M. Ganapathi

Bio: M. Ganapathi is an academic researcher from VIT University. The author has contributed to research in topics: Finite element method & Rotary inertia. The author has an hindex of 33, co-authored 102 publications receiving 3142 citations. Previous affiliations of M. Ganapathi include Indian Institute of Technology Madras & Indian Institute of Technology Delhi.

A New C Eight-Noded Plate Element for Static & Dynamic , Analyses of Composite Laminates

Abstract: This paper deals witU a new 48-degrees-of-freedom rectangular finite element for analysing moderately thick multilayered composite plates. The formulation is based on a kinematics which allows one to exactly ensure the continuity conditions for the displacements, and the transverse strsses at the interfaces between the layers of a laminated structure and zeros1lress conditiQns at the top and bottom surfaces of the plate. The shear correction factorsare not required in the formulation, as the transverse shear deformations are defined usingtrigonometric 'runctions that are of higher order. The effectiveness of the element is testedagainst standard problems concerning statics, vibration and buckling, for which exact three dimensional/numerical solutions areiavailable.

Nonlinear Asymmetric Dynamic Buckling of Isotropic/Laminated Orthotropic Spherical Caps

Abstract: Here, the nonlinear dynamic behavior of clamped isotropic/laminated composite spherical caps under suddenly appliedloadsisstudiedusingathree-nodedaxisymmetriccurvedshellelementbasedone eldconsistencyapproach. The formulation is based on e rst-order shear deformation theory, and it includes the in-plane and rotary inertia effects.Geometricnonlinearity is introduced in theformulationusing von Karman’ sstrain-displacementrelations. The governing equations obtained are solved employing the Newmark’ s integration technique coupled with a modie edNewton‐ Raphsoniteration scheme.Theload beyond which themaximum averagedisplacementresponse shows signie cant growth in the time history of the shell structure is taken as dynamic buckling pressure. The present model is validated against theavailableanalytical solutions and also with the results evaluated using threedimensional e nite element method. A detailed parametric study is carried out to bring out the effects of shell geometries, orthotropicity, and the number of layers in the cross-ply laminates on the axisymmetric/asymmetric dynamic buckling load of shallow spherical shells. I. Introduction T HIN spherical shells form an important class of structural components, with many signie cant applications in engineering e elds. These shells subjected to dynamic load could encounter dee ections of the order of the thickness of the shell. The dynamic response of such shells can lead to the phenomenon of dynamic snapping or dynamic buckling. Because these kinds of responses cannot be determined accurately using small displacement theory, nonlinear dynamic analysis is required, and such study has received considerable attention in the literature. However, most of the available works are related to axisymmetric behavior of homogeneous, isotropic, or single-layered orthotropic spherical shells subjected to the step pressure load of ine nite duration. The present tendency to use e ber-reinforced composite materials for the structural components necessitates the analysis of shells made up of layers of such materials, leading to anisotropic behavior. Moreover, quite often, the asymmetric modes of these shells might be excited as a result of the introduction ofslight deviation in perfectaxisymmetric loading, geometric imperfection, and/or initial displacement/velocity to the shells. The anisotropic material properties coupled with the asymmetric structural behavior render the failure analysis of these shells quite complex. Hence, there is a growing appreciation of the importance of studying the dynamic response, in particular, dynamic bucklingoflaminatedcompositesphericalshellsandhasconstituted a major e eld of research in structural mechanics. First, a brief review of important contributions to the axisymmetric dynamic snap-through buckling of spherical case is presented here. The analysis of isotropic shallow spherical shells has been carried out by Budiansky and Roth, 1 Simitses, 2 Huang, 3 Stephens andFulton, 4 BallandBurt, 5 andStricklinandMartinez. 6 Budiansky and Roth 1 have employed the Galerkin method, whereas Simitses 2 adoptedtheRitz ‐Galerkinprocedure.Ae nitedifferenceschemehas been introduced in the method of solution by Huang, 3 Stephens and Fulton, 4 andBallandBurt, 5 whereasStricklinandMartinez 6 utilized

