Vibration of a Reissner–Mindlin–Timoshenko plate–beam system

In this paper, we consider a plate–beam system in which the Reissner–Mindlin plate model is combined with the Timoshenko beam model. Natural frequencies and vibration modes for the system are calculated using the finite element method. The interface conditions at the contact between the plate and beams are discussed in some detail. The impact of regularity on the enforcement of certain interface conditions is an important feature of the paper.     

A variant of the refined theory of bending for a laminar plastic beam

The present article considers the bending of a beam fabricated from a material with a low shear rigidity. A bending-theory variant that does not involve the hypothesis of plane cross sections is presented, assuming the material to be incompressible in the direction of the transverse coordinate. Results previously obtained in this area and an appropriate bibliography were given in an earlier article [3]. A solution is given that permits precise satisfaction of the condition for rigid fastening of the end of the beam. An attempt is made to take into account the actual character of the mounting.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 4, pp. 674–681, July–August, 1972.     

Exact Controllability and Perturbation Analysis for Elastic Beams

The Rayleigh beam is a perturbation of the Bernoulli–Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli–Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials.     

Stationary wave beams in strongly nonlinear three-dimensional inhomogeneous media

We derive an asymptotic expression for the evolution of stationary beams in strongly nonlinear three-dimensional media. Formulas are obtained for the distribution of the beam amplitude and phase velocity, and effectively solvable equations are constructed for the beam axial line. It is shown that with power-function nonlinearity, the determination of the beam axial line is separated from the determination of the field concentrated near this line.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 52–60, 1985.     

Free vibrations of a viscoelastic beam

The method of averaging is used to investigate the free transverse vibrations of a viscoelastic beam supported at the ends. The material properties of the beam are described by a certain nonlinear integral equation of Volterra type.Institute of Mechanics and Seismic Stability of Structures, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 4, pp. 752–756, July–August, 1971.     

Investigations of interlaminar fracture toughness of laminated polymeric composites

The behavior of interlaminar fracture of fiber reinforced laminated polymeric composites has been investigated in modes I, II, and different mixed mode I/II ratios. The experimental investigations were carried out by using conventional beam specimens and the compound version of the CTS (compact tension shear) specimen. In this study, a compound version of the CTS specimen is used for the first time to determine the interlaminar fracture toughness of composites. In order to verify the results obtained by the CTS tests, conventional beam tests were also carried out. In the beam tests, specimens of double cantilever beam (DCB) and end notched flexure (ENF) were used to obtain the critical rates of the energy release for failure modes I and II. The CTS specimen is used to obtain different mixed mode ratios, from pure mode I to pure mode II, by varying the loading conditions. The highest mixed mode ratio obtained in the experiment was G _I /G _II =60. The data obtained from these tests were analyzed by the finite element method. The separated critical rates G _I and G _II of the energy release were calculated by using the modified virtual crack closure integral (MVCCI) method. The experimental investigations were performed on a unidirectional glass/epoxy composite. The results obtained by the beam and CTS tests were compared. It was found that the interlaminar fracture toughness G _IC ^init of mode I at crack initiation and the corresponding value G _II ^Cinit of mode II obtained by the conventional beam and the CTS tests were in rather good agreement. The experimental results of interlaminar fracture of mixed mode were used to obtain the parameters required for the failure criterion. The two different failure criteria were compared. The best correlation with the experimental data was obtained by using the failure criterion proposed by Wu in 1967 containing linear and quadratic terms of the rates of the energy release.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 307–322, May–June, 1998.     

Natural frequencies of a functionally graded cracked beam using the differential quadrature method

The present work is concerned with the free vibration analysis of an elastically supported cracked beam. The beam is made of a functionally graded material and rested on a Winkler–Pasternak foundation. The line spring model is employed to formulate the problem. The method of differential quadrature is applied to solve it. The obtained results agreed with the previous similar ones. Further, a parametric study is introduced to investigate the effects of the geometric and elastic characteristics of the problem on the values of natural frequencies and mode shape functions.     

Distortion of cross sections during deformation of oriented glass-reinforced plastics

Test pieces equipped with wire strain gauges were used to investigate the distortion of cross sections of bars made of oriented glass-reinforced plastics (GRP) in tension and bending. The need for modified design formulas, obtained without use of the simplifying hypothesis of plane sections, is demonstrated. The previously obtained theoretical results of [2, 3] are experimentally confirmed. The effect of the free ends on beam deflection is found to be unimportant.Mekhanika Polimerov, Vol. 1, No. 5, pp. 107–113, 1965     

Delamination of composite plates under tensile load

Conclusions Among the two configurations discussed, the beam has a rather theoretical importance, as an extension and generalization of the cracked beam problem. Unlike this, embedded delaminations can be found often in real constructions. The fact that the maximum value of SERR vs. fibre orientation angle curve for the circular embedded delamination is surpassed by that for the split beam only by three times and by that for the split beam under mode II loading approximately six times means that an embedded delamination can lead to difficulties when the plate is tensed (or compressed — even in an underbuckled state — within the linear approach the non-opening modes of stress concentration will just change their signs when the load changes its sign), especially under a cyclic loading. Of course, the shell model used is fairly rough and does not take in account several features or real delaminations extension and does not allow one to evaluate properly the stress field near the crack front; thus, more analytical and experimental studies would be needed, to establish the crack development process. The 3D analysis is necessary when initiating delaminations are studied, for the beam/plate assumptions can no longer be regarded as necessary since the delamination linear dimensions are comparable to or less than the thickness of the sublaminate.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 45–50, January–February, 1995.     

