Effect of the arrangement of the reinforcement on the stability of circular,cylindrically orthotropic plates with low shear strength

The Bubnov-Galerkin method is used to find the critical loads for cylindrically orthotropic circular continuous and annular plates with different edge conditions in axisymmetric buckling. The effect of the ratio of the Young moduli in the circumferential (E) and radial (E_r) directions and the ratio of E to the interlaminar shear modulus G_rz is investigated. The results are in qualitative agreement with the experimental data of [13].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 275–283, March–April, 1971.     

Dynamic bending of plates with low shear strength

The dynamic problem of the natural vibrations of glass-reinforced plastic plates with low shear strength is examined. The calculations are based on the Timoshenko model (allowance for shear strains and rotational inertia). It is shown that disregarding effects associated with the large shear compliance of glass-reinforced plastic plates leads to appreciable errors in determining the dynamic characteristics.Institute of Polymer Mechanics, Academy of Sciencies of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 698–704, July–August, 1968.     

Dynamic and static nonlinear analysis of cylindrically orthotropic circular plates with nonuniform edge constraints

Based on dynamic von Kármán-type equations a single-mode analysis is carried out for large-amplitude flexural forced vibration of a cylindrically orthotropic circular plate with its edge restrained nonuniformly and elastically against rotation. Numerical results are presented for static large deflection and nonlinear free and forced vibrations of isotropic and cylindrically orthotropic plates with sinusoidally restrained edges. Present values are compared with available data.

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Zusammenfassung Aus dynamischen Gleichungen vom von Kármánschen Typus für die erzwungenen Schwingungen einer zylindrisch-orthotropischen Kreisplatte mit großen Amplituden und mit variabler elastischer Einspannung längs des Randes ausgehend wird eine einzelne Schwingungsform analysiert. Numerische Resultate für große statische Auslenkungen und für nichtlineare freie und erzwungene Schwingungen isotroper und zylindrisch-orthotroper Platten mit sinusoidaler Entspannung längs des Randes werden vorgelegt. Diese Resultate werden mit Werten aus der Literatur verglichen.

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On leave from Tamkang University, Taiwan, China.

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On leave from Wuhan Institute of Building Materials, Wuhan, Hubei, China.     

Combined bending and axial loading of beams made of materials with low shear strength

The effect of shear stresses on the deflection of glass-reinforced plastic beams in bending with axial loading is investigated in the case of hinged supports. The critical axial compressive load is determined with allowance for shear and the limiting value of the axial tensile load is estimated.Mekhanika Polimerov, Vol. 4, No. 1, pp. 124–130, 1968     

Bending of long rectangular plates with low shear strength

The bending of rectangular glass-reinforced plastic plates is investigated for various edge conditions on the basis of generalized applied theories of the Timoshenko and Ambartsumyan types [4]. A series of qualitative and quantitative differences is obtained as compared with the corresponding results of the classical Kirchhoff theory [1].L'vov Polytechnic Institute; Ivano-Frankovsk Institute of Oil and Gas; Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 945–950, September–October, 1969.     

Cylindrically orthotropic circular plates with large deflections

Zusammenfassung Es werden die Verschiebungs- und Spannungszustände in einer Kreisplatte mit grossen Durchbiegungen und zylindrischer Orthotropie mit Hilfe zweier Methoden untersucht, nämlich der Methode des kleinen Parameters vonPoincaré und einer modifizierten Methode vonGalerkin.Ein numerisches Beispiel für gleichmässige Belastung der Platte, die Poissonsche Zahlv =1/4 und die Beziehungv :v _r =4 wird gegeben.

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This work has been sponsored by the United States Army under contract No. DA-11-002-ORD-2059     

Experimental investigation of the transverse shear effect in the bending of cantilevered plates with low shear stiffness

The state of stress of cantilevered plates made of different materials (steel and glass-reinforced plastic) has been experimentally investigated. The results obtained are compared with the known theoretical solutions. It is shown that in certain cases it is necessary to take into account the effects associated with the low shear stiffness of the plate.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov; Kamenets-Podol'skii General Engineering Department of Khmel'nitskii Technological Institute. Translated from Mekhanika Polimerov, No. 4, pp. 736–738, July–August, 1971.     

Asymptotic considerations for transverse bending of orthotropic sheardeformable plates

Departing from the known reduction of the sixth order linear theory problem of orthotropic shear deformable plates to two simultaneous third-order equations for the deflectionw and for a stress function variableJ we are concerned with the asymptotic decomposition ofw andJ into interior and edge zone solution contributions, and with the derivation of sequential boundary value problems for the leading terms of these two types of contributions, in generalization of known results for isotropic plates for which the decomposition is exact rather than asymptotic. Application of the general results to the solution of a specific problem is shown to be associated with a transverse shear stress resultant concentration factor which tends to infinity in the limit of absent transverse sheardeformability.

