Homogenization and free-vibration analysis of elastic metamaterial plates by Carrera Unified Formulation finite elements
04 Mar 2021-Mechanics of Advanced Materials and Structures (Taylor & Francis)-Vol. 28, Iss: 5, pp 476-485
TL;DR: In this paper, the authors focus on the assessment of a novel so-called "homogenization method" allowing to transform a heterogeneous material with inclusions or holes into an equivalent homogenous material with holes.
Abstract: This work focuses on the assessment of a novel so-called “homogenization method” allowing to transform a heterogeneous material with inclusions or holes into an equivalent homogeneous material with...
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TL;DR: In this article , the authors proposed an applicable and impressive analytical model of Aircraft Engine Cowl (AEC) due to auspicate its frequency parameter, which is implemented by obtaining the governing motion organization of differential equations affiliated with the Joined Elliptical-Conical Shells (JECS) in line with first-order shear deformation theory (FSDT) and General Shell Formulation (GSF).
Abstract: Abstract The present research proposes an applicable and impressive analytical model of Aircraft Engine Cowl (AEC) due to auspicate its frequency parameter. For the first time, the authors configured the structure of AEC by joining two well-known shapes of shell, including elliptical and conical. This procedure is implemented by obtaining the governing motion organization of differential equations affiliated with the Joined Elliptical-Conical Shells (JECS) in line with first-order shear deformation theory (FSDT) and General Shell Formulation (GSF). Moreover, Functionally Graded Materials (FGMs) with various spreading forms along the structure’s thickness are used to enhance the dynamic performance of AEC. It is worth mentioning that the recognized Rule of Mixture (RM) is engaged for achieving the equivalent mechanical characteristics of FGM. Finally, a well-known semi-analytical Generalized Differential Quadrature (GDQ) procedure is hired to extract the resulting system of motion equations to access the free vibration responses of AEC with diverse Boundary Conditions (BCs). It is worth mentioning that an applicable and interesting numerical model is done to inspect the remnants of geometric and material features on the oscillation demeanor of AEC structures. It will be verified that the projected procedure can be helpful for AEC’s vibration analysis and extendable for other types of studies to predict the AEC structure's static and dynamic treatment.
19 citations
TL;DR: In this article, the authors investigate the soundproofing level of passive acoustic metamaterials made of Melamine Foam and cylindrical Aluminum inclusions, using a frequency-dependent approach.
17 citations
TL;DR: In this paper, the hygrothermal response of free vibration of laminated composite plates is discussed, and the formulation of the nth-order shear deformation theory is modified to discuss the hydrastic response.
Abstract: The formulation of the nth-order shear deformation theory was modified to discuss the hygrothermal response of free vibration of laminated composite plates. Current theory has four unknown variable...
15 citations
TL;DR: In this paper, a bi-stage micromechanical homogenization technique is implemented to attain the effective modulus of such meta-nanocomposites, and the effects of CNT agglomerates on the modulus estimation are captured.
Abstract: Enhancement of the structural elements’ stiffness as well as reducing their weight can be made possible by arranging nanocomposites in an auxetic form. Motivated by this reality, this work undergoes with the postbuckling characteristics of thin beams made from auxetic carbon nanotube-reinforced nanocomposites for the first time. A bi-stage micromechanical homogenization technique is implemented to attain the effective modulus of such meta-nanocomposites. In this method, the effects of CNT agglomerates on the modulus estimation will be captured. Next, the von Karman strain–displacement relations will be hired as well as Euler–Bernoulli beam theory to find the nonlinear strain of the continuous system. Using the principle of virtual work, the nonlinear governing equation of the problem will be gathered. Then, Galerkin’s analytical method will be employed to find the nonlinear buckling load of the auxetic nanocomposite beams with simply supported and clamped ends. After proving the validity of the presented modeling, illustrative case studies are provided for reference. The highlights of this article indicate on the fact that the meta-nanocomposite beam will be strengthened against buckling-mode failure if small auxeticity angles are selected. Also, it is demonstrated that the structure fails under smaller buckling loads if a wide auxetic lattice is employed. Furthermore, it is shown that how can the buckling resistance of the auxetic nanocomposite beam be affected by the agglomeration phenomenon.
13 citations
TL;DR: In this article, the static and mechanical buckling analysis of functionally graded (FG) plates was performed using Carrera's unified formulation (CUF) and the principle of virtual displace.
Abstract: This paper presents the static and mechanical buckling analyses of thick functionally graded (FG) plates. For this purpose, Carrera’s unified formulation (CUF) and the principle of virtual displace...