A new shear flexible cubic spline plate element for vibration analysis

Abstract: Here, a new cubic B-spline plate element is developed using field consistency principle, for vibration analysis. The formulation includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects. The element is based on a laminated refined plate theory, which satisfies the interface transverse shear stress and displacement continuity, and has a vanishing shear stress on the top and bottom surfaces of the plates. The lack of consistency in the shear strain field interpolations in its constrained physical limits produces poor convergence and results in unacceptable solutions due to locking phenomenon. Hence, numerical experimentation for the evaluation of natural frequencies of plates is carried out to check this deficiency with a series of assumed shear strain functions, redistributed in a field consistent manner.

Nonlinear Stability of Functionally Graded Plates Subjected to Aero-thermo-mechanical Loads

Abstract: The nonlinear stability behaviors of functionally graded material plates subjected to aero-thermo-mechanical loads are studied. The material properties are graded in the thickness direction according to power-law distribution. A finite element method is employed with a eight-noded Co shear flexible quadrilateral plate element. The influences of material gradient index, thickness of plate, boundary condition, and aspect ratio on the nonlinear characteristics of functionally graded plates are investigated.

Modeling and Analysis of Functionally Graded Materials and Structures

Abstract: This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

Liquid Sloshing Dynamics

Abstract: Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

Nonlinear Vibrations and Stability of Shells and Plates

Abstract: Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells

Abstract: This work is an overview of available theories and finite elements that have been developed for multilayered, anisotropic, composite plate and shell structures. Although a comprehensive description of several techniques and approaches is given, most of this paper has been devoted to the so called axiomatic theories and related finite element implementations. Most of the theories and finite elements that have been proposed over the last thirty years are in fact based on these types of approaches. The paper has been divided into three parts. Part I, has been devoted to the description of possible approaches to plate and shell structures: 3D approaches, continuum based methods, axiomatic and asymptotic two-dimensional theories, classical and mixed formulations, equivalent single layer and layer wise variable descriptions are considered (the number of the unknown variables is considered to be independent of the number of the constitutive layers in the equivalent single layer case). Complicating effects that have been introduced by anisotropic behavior and layered constructions, such as high transverse deformability, zig-zag effects and interlaminar continuity, have been discussed and summarized by the acronimC -Requirements. Two-dimensional theories have been dealt with in Part II. Contributions based on axiomatic, asymtotic and continuum based approaches have been overviewed. Classical theories and their refinements are first considered. Both case of equivalent single-layer and layer-wise variables descriptions are discussed. The so-called zig-zag theories are then discussed. A complete and detailed overview has been conducted for this type of theory which relies on an approach that is entirely originated and devoted to layered constructions. Formulas and contributions related to the three possible zig-zag approaches, i.e. Lekhnitskii-Ren, Ambartsumian-Whitney-Rath-Das, Reissner-Murakami-Carrera ones have been presented and overviewed, taking into account the findings of a recent historical note provided by the author. Finite Element FE implementations are examined in Part III. The possible developments of finite elements for layered plates and shells are first outlined. FEs based on the theories considered in Part II are discussed along with those approaches which consist of a specific application of finite element techniques, such as hybrid methods and so-called global/local techniques. The extension of finite elements that were originally developed for isotropic one layered structures to multilayerd plates and shells are first discussed. Works based on classical and refined theories as well as on equivalent single layer and layer-wise descriptions have been overviewed. Development of available zig-zag finite elements has been considered for the three cases of zig-zag theories. Finite elements based on other approches are also discussed. Among these, FEs based on asymtotic theories, degenerate continuum approaches, stress resultant methods, asymtotic methods, hierarchy-p,_-s global/local techniques as well as mixed and hybrid formulations have been overviewed.