Analysis of the anisotropic properties of honeycomb sandwich plates

A mathematical model has been described and an approach proposed to the diagnostics of the anisotropic properties of the relative elasticity constants of three-layer (sandwich) plates with a honeycomb filler. Compact analytical relationships between the anisotropy coefficients and the geometrical dimensions of the cells have been obtained. A practical approach has been proposed for the selection of rational parameters of the honeycomb structure, at which its anisotropic properties would be in the chosen region of the functional space. The conditions have been formulated at which the constructive anisotropy, inherent to honeycomb structures, degenerates to isotropy for some relative elastic constants.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 482–487, July–August, 1995.     

Experimental characterization of dynamic properties of honeycomb sandwich joints and plates

In lots of lightweight applications, constructions are also made by honeycomb sandwiches but little is known about failure and dynamic behavior of sandwich plate connections. In this research, an experimental and simulation study of the mechanical and failure behavior of honeycomb sandwich plates and joints are performed. In detail, series of tensile test have been conducted under quasi static conditions and failure behavior and resistance of the specimens are investigated. The specimens are made by phenolic resin-impregnated aramid paper as core and two different layers of glass fiber reinforced plastic as face sheets in each side. In addition to the experimental tests, numerical simulation with finite element models are performed in Abaqus. Failure modes are investigated and finally a good agreement between test data and simulation results is achieved. (© 2016 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 forms of homogeneous and sandwich plates in pure shear in tangential directions

The mathematical problem of the plane shear buckling form (BF) of sandwich plates and plates homogeneous across the thickness in pure shear is considered. The solution to this problem is compared with the solution to the problem of a flexural BF which is realized in these plates with the formation of oblique waves. It is established that, in the case of plates homogeneous across the thickness, the critical loads corresponding to the plane shear BF are maximum for isotropic ones. In real one-layer structural elements manufactured both of isotropic homogeneous and orthotropic composite materials, these critical loads cannot be reached since they exceed considerably the critical loads for the flexural BFs with oblique waves. The critical loads corresponding to the two BFs are comparable only for relatively thick plates. However, the plane shear BF can be realized in sandwich plates earlier than the flexural one even if the plates are thin. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 215–228, 2000.     

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.     

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)     

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.

     

Elastoplastic stability of sandwich plates with a light core

The elastoplastic stability of sandwich plates with a light core is theoretically investigated. Certain specific problems are considered.Tashkent Lenin State University. Translated from Mekhanika Polimerov, No. 3, pp. 568–571, May–June, 1971.     

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.     

The bending equations of sandwich plates with a prestressed filling

An approximate model of the linear bending of an orthotropic sandwich plate is proposed, taking into account the excess pressure in the space of the filling and the difference in the areas of the surfaces of the elastically curved supporting layers, and the dependence of the shear modulus of the filling on the pressure is postulated. The bending equations of the plate are also given, taking into account the external excess pressure. The value of the transverse distributed force acting on the plate due to the excess pressure in the space of the middle layer and the curvature of the elastic line is obtained. It is shown that this pressure leads to an increase in the bending. If the space of the filling is closed, so that stretching forces due to the pressure act on the boundary sections, the bending is independent of the pressure drop. The dependence of the distributed transverse force on the external pressure is derived. The change in the shear modulus of the filling as a function of the external pressure drop is also considered.     

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.     

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.     

Optimization of sandwich structures with damping properties

Maximum viscoelastic damping characteristics of sandwich structures are designed using finite element and informative planning methods. Two basic design problems were considered: addition of a damping coating to a given homogeneous structure and building a sandwich structure subjected to a given set of constraints. The methods of complex eigenvalues and direct calculation of the frequency characteristics were used. Numerical examples of optimizing sandwich beams are presented for both design problems.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 653–656, September–October, 1993.     

Elastic deformation of thick plates with sliding restraint of the end faces

The article presents homogeneous solutions of problems of the theory of elasticity for the case of sliding restraint of end faces. It investigates the nature of the state of stress of a short hollow circular cylinder deformed by external forces on the lateral surfaces, when the cylinder is clutched without friction between two absolutely rigid cavities.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 14–20, 1988.     

On topological properties of poly honeycomb networks

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as the Randi?, the atom-bond connectivity (ABC) and the geometric-arithmetic (GA) indices are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study poly honeycomb networks which are generated by a honeycomb network of dimension n and derive analytical closed results for the general Randi? index \(R_\alpha (G)\) for different values of \(\alpha \), for a David derived network \((\textit{DD}(n))\) of dimension n, a dominating David derived network \((\textit{DDD}(n))\) of dimension n as well as a regular triangulene silicate network of dimension n. We also compute the general first Zagreb, ABC, GA, \(\textit{ABC}_4\) and \(\textit{GA}_5\) indices for these poly honeycomb networks for the first time and give closed formulas of these degree based indices in case of poly honeycomb networks.     

Contact statement of mechanical problems of reinforced on a contour sandwich plates with transversally-soft core

For the sandwich plates and shells with transversally-soft core and carrier layers having on the outer contour of the reinforcing rod, for small deformations, and middle displacements we construct refined geometrically nonlinear theory. This theory allows to describe the process of the subcritical deformation and identify all possible buckling of carrier layers and reinforcing rods. It is based on the introduction as unknown contact forces at the points of interaction mating surface of the outer layers with core and carrier layers and a core with reinforcing rods at all points of the surface of their conjugation to the shell contour. To derive the basic equations of equilibrium, static boundary conditions for the shell and reinforcing rods, as well as conditions of the kinematic coupling of the carrier layers with a core, the carrier layers and a core with reinforcing rods we use previously proposed generalized Lagrange variational principle.