Showing papers by "Sundararajan Natarajan published in 2014"

Analysis of functionally graded material plates using triangular elements with cell-based smoothed discrete shear gap method

Abstract: A cell-based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, and mechanical and thermal buckling behaviour of functionally graded material (FGM) plates. The plate kinematics is based on the first-order shear deformation theory and the shear locking is suppressed by the discrete shear gap method. The shear correction factors are evaluated by employing the energy equivalence principle. The material property is assumed to be temperature dependent and graded only in the thickness direction. The effective properties are computed by using the Mori-Tanaka homogenization method. The accuracy of the present formulation is validated against available solutions. A systematic parametric study is carried out to examine the influence of the gradient index, the plate aspect ratio, skewness of the plate, and the boundary conditions on the global response of the FGM plates. The effect of a centrally located circular cutout on the global response is also studied.

A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

Abstract: In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition.

Analysis of cross-ply laminated plates using isogeometric analysis and unified formulation

Abstract: In this paper, we study the static bending and free vibration of cross-ply laminated composite plates us- ing sinusoidal deformation theory. The plate kinematics is based on the recently proposed Carrera Unied For- mulation (CUF), and the eld variables are discretized with the non-uniform rational B-splines within the frame- work of isogeometric analysis (IGA). The proposed ap- proach allows the construction of higher-order smooth functions with less computational eort. Moreover, within the framework of IGA, the geometry is represented exactly by the Non-Uniform Rational B-Splines (NURBS) and the isoparametric concept is used to dene the eld variables. On the other hand, the CUF allows for a systematic study of two dimensional plate formulations. The combination of the IGA with the CUF allows for a very accurate predic- tion of the eld variables. The static bending and free vi- bration of thin and moderately thick laminated plates are studied.Thepresentapproachalsosuersfromshearlock - ing when lower order functions are employed and shear locking is suppressed by introducing a modication fac- tor. The eectiveness of the formulation is demonstrated

Numerical analysis of the inclusion-crack interaction by the extended finite element method

Abstract: One of the partition of unity methods, the extended finite element method (XFEM), is applied to study the inclusion-crack interactions in an elastic medium. Both the inclusions and the crack are modelled within the XFEM framework. A structured quadrilateral mesh is used and the influence of crack length, the number of inclusions, and the geometry of the inclusions on the crack tip stress field are numerically studied. The interaction integral for non-homogeneous materials is used to compute the stress intensity factors ahead of the crack tip. The accuracy and flexibility of the XFEM is demonstrated by various numerical examples.

Towards Automatic Stress Analysis using Scaled Boundary Finite Element Method with Quadtree Mesh of High-order Elements

Abstract: This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons that can have any number of edges, be of any high orders and represent the stress singularity around a crack tip accurately without asymptotic enrichment or other special techniques. Owing to these features, a simple and automatic meshing algorithm is devised. No special treatment is required for the hanging nodes and no displacement incompatibility occurs. Curved boundaries and cracks are modelled without excessive local refinement. Five numerical examples are presented to demonstrate the simplicity and applicability of the proposed technique.

Assessment of certain higher-order structural models based on global approach for bending analysis of curvilinear composite laminates

Abstract: In this paper, the performance of different structural models based on global approach in evaluating the static response of curvilinear fibre composite laminates is analyzed. A Co shear flexible Quad-8 element developed based on higher-order structural theory is employed for the present study. The structural theory accounting for the realistic variation of displacements through the thickness and the possible discontinuity in the slope at the interface is considered. Four alternate discrete structural models, deduced from the generic structural model by retaining various terms in the displacement functions are examined for their applicability. The accuracy of the present formulation is demonstrated considering the problems for which analytical solutions are available. A systematic numerical study, assuming different ply-angle and lay-up, is conducted in bringing out the influence of various structural models on the static response of composite laminates with curvilinear fibres.

On the application of the partition of unity method for nonlocal response of low-dimensional structures

Abstract: Abstract The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen’s nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

On the equivalence between the cell-based smoothed finite element method and the virtual element method

Abstract: We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D.

A quadtree-based scaled boundary finite element method for crack propagation modelling

Abstract: The quadtree is a hierarchical-type data structure where each parent is recursively divided into four children. This structure makes it particularly efficient for adaptive mesh refinement in regions with localised gradients. Compared with unstructured triangles, mesh generation is more efficient using quadtree decompositions. The finite number of patterns in the quadtree decomposition makes it efficient for data storage and retrieval. Motivated by these advantages, a crack propagation modelling approach using a quadtree-based scaled boundary finite element method (SBFEM) is developed. Starting from the formulation of an arbitrary n-sided polygon element, each quadrant in the quadtree mesh is treated as a polygon within the framework of the SBFEM. Special techniques to treat the hanging nodes are not necessary. Moreover, the SBFEM enables accurate calculation of the stress intensity factors directly from its solutions without local mesh refinement or asymptotic enrichment functions. When a crack propagates, it is only necessary to split each quadrant cut by the crack into two. These quadrants are polygons that can be directly modelled by the SBFEM. Changes to the mesh are minimal. The efficiency of this approach is demonstrated using numerical benchmarks.

Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets

Abstract: In this paper, the bending and free flexural vibration behaviour of sandwich plates with carbon nanotube (CNT) reinforced facesheets are investigated using QUAD-8 shear flexible element developed based on higher-order structural theory. This theory accounts for the realistic variation of the displacements through the thickness, and the possible discontinuity in slope at the interface, and the thickness stretch affecting the transverse deflection. The in-plane and rotary inertia terms are considered in the formulation. The governing equations obtained using Lagrange's equation of motions are solved for static and dynamic analyses considering a sandwich plate with homogeneous core and CNT reinforced face sheets. The accuracy of the present formulation is tested considering the problems for which solutions are available. A detailed numerical study is carried out based on various higher-order models deduced from the present theory to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness and the plate thickness ratio on the global/local response of different sandwich plates.

A hybrid T-Trefftz polygonal finite element for linear elasticity

Abstract: In this paper, we construct hybrid T-Trefftz polygonal finite elements. The displacement field within the polygon is represented by the homogeneous solution to the governing differential equation, also called as the T-complete set. On the boundary of the polygon, a conforming displacement field is independently defined to enforce continuity of the displacements across the element boundary. An optimal number of T-complete functions are chosen based on the number of nodes of the polygon and degrees of freedom per node. The stiffness matrix is computed by the hybrid formulation with auxiliary displacement frame. Results from the numerical studies presented for a few benchmark problems in the context of linear elasticity shows that the proposed method yield highly accurate results.