M. Touratier

Bio: M. Touratier is an academic researcher from Pierre-and-Marie-Curie University. The author has contributed to research in topics: Rotary inertia & Finite element method. The author has an hindex of 5, co-authored 6 publications receiving 149 citations.

Application of spline element for large-amplitude free vibrations of laminated orthotropic straight/curved beams

Abstract: Using a cubic B-spline shear flexible curved element, based on the field consistency principle, the nonlinear free flexural vibrations of isotropic/laminated orthotropic straight/curved beams have been studied. The nonlinear governing equations are solved by employing Newmark's numerical integration scheme coupled with modified Newton-Raphson iteration technique. Amplitude-frequency relationships are obtained from the non-linear dynamic response history. Detailed numerical results are presented for various parameters for isotropic and laminated orthotropic beams. The present study brings out the type of non-linearity associated with the curved beams and its dependency on the interaction of curvature with initial amplitude of the beams.

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.

Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method

Abstract: Here, asymmetric free vibration characteristics and thermoelastic stability of functionally graded circular plates are investigated using finite element procedure. A three-noded shear flexible plate element based on the field-consistency principle is used. Temperature field is assumed to be a uniform distribution over the plate surface and varied in thickness direction only. Material properties are graded in the thickness direction according to simple power law distribution. For the numerical illustrations, aluminum/alumina is considered as functionally graded material. The variation in critical buckling load is highlighted considering gradient index, temperature, radius-to-thickness ratios, circumferential wave number and boundary condition of the plate.