvectors in the original and the rotated coordinate system is given. The fundamental elastic plate matrix associated with the eigenrelation referring to the dual coordinate systems, N(0), is studied. The major properties that hold in the Stroh sextic formalism for generalized plane strain problems are also valid in the octet formalism for thin plate bending problems. In particular, we generalize a property in Stroh's formalism for any non-semisimple matrix N(0). We show a new property in the octet formalism. The non-semisimple cases of N(0) are discussed. Finally, we make it transparent that the mixed/hybrid formalism of others is precisely one of sixteen permuted forms of the octet formalism.

Finite Element Modeling for Scratch Damage of Polymers

Abstract: This chapter is concerned with the numerical simulation of scratch deformation on a polymer substrate by a semispherical indenter. A commercial finite element (FE) package, ABAQUS®, is used to study elasto-plastic scratch behavior on polymer surfaces. The study provides insightful mechanistic information that can be correlated to surface deformation and damage using material parameters. Of notable significance is that the FE analysis approach can be used to conduct parametric studies on material and geometric parameters that aid the construction of a physics-based model for describing the scratch behavior of polymers.

Thermo-Mechanical Analysis of Composites Under Combined Conduction Heating and Large Deflection Bending

Abstract: A novel conduction heating apparatus that combines thermal loading with large deflection bending is introduced, and its effectiveness for thermo-mechanical stress analysis was investigated. By clamping composite specimens (M40J/PMR-II-50, [0,90]s , a uni-tape cross-ply) on the radial sides of half cylinders having two different radii (78.74mm and 37.96mm), three different in-plane strains including a no strain condition were applied to the composites. Three different thermal loading experiments, 1) 23°C to −196°C to 250°C, 2) 23°C to 250°C, and 3) 23°C to −196°C were performed as a function of mechanical in-plane strain levels. The apparatus was excellent enough to generate cracks related to the in-plane stresses (or strains) on plies. The quadratic failure criteria solution based on the thermal residual stresses shows a good agreement with the experimental results at low temperatures, but does not supply a good agreement at high temperatures. A weak adhesion of fiber/matrix interface at high temperatures (250°C) might cause the de-bonding at the interface and subsequent exposure to −196°C caused the intensive crack propagation.© 2005 ASME