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

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

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.

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Liquid Sloshing Dynamics

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.

/pdf/nonlinear-vibrations-and-stability-of-shells-and-plates-4zhg0tiabh.pdf

Nonlinear Vibrations and Stability of Shells and Plates

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.

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

A critical review of recent research on functionally graded plates

Large amplitude vibrations of circular cylindrical shells

Thermal buckling of simply supported functionally graded skew plates

This paper deals with an accurate higher-order theory employing finite element procedure for the free vibration analysis of multi-layered thick composite plates. The theory accounts for the realistic variation of in-plane and transverse displacements through the thickness. The accuracy of the present model is verified by comparison with three-dimensional elasticity solutions for the vibration study of the composite laminates. The performance and the applicability of the proposed discrete model are also discussed among developed elements and alternate models, considering different parameters such as ply-angle, degree of orthotropicity, aspect ratio and boundary conditions.

Free vibration analysis of multi-layered composite laminates based on an accurate higher-order theory

Using a C0 eight-noded plate element developed based on an accurate higher-order theory, the nonlinear dynamics analysis of thick composite and sandwich plates are investigated. The formulation is based on a theory that accounts for the realistic variation of in-plane and transverse displacements through the thickness. It also includes the inertia terms pertaining to the higher-order terms involved in the displacement functions. The geometric nonlinearity is introduced in the formulation based on the relevant Green's strain vector for the laminate. The governing equations of motion obtained here are solved through eigenvalue solution for free vibration case whereas the direct integration technique is employed for the transient response analysis. The performance and the applicability of the proposed discrete model for the nonlinear free flexural and forced vibration responses of thick laminates are discussed among alternate models, considering multi-layered cross- and angle-ply, and sandwich plates.

https://web.iitd.ac.in/~bppatel/publicatios/Nonlinear%20dynamic%20analysis%20of%20thick%20composite%20sandwich%20laminates.pdf

M. Ganapathi

Papers

Large amplitude vibrations of circular cylindrical shells

Thermal buckling of simply supported functionally graded skew plates

Free vibration analysis of multi-layered composite laminates based on an accurate higher-order theory

Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory

Nonlinear free flexural vibrations/post-buckling analysis of laminated orthotropic beams/columns on a two parameter elastic foundation