10 citations
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TL;DR: In this article, the design principles leading to these properties are identified and discussed, in particular, linear and mechanism-based metamaterials (such as origami-based and kirigami based metammaterials), harnessing instabilities and frustration, and topological and nonlinear metam materials.
Abstract: Mechanical metamaterials exhibit properties and functionalities that cannot be realized in conventional materials. Originally, the field focused on achieving unusual (zero or negative) values for familiar mechanical parameters, such as density, Poisson's ratio or compressibility, but more recently, new classes of metamaterials — including shape-morphing, topological and nonlinear metamaterials — have emerged. These materials exhibit exotic functionalities, such as pattern and shape transformations in response to mechanical forces, unidirectional guiding of motion and waves, and reprogrammable stiffness or dissipation. In this Review, we identify the design principles leading to these properties and discuss, in particular, linear and mechanism-based metamaterials (such as origami-based and kirigami-based metamaterials), metamaterials harnessing instabilities and frustration, and topological metamaterials. We conclude by outlining future challenges for the design, creation and conceptualization of advanced mechanical metamaterials.
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TL;DR: This review traces the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values, and their implications for acoustic wave behaviors.
Abstract: Within a time span of 15 years, acoustic metamaterials have emerged from academic curiosity to become an active field driven by scientific discoveries and diverse application potentials. This review traces the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values, and their implications for acoustic wave behaviors. We survey the more recent developments, which include compact phase manipulation structures, superabsorption, and actively controllable metamaterials as well as the new directions on acoustic wave transport in moving fluid, elastic, and mechanical metamaterials, graphene-inspired metamaterials, and structures whose characteristics are best delineated by non-Hermitian Hamiltonians. Many of the novel acoustic metamaterial structures have transcended the original definition of metamaterials as arising from the collective manifestations of constituent resonating units, but they continue to extend wave manipulation functionalities beyond those found in nature.
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01 Dec 1976
TL;DR: The theory and recent applications of wave propagation in periodic structures are reviewed in this paper, and speculations about future problems and development in the field of waves in periodic structure are given.
Abstract: The theory and recent applications of waves in periodic structures are reviewed. Both the Floquet and coupled waves approach are analyzed in some detail. The theoretical part of the paper includes wave propagation in unbounded and bounded active or passive periodic media, wave scatterring from periodic boundaries, source radiation (dipole, Cerenkov, transition, and Smith-Purcell) in-periodic media, and pulse transmission through a periodic slab. The applications part covers the recent development in a variety of fields: distributed feedback oscillators, filters, mode convertors, couplers, second-harmonic generators, deflectors, modulators and transducers in the fields of integrated optics and integrated surface acoustics. We also review the work on insect compound eyes, mehanical structures ocean waves, pulse compressions, temperature waves, and cholestric liquid crystals. Particles interaction with crystals is briefly reviewed, especially in the case of zeolite crystals and supelattices. Recent advances in fabrication techniques for very fine gratings me also covered. Finally, speculations about future problems and development in the field of waves in periodic structures are given.
468 citations
TL;DR: The notion of a “transfinite element” is introduced which, in brief, is an invertible mapping from a square parameter domainJ onto a closed, bounded and simply connected regionℛ in thexy-plane together with a ‘transFinite’ blending-function type interpolant to the dependent variablef defined overℚ.
Abstract: In order to better conform to curved boundaries and material interfaces, curved finite elements have been widely applied in recent years by practicing engineering analysts. The most well known of such elements are the "isoparametric elements". As Zienkiewicz points out in [18, p. 132] there has been a certain parallel between the development of "element types" as used in finite element analyses and the independent development of methods for the mathematical description of general free-form surfaces. One of the purposes of this paper is to show that the relationship between these two areas of recent mathematical activity is indeed quite intimate. In order to establish this relationship, we introduce the notion of a "transfinite element" which, in brief, is an invertible mapping $$\vec T$$ from a square parameter domainJ onto a closed, bounded and simply connected region? in thexy-plane together with a "transfinite" blending-function type interpolant to the dependent variablef defined over?. The "subparametric", "isoparametric" and "superparametric" element types discussed by Zienkiewicz in [18, pp. 137---138] can all be shown to be special cases obtainable by various discretizations of transfinite elements Actual error bounds are derived for a wide class of semi-discretized transfinite elements (with the nature of the mapping $$\vec T$$ :J?? remaining unspecified) as applied to two types of boundary value problems. These bounds for semi-discretized elements are then specialized to obtain bounds for the familiar isoparametric elements. While we consider only two dimensional elements, extensions to higher dimensions is straightforward.
465 citations