Plane finite element for static and free vibration analysis of sandwich plates

Conclusions Triangular sandwich finite elements (MPLW30) with 30 DOF have been developed for the static and free vibration analysis of sandwich plates with thin faces and low core shear modules. The results of numerical examples presented here demonstrate the accuracy and suitability of the formulations for the analysis of sandwich plates with k_H > 25 and k_E > 200.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 2, pp 238–248, March–April, 1994.     

The role of transverse stretching in the delamination fracture of softcore sandwich plates

This paper presents the semi-layerwise analysis of structural sandwich plates with through-width delamination. The mechanical model of rectangular plates is based on the method of four equivalent single layers and the system of exact kinematic conditions. An important improvement compared to a previous formulation is the consideration of linear and quadratic stretching term in the transverse displacement component. Three different delamination scenarios are investigated: core-core failure, face-core delamination and the face-face failure. By applying the first- and second-order laminated plate theories and the principle of virtual work the governing equations are derived. The equilibrium equations are solved under Lévy type boundary conditions using the state-space approach. Solutions for the mechanical fields are provided and compared to 3D finite element results. The energy release rate distributions along the delamination front are also determined using the J-integral. Although the stress resultants by transverse stretching do not influence directly the J-integral, the results indicate that this effect improves the accuracy of the model in general, and substantially influences the results of the first-order plate theory in the case of the face-face delamination.     

Theories for laminated and sandwich plates

The growing use of sandwich and laminated plates requires a theoretically based prediction of the mechanical behavior of structural elements of such type. Starting with the pioneering studies of Reissner, a great number of theories for the engineering calculations have been developed. The review deals with the classification of the theories and discusses some of them in detail.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Martin Luther Universität, Halle-Wittenberg, Fachbereich Werkstoffwissenschaften, D-06099 Halle, Germany. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 333–348, 1998.     

Finite element buckling and postbuckling solutions for multilayered composite panels

A study is made of the buckling and postbuckling responses of flat, unstiffened composite panels subjected to various combinations of mechanical and thermal loads. The analysis is based on a first-order shear deformation von Karman-type plate theory. A mixed formulation is used with the fundamental unknowns consisting of the strain components, stress resultants and the generalized displacements of the plate. The stability boundary, postbuckling response and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented for both solid panels and panels with central circular cutouts. The results show the effects of the variations in the fiber orientation angles, aspect ratio of the panel, and the hole diameter (for panels with cutouts) on the stability boundary, postbuckling response and sensitivity coefficients.     

Methods of finite element analysis of arbitrary buckling forms of sandwich plates and shells

Two statements of the problem of arbitrary buckling forms (BFs) (including synphasic, antiphasic, mixed flexural, flexural-shear, and shear forms in the tangential directions) of general-form sandwich shells and two schemes of its solution by the FEM are given. The first of the schemes is based on the use of refined linear equations for determination of the precritical stress-strain state and linearized equations of neutral equilibrium with all parametric addends necessary to determine the critical loads and reveal the possible BFs. The second one uses the general geometrically nonlinear relations of elasticity theory for investigation of the whole deformation process up to buckling in terms of a modified incremental (stepwise) statement of the problem. Examples of solution of particular problems are given.Center for Study of Dynamics and Stability, Tupolev Kazan' State Technical University, Kazan', Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 473–486, July–August, 2000.     

Dynamic behaviour of sandwich plates

Summary This paper discusses the physical behaviour of bending waves in sandwich plates in which the facings are thin, stiff and heavy as compared with the core. By means of asymptotic expansions of the basic equations of linear elasticity, it is shown that different physical mechanims predominate in different frequency ranges. The consequence is that different, but relatively simple equations of motion may be used within limited frequency ranges. The predictions of such an equation, valid for moderate frequencies, are compared with measurements performed on glass-polyurethane sandwich plates. The agreement of theoretical and experimental dispersion curves for axisymmetric waves, and hence for plane waves as well, was found to be very satisfactory.

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Zusammenfassung Die vorliegende Arbeit diskutiert das physikalische Verhalten von Biegewellen in Sandwichplatten mit im Vergleich zum Kern dünnen, steifen und schweren Druckplatten. Mit Hilfe asymptotischer Entwicklungen der Grundgleichungen des linearelastischen Kontinuums wird gezeigt, daß in verschiedenen Frequenzbereichen ganz verschiedene physikalische Verhaltensweisen vorherrschen. Innerhalb beschränkter Frequenzbereiche können daher verschiedene, dafür verhältnismäßig einfache Bewegungsgleichungen Verwendung finden. Die Voraussagen einer solchen Gleichung, gültig für mäßige Frequenzen, werden verglichen mit Messungen, die an Glas-Polyurethan-Sandwichplatten ausgeführt worden sind. Die theoretischen und die experimentellen Dispersionskurven für rotationssymmetrische und somit auch für ebene Wellen stimmen gut überein.

