Three-layer Shell Research Articles

Динаміка тришарових циліндричних оболонок еліптичного перерізу з поздовжнім ребристим наповнювачем при нестаціонарних навантаженнях

Динаміка тришарових циліндричних оболонок еліптичного перерізу з поздовжнім ребристим наповнювачем при нестаціонарних навантаженнях

Nonlocal problems in the mechanics of three-layer shells

We consider an elastic system consisting of two coaxial cylindrical shells connected by goffered filler. Using a variational principle, this model is reduced to a boundary value problem for strongly elliptic system of differential-difference equations. It is proved the existence and uniquenesss of generalized solution of the above problem, smoothness of solution, and convergence of the Ritz method.

Multi-layered elastic shell metamaterial elements for improved transmission in sonic crystals

A metamaterial-based sonic crystal, comprised of a lattice arrangement of cylindrical elastic shells, can be tuned to provide wave steering or phononic band filtering. The effective acoustic properties of such sonic crystals are determined by the geometric and material properties of each individual shell and the lattice spacing between shells. By matching the effective acoustic properties to those of the surrounding fluid, the sonic crystal can be made acoustically transparent at low frequencies, leading to improved transmission over that of non-matched shells. Bi-layered shells provide additional design parameters to broaden the region of acoustic transparency provided by a simple shell. In this effort, three-layered shells are employed to improve transmission further. Transformation acoustics analysis is applied to determine theoretical density and bulk modulus distributions, and then real-world materials are selected which best match these theoretical distributions. Finally, shell geometry is optimized to minimize scattering while constraining the effective acoustic properties to match those of the external fluid.

Calculation of the Three-layer Shell Taking into Account Creep

We obtained resolving equations of finite element method to calculate the three-layer shells taking into account the creep of the middle layer. The outer layers of the shell are considered elastic and isotropic. We investigated the influence of curvature of a shell on the growth of deflection due to creep. The example of calculation is given for a spherical shell, hinged along the contour and loaded by uniformly distributed load. It was found that with increasing of curvature of the shell influence of creep on deflection has reduced.

Rapid heating-induced vibration of composite magnetostrictive shells

ABSTRACTThe generalized differential quadrature method is used to obtain the computational results of three-layer cross-ply composite magnetostrictive shells under sudden uniform heat-induced vibration. In the thermal vibration analyses of a laminated magnetostrictive shell, the sudden uniform heat input over its inner surface only and temperature load is linear of axial coordinate. The shell with velocity feedback control loop and with suitable gain value can reduce the amplitudes of displacement and stress to smaller values, respectively, almost to a 0 value due to the control law contribution of the magnetostrictive layer.

Limit State of a Composite Three-Layered Cylindrical Shell under Internal Pressure

The method is proposed for determining the limit state of a cylindrical shell with the bottom considered as a three-dimensional body that is under internal pressure, has no damage and has local damage in the form of a crack. The problem is solved experimentally and by numerical and analytical method using the finite element technique.

ИМПУЛЬСНЫЕ ВОЗДЕЙСТВИЯ НА ТРЕХСЛОЙНЫЕ КРУГОВЫЕ ЦИЛИНДРИЧЕСКИЕ ОБОЛОЧКИ В УПРУГОЙ СРЕДЕ

ИМПУЛЬСНЫЕ ВОЗДЕЙСТВИЯ НА ТРЕХСЛОЙНЫЕ КРУГОВЫЕ ЦИЛИНДРИЧЕСКИЕ ОБОЛОЧКИ В УПРУГОЙ СРЕДЕ

An inverse parallel genetic algorithm for the identification of skin/core debonding in honeycomb aluminium panels

Honeycomb sandwich structures are used in a wide variety of applications. Nevertheless, because of manufacturing defects or impact loads, these structures can experience imperfect bonding or debonding between the skin and the honeycomb core. Instances of debonding reduce the bending stiffness of the composite panel, which causes detectable changes in its vibration characteristics. This article presents a new methodology to identify debonded regions in aluminium honeycomb panels that uses an inverse algorithm based on parallel genetic algorithms. The honeycomb panels are modelled with finite elements using a simplified three-layer shell model. The adhesive layer between the skin and core is modelled using linear springs, with reduced rigidity for the debonded sectors. The algorithm is validated using experimental data from an aluminium honeycomb panel containing different damage scenarios. Copyright © 2015 John Wiley & Sons, Ltd.

Natural vibrations of three-layer circular cylindrical shells in an elastic medium

Free vibrations of a three-layer cylindrical circular shell in an elastic medium are considered. It is assumed that the bearing layers satisfy the Kirchhoff-Love hypotheses. The work of transverse shear and the compression over the thickness are taken into account in the thick filler. It is assumed that the variations in the displacements are linear in the transverse coordinate. The displacement continuity conditions are used on the boundaries of contact. The Winkler hypothesis is accepted for the elastic inertialess environment. The variation in the natural vibration frequencies depending on the rigidity characteristics of the shell-environment system is studied.