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Zusammenfassung Wir gehen aus von dem bekannten Resultat, dass die lineare Theorie sechster Ordnung von schubverformbaren orthotropischen elastischen Platten auf ein System von zwei Gleichungen dritter Ordnung für die Durchbiegungw und für eine SpannungsfunktionJ reduziert werden kann. Unsere Aufgabe ist die asymptotische Separation von Innenlösungsbeiträgen und Grenzschichtlösungsbeiträgen zuw undJ, und die Formulierung von rationellen Randwertproblemen für die führenden Glieder in der Entwicklung der Lösungsbeiträge, in Verallgemeinerung bekannter Resultate für dieisotropische Platte, für welche die asymptotische Separation in eine exakte ausartet. Die Anwendung unserer Ergebnisse auf ein Spezialproblem zeigt unter anderem die Existenz einer Spannungskonzentration, welche im Grenzfall der verschwindenden Schubverformbarkeit auf das Unendliche strebt.

     

Geometrically non-linear problems of the bending of orthotropic annular and sectoral plates

Research on calculating the geometrically non-linear stress-strain state of thin elastic orthotropic annular and sectoral plates, acted upon by static loads, is reviewed. The research considered is classified with respect to the form of the loading and clamping of the plates and with respect to their geometrical characteristics. It is shown that this area of the theory of plates, despite the fact that it appears to have been fully investigated, cannot be regarded as completed.     

The transmission problem in bending of plates with transverse shear deformation

The existence of weak solutions is proved for contact problemsin bending of elastic plates with transverse shear deformation,and for various boundary integral equations arising from potentialrepresentations of such solutions.     

A fundamental solution of the equations of thermoelastic bending of orthotropic plates

We construct a fundamental solution of the equations of thermoelastic bending of orthotropic plates under symmetric heat transfer and a linear heart distribution over the thickness. On the lateral surfaces convective heat transfer with a surrounding medium occurs in accordance with Newton's law. The effect of the orthotropy parameters and heat transfer on the magnitude of the bending moment and torque is studied numerically. Two figures. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 87–92.     

Thermoelastic bending of orthotropic plates acted on by concentrated heat sources with arbitrary heat transfer

The thermoelastic problem is solved for an infinite thin orthotropic plate acted on by internal heat sources. Arbitrary heat transfer is assumed between the plate and its surroundings. Results from a numerical study are presented. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 96–102, 1999.     

Contact problems for beams and plates with low shear stiffness

The low shear stiffness and strength of unidirectionally reinforced plates and beams predetermines the choice of calculation model in specific problems [4]. The contact problem is considered for a glass-reinforced plastic plate resting on a Winkler foundation; the deformation properties of the plate are described by the equations of an orthotropic material; the investigation is based on generalized applied theories of the Timoshenko and Ambartsumyan types [5–8], which permit the high shear compliance of thin-walled structures to be taken into account.L'vov Polytechnic Institute; Ivan Franko Institute of Petroleum and Gas. Translated from Mekhanika Polimerov, No. 4, pp. 715–720, July–August, 1970.     

Two new hyperbolic shear displacement models for orthotropic laminated composite plates

Two hyperbolic displacement models, HPSDT1 and HPSDT2, are developed for a bending analysis of orthotropic laminated composite plates. These models take into account the parabolic distribution of transverse shear stresses and satisfy the condition of zero shear stresses on the top and bottom surfaces of the plates. The accuracy of the analysis presented is demonstrated by comparing the results with solutions derived from other higher-order models and with data found in the literature. It is established that the HPSDT1 model is more accurate than some theories of laminates developed previously, and therefore the analysis can be expanded to laminated composite shells.     

On the bending of plates with transverse shear deformation and mixed periodic boundary conditions

The method of matched asymptotic expansions is used to find a homogenized problem whose solution is an approximation to the solution of a mixed periodic boundary value problem in the theory of bending of thin elastic plates. A critical size for the fixed parts of the boundary is found such that the boundary condition of the homogenized problem is an intermediate case between that for the clamped edge plate and that for the free boundary plate.     

Elastoplastic deformation of flexible reinforced plates with a reduced shear strength

The problem of the elastoplastic deformation of reinforced plates taking account of their reduced shear strength is formulated in rectangular Cartesian and cylindrical systems of coordinates within the framework of deformation-type constitutive relations based on the first version of Timoshenko's theory. The mechanical behaviour of annular plates with different helical reinforcement structures is investigated and it is shown that the use of classical theory to calculate the elastoplastic bending of relatively thick and, in some cases, relatively thin reinforced plates leads to an unjustified prediction of the compliance of thin-walled composite structures that is too low. The calculations carried out demonstrate the development of considerable shear deformations in the binder of such plates, that have to be taken into account, since it determines the deformation characteristics of the structures studied. The results of calculations obtained using two structural models are compared.