     

Design of axisymmetric sandwich plates for alternative loads

The minimal-weight design of sandwich plates whose rigidplastic face sheets obey the Tresca yield condition and which are subjected to two alternative loads is systematically determined by the method of stress variation. It is shown that, when the loads are unidirectional, the general solution for a certain class of edge conditions consists of five fundamentally different designs. The totality of optimal design solutions is depicted in the form of a design chart. A comprehensive example is presented to illustrate the method.This paper is based in part upon a dissertation submitted by the first author to The University of Iowa in partial fulfillment of requirements for the PhD Degree.     

Multi-dimensional deformation tests of sandwich plates

Sandwich-type plates are widely used in present technical structures. A variety of special sandwich theories and composite laminated plate theories (CLT, FSDT, HSDT) are available for calculating plate deflections. Since the problem of assessing these theories still exists, a new test apparatus for multilayered composite and sandwich plates was developed. Different types of sandwich plates were used in quasistatic multidimensional deformation tests. Deflections and thickness reductions are compared with the theoretical results obtained by sandwich theories, CLT-, FSDT-, HSDT-, and 3D-solutions.Submitted to the 10th International Conference on Mechanics of Composite Materials, Riga, April 20–23, 1998.Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 612–625, September–October, 1997.     

A homogeneous limit methodology and refinements of computationally efficient zigzag theory for homogeneous,laminated composite,and sandwich plates

The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is revisited to offer a fresh insight into its fundamental assumptions and practical possibilities. The theory is introduced from a multiscale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first‐order shear‐deformation theory, whereas the fine displacement field has a piecewise‐linear zigzag distribution through the thickness. The resulting kinematic field provides a more realistic representation of the deformation states of transverse‐shear‐flexible plates than other similar theories. The condition of limiting homogeneity of transverse‐shear properties is proposed and yields four distinct variants of zigzag functions. Analytic solutions for highly heterogeneous sandwich plates undergoing elastostatic deformations are used to identify the best‐performing zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse‐shear‐stress equilibrium constraints. For all material systems, there are no requirements for use of transverse‐shear correction factors to yield accurate results. To model homogeneous plates with the full power of zigzag kinematics, infinitesimally small perturbations in the transverse shear properties are derived, thus enabling highly accurate predictions of homogeneous‐plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. This theory, which is derived from the virtual work principle, is well‐suited for developing computationally efficient, C⁰ a continuous function of (x₁,x₂) coordinates whose first‐order derivatives are discontinuous along finite element interfaces and is thus appropriate for the analysis and design of high‐performance load‐bearing aerospace structures. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

A finite element formulation for the analysis of interlaminar shear stresses in layered composite plates

Fiber reinforced composite plates are often highly stressed structures. For an efficient design of such plates interlaminar stresses have to be evaluated as precisely as possible. In this paper we propose a finite element formulation for the analysis of transverse shear stresses in layered composite plates. For this purpose the equilibrium equations are exploited with appropriate shape functions in weak form which leads to a local discrete boundary value problem. Two different models to compute the derivatives of the strains are considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastic impact of spheres on sandwich plates

An integro-differential equation for the elastic impact of spheres on soft core sandwich plates is analytically derived. The impact equation is numerically integrated and the displacement of the sandwich plate underneath the point of impact is calculated as a function of time. Fairly good agreement with experimental results obtained by the author was found. It is emphasized that, physically, the impact response of a sandwich plate is fundamentally different from the response of an isotropic plate.

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Zusammenfassung Die vorliegende Arbeit behandelt den elastischen Stoß von Kugeln auf Sandwichplatten mit weichem Kern. Eine Integro-Differentialgleichung für den Stoßprozeß wird analytisch hergeleitet und numerisch integriert. Die Auslenkung der Platte unter der Aufprallstelle wird als Funktion der Zeit berechnet; es ergibt sich eine befriedigende Übereinstimmung mit experimentellen Werten. -Im Vordergrund steht das Resultat, daß dünne isotrope Platten und Sandwichplatten grundsätzlich verschieden auf einen Stoß reagieren.