Fonksiyonel Değişimli Çekirdeğe Sahip Üç Tabakalı Silindirik Kabukların Parametrik Titreşimi

In this study, the parametric vibration of three-layered cylindrical shells with functionally graded (FG) core is investigated. Firstly, analytical models of an FG core, which uses the intermediate member and outer sheath layers of the cylindrical shell formed from metal-rich and ceramic-rich represented as ternary systems. The governing equations of three-layered cylindrical shells with an FG core are derived and are reduced Mathieu-Hill equation by using Galerkin method. The expressions for non-dimensional frequency, critical axial load and boundaries of instability regions of three-layered cylindrical shell with an FG core are found. The expressions for non-dimensional frequency parameter, critical axial load and boundaries of instability regions are obtained for the monolayer FGM, pure metal and pure ceramic cylindrical shells, as a special case. Finally, the effects of variations of volume fractions, shell characteristics and variations of the thickness of a core on the values of critical parameters of three-layered cylindrical shells made of different types of FG core are studied numerically. Comparisons are made with the available studies in the open literature to validate this study

Stability of three-layer cylindrical shell ​​of composite material with orthotropic intermediate layer

The article deals with the stability of a three-layer cylindrical shell under external hydrostatic pressure. The intermediate layer (filler) is considered as a three-dimensional orthotropic body. The proposed algorithm for calculation of the upper critical pressure is tested on well-known solutions of the stability of three-layer cylindrical shells.

Non-linear vibrations of three-layer non-homogeneous circular cylindrical shells

The problem of nonlinear vibrations of three-layer non-homogeneous circular cylindrical shells is studied in the paper. It is assumed that layers are made of various heterogeneous isotropic materials, and elastic characteristics are continuous coordinate functions of the shell thickness. Taking the validity of the Kirchhoff-Love hypothesis for the whole element, the expressions for the forces and moments are obtained, and generalized stiffness characteristics for the considered three-layer circular cylindrical shell are defined. In general, all basic relations and system of motion equations of shell taking into account geometric nonlinearity are obtained. Approximate formulation of the problem is also considered. Two motion equations of the problem with respect to deflection and stress function are obtained in the approximate formulation of the problem. The solution on nonlinear vibration of three-layer cylindrical panel with pin-edge fixing is studied in detail. An analytical solution is obtained, and the dependence of the amplitude-frequency characteristics is determined. To perform numerical calculations, inhomogeneity functions of the layer material were taken as linear coordinate functions of the shell thickness. The results of numerical calculations are presented in the form of the characteristic graph.

A Maximum Entropy Approach to Assess Debonding in Honeycomb aluminum Plates

Honeycomb sandwich structures are used in a wide variety of applications. Nevertheless, due to manufacturing defects or impact loads, these structures can be subject to imperfect bonding or debonding between the skin and the honeycomb core. The presence of debonding reduces the bending stiffness of the composite panel, which causes detectable changes in its vibration characteristics. This article presents a new supervised learning algorithm to identify debonded regions in aluminum honeycomb panels. The algorithm uses a linear approximation method handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of neural networks. The honeycomb panels are modeled with finite elements using a simplified three-layer shell model. The adhesive layer between the skin and core is modeled using linear springs, the rigidities of which are reduced in debonded sectors. The algorithm is validated using experimental data of an aluminum honeycomb panel under different damage scenarios.

Brachiopod fabric, classes and biogeochemistry: Implications for the reconstruction and interpretation of seawater carbon-isotope curves and records

Shell calcite of modern and ancient brachiopods is an important proxy in reconstructing oceanographic conditions of seawater. Our investigation reveals significant magnesium and carbon isotope relationships between two classes of ancient brachiopods. Brachiopods of the extinct Class Strophomenata constructed two- or three-layer shells with a primary layer of randomized granular calcite, a secondary layer of cross-bladed laminar calcite and, at times, a tertiary layer of large prismatic calcite. Contemporaneous, but extant, Rhynchonellata also have two- or three-layer shells, but their secondary layer consists of calcite fibers instead of cross-bladed laminar calcite. Furthermore, inter-crystalline space is limited in between the fibers of the secondary layer of the Rhynchonellata but higher in the laminar secondary layer of Strophomenata. δ18O values of the two classes of brachiopods from the same stratigraphic interval of the Lopingian Nesen Formation of North Iran show a considerable overlap with no significant difference (p=0.263). In contrast, carbon isotope values are significantly different (p=0.001) between contemporaneous Strophomenata (mean: +2.18‰) and Rhynchonellata (mean: +4.13‰). An evaluation of literature data of Permian (Asselian) and Carboniferous (Visean and Serpukhovian) Strophomenata (mean: +2.32‰, N=59) and Rhynchonellata (mean: +4.94‰, N=105) confirms a similar differentiation in their carbon isotope values.Its higher magnesium contents suggest that the Strophomenata probably secreted shell calcite at a faster rate than their coeval Rhynchonellata. This process may account for the δ13C differentiation observed between specimens of these two brachiopod classes. However, the different amount and composition of the organic matter of the Strophomenata may also play a role in shaping their more negative carbon isotope signature. Thus, the class of brachiopod and their associated different fabric must be adjusted for in their δ13C results and taken into consideration during the reconstruction of Paleozoic global δ13C carbonate-based seawater curves. Invariably, in some earlier studies undetected impacts imposed by the class-fabric on δ13C may account for some of the variation or trends documented in Deep–Time seawater–13C curves reconstructed with brachiopod populations from North America, Europe and Russia.