Ein Impulsgenerator mit Sekundäremissionsröhren

Summary A pulse generator employing secondary emission valves is described. The generator produces positive and negative output pulses with adjustable pulse duration from 10^–7 to 10^–5 s and a rise time of about 1,3·10^–8s. In addition to these test-pulses, signals for the beam brightening and the sweep of a cathode-ray oscillograph are generated, permitting the study of high-speed transients with an ordinary oscilloscope.     

Mechanism of failure of reinforced beams in bending

The mechanism of shear failure is investigated. A theoretical analysis makes it possible to determine the limits of shear failure of reinforced beams in relation to the geometric parameters of the beam, the mechanical properties of the reinforcement and the resin, their volume content, and the loading and support conditions. The results obtained are consistent with the experimental data of [1]. It is shown that in the process of shear failure the axial displacement distribution is modified and that the shear failure mechanism depends on the type of loading and the support conditions.Institute of Hydrodynamics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Mekahnika Polimerov, No. 4, pp. 698–709, July–August, 1973.     

Frequency response analysis of laminated composite beams

Conclusions The modeling of laminated composite beams has been derived systematically from the three-dimensional elasticity relations. The correctness of the solution found by using the present finite element model is verified by comparison with the results obtained by analytical solutions and other results presented in the literature. Numerical results indicate that the present technique can given accurate results for frequency response analysis for laminated composite beams. Loss factors of structures obtained by the method of complex eigenvalues and the direct frequency response method exhibit very good agreement. Optimum design of a laminated composite beam by the finite element method and the method of experiment planning has been successfully presented.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 5, pp. 664–674, September–October, 1994.     

Distribution of shearing stresses under three-point flexure in beams made of composite materials

Conclusions 1. When short beams made of composite materials with span-to-height ratios within the 4.0–5.0 range are tested in three-point flexure, the profile of shearing stresses over the height of a beam cross section departs appreciably from a parabolic one over approximately 40% of the span length.2. The zones of a perturbed state of stress, which appear in short beams tested in three-point flexure, render this method unusable for determining the interlayer shear strength of composite materials on "ultrashort" specimens.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 56–62, January–February, 1977.     

Creep of a nonlinear viscoelastic beam bent by a random moment

The moments of the stress distribution are calculated for a beam made of unidirectional glass-reinforced plastic bent by a random moment. The method previously proposed in [1] is used to solve the statistical boundary value problem.V. A. Steklov Mathematical Institute, Sverdlovsk Branch, Academy of Sciences of the USSR, Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 731–734, July–August, 1968.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.Department of Materials Science, University of Lecce, Via per Arnesano, 73100 Lecce, Italy. Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 163–172, March–April, 1999.     

The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique

The purpose of this study is to implement Adomian–Pade (Modified Adomian–Pade) technique, which is a combination of Adomian decomposition method (Modified Adomian decomposition method) and Pade approximation, for solving linear and nonlinear systems of Volterra functional equations. The results obtained by using Adomian–Pade (Modified Adomian–Pade) technique, are compared to those obtained by using Adomian decomposition method (Modified Adomian decomposition method) alone. The numerical results, demonstrate that ADM–PADE (MADM–PADE) technique, gives the approximate solution with faster convergence rate and higher accuracy than using the standard ADM (MADM).     

A Theoretical Model and Experimental Investigation of a Nonlinear Constitutive Equation for Elastic Porous Metal Rubbers

Starting from the theory of porous materials, the nonlinear theory of dry friction, and the model of a bent slender beam, a nonlinear constitutive equation for elastic porous metal rubbers is constructed. Static compressive experiments were carried out on hollow cylinders of such a rubber, from which relations between all coefficients of the constitutive equation and the material density were determined. Based on the data obtained, the constitutive equation of the material was predicted successfully. The effect of density of the metal rubber on its stiffness and on the nonlinear constitutive equation was revealed by experiments.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 449–460, July–August, 2005.     

Imposing boundary conditions in Sinc method using highest derivative approximation

Sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities. A recent implementation of the Sinc method [Li, C. and Wu, X., Numerical solution of differential equations using Sinc method based on the interpolation of the highest derivatives, Applied Mathematical Modeling 31 (1) 2007 1–9] in which Sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired. We suggest an alternative approach for specifying the boundary conditions, and we compare the numerical results for analysis of a laminated composite Timoshenko beam, implementing both Li and Wu’s approach and our alternative approach for applying the boundary conditions. For the Timoshenko beam problem, we obtain accurate results using both approaches, including transverse shear stress by integration of the 3D equilibrium equations of elasticity. The beam results indicate our approach is less dependent on the selection of the Sinc mesh size than Li and Wu’s SIHD. We also apply SIHD to analyze a classical laminated composite plate. For the plate example, we experience difficulty in obtaining a complete system of equations using Li and Wu’s approach. For our approach, we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge. Using this technique, we obtain accurate results for deflection and stresses, including interlaminar stresses by integration of the 3D equilibrium equations of elasticity. Our results for both the beam and the plate problems indicate that this approach is easily implemented, has a high level of accuracy, and good convergence properties.