     

Buckling delamination of a sandwich plate-strip with piezoelectric face and elastic core layers

In this study, the buckling delamination problem of a sandwich plate-strip with a piezoelectric face and elastic core layers is studied. It is assumed that the plate-strip is simply supported and grounded along its two parallel ends and is subjected to uniformly-distributed compressive forces on these ends. Moreover, we suppose that the plate-strip has two interface inner cracks between the face and the core layers and it is also supposed that before the plate-strip is loaded (i.e. in the natural state), the surfaces of these cracks have insignificant initial imperfections. Due to compressive forces acting along the cracks we investigate the evolution of the initial imperfections of the cracks’ surfaces. Hence, the values of the critical buckling delamination force of the considered plate-strip are determined from the criteria, according to which, the considered initial imperfections of the cracks’ surfaces grow indefinitely by the compressive forces. Mathematical modeling of the considered problem is formulated within the scope of the exact nonlinear equations of electro-elasticity in the framework of the piecewise homogeneous body model, the solution of which is found numerically by employing the finite elements method. Numerical results showing the influences of the geometrical and material parameters as well as the coupling of the electrical and mechanical fields on the values of the critical force are presented and analyzed.     

A system of steel-elastomer sandwich plates for strengthening orthotropic bridge decks

The use of a sandwich plate system (SPS) composed of two steel plates with a solid polymer (polyurethane) core has been introduced as a refurbishment procedure for steel decks of bridges, the so-called orthotropic decks consisting of a deckplate with longitudinal stiffeners and transverse crossbeams. Unfortunately, a great many of existing steel bridges still have structural members that do not comply with the recommendations given in design codes, and therefore damages have developed in them. For a satisfactory refurbishment of the bridges, the SPS technique fulfils all necessary requirements. To this end, both experimental and calculative investigations were carried out at RWTH Aachen to demonstrate the reinforcing and stiffening effect and to prove the suitability of the SPS-overlay technique for general use. The practical applicability of a SPS has been tested successfully in a pilot project for a German motorway bridge under severe traffic. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 271–282, March–April, 2007.     

Free vibration of sandwich plates with impact-induced damage

Free vibrations of impact-damaged sandwich plates with honeycomb and foam cores are studied. It is assumed that damages caused by impact events are to exist before the vibration start and to be constant during oscillations. The influence of the impact damage modes involving the core crushing (planar damage), face sheets fracture (indentation) and the core to face sheets interface degradation (debonding) on the natural frequencies and associated mode shapes of the sandwich plates was investigated using commercially available finite element code ABAQUS. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates

This paper presents an alternative alpha finite element method using triangular meshes (AαFEM) for static, free vibration and buckling analyses of laminated composite plates. In the AαFEM, an assumed strain field is carefully constructed by combining compatible strains and additional strains with an adjustable parameter α which can produce an effectively softer stiffness formulation compared to the linear triangular element. The stiffness matrices are obtained based on the strain smoothing technique over the smoothing domains and the constant strains on triangular sub-domains associated with the nodes of the elements. The discrete shear gap (DSG) method is incorporated into the AαFEM to eliminate transverse shear locking and an improved triangular element termed as AαDSG3 is proposed. Several numerical examples are then given to demonstrate the effectiveness of the AαDSG3.     

The minimum weight design of circular sandwich plates

Résumé Dans ce mémoire nous étudions le problème statique du choix des dimensions suivant: Comment doit varier l'épaisseur de point en point dans les plaques circulaires fléchies du type sandwich, pourque leur poids soit minimum, mais sans qu'il existe du fluage illimité? Comme hypothèse de base, nous avons pris la condition de plasticité devon Mises et la règle de fluage associée. Les plaques sont simplement posées ou encastrées le long de leur contour et portent une charge répartie symétriquement par rapport à l'axe. Les résultats obtenus sont comparés à ceux du problème analogue, où l'on utilise la condition de plasticité deTresca. Nous avons présenté finalement quelques résultats numériques.     

Transient dynamics of composite sandwich plates using 4-, 8-, 9-noded isoparametric quadrilateral elements

A finite element method based on Mindlin's theory is employed in the prediction of the dynamic transient response of multilayered composite sandwich plates. Numerical convergence and stability of 4-noded linear, 8-noded serendipity, and 9-noded Lagrangian elements are established using an explicit time integration technique. A special mass matrix diagonalization scheme is adopted which conserves the total mass of the element and includes the effects due to rotary inertia terms. The parametric effects of the time step, finite element mesh, lamination scheme, and orthotropy on the transient response are investigated. Numerical results for deflections and stresses are presented under various boundary conditions and loadings. The results presented herein should be of interest to composite-structure designers, experimentalists, and numerical analysists in verifying their results.