Fatigue modelling of aluminium plates reinforced with bonded fibre metal laminates

Purpose – This paper aims to present the implementation of a finite element (FE) model used to establish crack and delamination development in a Glare reinforced aluminium plate under fatigue loading. This model predicts the behaviour of bonded GLARE straps used as crack retarders for life extension of aircraft structures. In particular, it takes into account the interaction that exists between the substrate crack and the delamination crack at the interface with the reinforcement. Design/methodology/approach – In this work, a 3D FE model with three-layer continuum shell elements has been developed to calculate changes in substrate stress intensity and in fatigue crack growth (FCG) rate produced by bonded strap reinforcement. Both circular and elliptical strap delamination geometries were incorporated into the model. Calculated stress intensity factors (SIFs) were used together with measured FCG data for substrate material to predict FCG rates for the strapped condition. Findings – The model predicted a decrease in the SIF and a retardation of FCG rates. The SIF was predicted to vary through the thickness of the substrate due to the phenomenon of secondary bending and also the bridging effect caused by the presence of the strap. The influence of delamination shape and size on substrate crack stress intensity and delamination strain energy release rate has been calculated. Originality/value – This research aims at developing modelling techniques that could be used when studying larger reinforced structures found in aircraft.

PARALLEL COMPUTING TECHNOLOGIES IN THE FINITE ELEMENT METHOD

Nowadays engineers and researchers are faced with solving very complex problems in a mathematical modeling and design. Numerical analysis naturally finds applications in all fields of engineering and the physical sciences. The finite element method is a powerful tool for the numerical simulation of a wide range of problems. Implementation of the finite element method in CAD systems on the basis of modern computers allows researchers to solve large scale problems. The finite element method uses a discretization of a continuum domain into a mesh as the starting point. The discretization of complex domains may give large numbers of elements, thus increasing the requirements of computer memory and speed. Modern parallel computers use multiple processing elements simultaneously to solve a problem. Thus implementation of parallel computing into the finite element method is urgent direction of the research. In the finite element method for the numerical solution of partial differential equations, the stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. Therefore the article describes parallel algorithms for assembly of stiffness matrix and for solution of linear equations. Also this article contains two numerical experiments: 1) Dirichlet problem on the complex domain (gear); 2) Elasticity problem of three-layer shell. In the end of the article author compares the speed of a solution of these problems with one, two and four parallel cores and makes discussion about the effectiveness of parallel finite element processing.

Effect of a functionally graded interlayer on the non-linear stability of conical shells in elastic medium

In this paper, the effect of a functionally graded (FG) interlayer on the non-linear stability of three-layered truncated conical shells surrounded by an elastic medium is investigated. The properties of functionally graded material (FGM) of the interlayer are assumed to be graded in the thickness direction according to a simple power law distribution. The Pasternak model is used to describe the reaction of the surrounded elastic medium on the truncated conical shell. The basic equations of the truncated conical shell with a FG interlayer resting on the Pasternak elastic foundation are derived using the Donnell shell theory with von Karman-type of kinematic non-linearity. The basic equations are solved by using Superposition and Galerkin methods. The numerical results reveal that variations of three-layered shell characteristics, Winkler foundation stiffness, shear subgrade modulus of the foundation and the compositional profiles of the FG layer have significant influences on the non-linear critical axial load. The results are verified by comparing the obtained values with those in the existing literature.

Solvability of a connected thermoelasticity problem for three-layer shells

Using a newmethod for obtaining a priori bounds, we prove the solvability of a connected thermoelasticity problem “with displacements” for shallow three-layer shells within the Grigolyuk and Chulkov conjectures, taking into account the geometric nonlinearity.

Stability Analysis of FGM Layered Shells in the Surrounding Medium

In this study, the stability analysis of three-layered shells containing a functionally graded material layer in the surrounding medium and subjected to the uniform lateral pressure is investigated. The surrounding elastic medium is modeled as a Pasternak foundation. The dimensionless critical lateral pressures of three-layered functionally graded material shells with and without elastic foundations are obtained. Effects of compositional profiles and elastic foundation on the dimensionless critical lateral pressures have been studied.

Forced vibrations of three-layer elliptic cylindrical shells under distributed loads

The dynamic behavior of a three-layer elliptic cylindrical shell is studied and associated problems are formulated. The refined Timoshenko model is used. The numerical method used to solve the equations of motion is based on the integro-interpolation differencing method. The dynamic behavior of a three-layer elliptic cylindrical shell under a distributed nonstationary load is studied.