Stress analysis of plates with a circular hole reinforced by flange reinforcing member

This paper deals with the problem of stress analysis of plates with a circular hole reinforced by flange reinforcing member. The so called flange reinforcing member here means that the reinforcing member is built up by setting shapes or bars with any section shape on both sides of the plates along the edge of the hole. Two cases of external loads are considered. In one case the external loads are stressesσ_X^(∞),σ_Y^(∞),and τ_XY^(∞) acting at infinite point of the plate, and in the other the external loads are linear distributed normal stresses. The procedure of solving the problems mentioned above consists of three steps. Firstly, the reinforcing member is taken out from the plates and considered to be a circular bar being solved to determine its deformation under the action of radial force q₀(θ) and tangential force t₀(θ) which are forces acting upon each other between reinforcing member and plate. Secondly, the displacements of plate with a circular hole under the action of q₀(θ) and t₀(θ) and external loads are determined. Finally, forces q₀(θ) and t₀(θ) are obtained by the compatibility of deformations between reinforcing member and plate. Then the internal forces and displacements of reinforcing member and plate are deduced from q₀(θ) and t₀(θ) obtained.     

Wave propagation in elastic plates

The problem of wave propagation within the framework of a complete linear theory of elastic plates is treated using the method of wave curves. A complete classification of the various extensional and bending waves is obtained, along with the corresponding speeds of propagation. These are shown to correspond to the phase velocities of harmonic waves for infinite wave number. The decay and coupling equations are found, and the problem of waves due to a punch applied to the plate surface is treated.

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Résumé On a étudié le problème de la propagation des ondes en utilisant la méthode des courbes ondiales et assumant la théorie linéaire et complète des plaques minces. On obtient une classification totale des ondes diverses, de l'extension et de la flexion, avec des vitesses de la propagation. On prouve aussi, que celles-ci correspondent avec des vitesses des phases de la propagation, en cas de nombre infinite des ondes. Les équations de la décadence et de l'accouplement sont derivées, et on a étudié le problème d'une onde, qui est produite par une emporte-pièce appliquée sur la surface d'une plaque.

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This work was supported in part by funds from the National Research Council of Canada, under Grant Number A3805.     

Diffraction of surface waves by floating elastic plates

Based on the dynamical theories of water waves and Mindlin thick plates, the diffraction of surface waves by a floating elastic plate is presented by using the Wiener–Hopf technique. Firstly, the problem is related to a wave guide in water of finite depth, which is analysed to determine the poles. The resulting hybrid boundary value problem is reduced to solving an infinite system of linear algebraic equations. The results obtained are compared with those calculated by an alternative analysis, and with experimental data. Finally, the effects of the geometric and physical parameters on the distribution of deflection and bending moments in plates are analysed and discussed.     

Crack growth in glass matrix composite reinforced by long SiC fibres

Theoretical and experimental work are made for bridged cracks in chevron-notched three point bend specimens made of glass matrix composite reinforced by long SiC fibres. The fracture toughness (K_IC) values are determined using the chevron-notch technique and compared with the theoretical predictions based on micromechanical analysis exploiting weight functions. The weight functions for orthotropic material are obtained numerically by means of detailed FEM analysis using the ANSYS package and they are further used together with appropriate bridging models for the theoretical prediction of the R-curve behaviours typical of the investigated composites.     

Harmonic waves in elastic sandwich plates

Motions of a sandwich plate with symmetric facings are studied in the framework of the three-dimensional equations of elasticity. Both the core and facings are assumed to be isotropic and linearly elastic.Harmonic wave solutions, which satisfy traction-free face conditions and continuity conditions of tractions and displacements at the interfaces, are obtained for four cases: symmetric plane strain solutions for extensional motion, antisymmetric plane strain solutions for flexural motion, and solutions for the symmetric and antisymmetric SH-waves. The dispersion relation for each of these cases is obtained and computed. In order to exhibit the effect of the ratios of facing to core thicknesses, elastic stiffnesses and densities, on the dynamic behavior of sandwich plates, dispersion curves are computed and compared for plates with thick, light, and soft facings as well as for plates with thin, heavy, and stiff facings. Asymptotic expressions of dispersion relations for extensional, flexural, and symmetric SH-waves are obtained in explicit form, as the frequencies and wave numbers approach zero.The thickness vibrations in sandwich plates are studied in detail. The resonance frequencies and modal functions of the thickness-shear and thickness-stretch motions are obtained. Simple algebraic formulas for predicting the lowest thickness-shear and the lowest thickness-stretch frequencies are deduced. The orthogonality of the thickness modal functions is established.     

Compliance of cylindrical elastic shells reinforced by fibers

Kazan Institute of Chemical Engineering. Translated from Prikladnaya Mekhanika, Vol. 26, No. 2, pp. 71–75, February, 1990.     

Plane infinitesimal waves in homogeneous elastic plates

Using the theory of elastic Cosserat plates, we obtain conditions for reality of the frequencies of vibration.

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Résumé En utilisant la théorie des plaques élastiques de Cosserat, on obtient les conditions pour réalité des fréquences de vibration.

     

Perforated grating stacks in thin elastic plates

The reflection and transmission spectrum of an individual grating, and repeated stacks of gratings, is computed using boundary integral methods for arrays of arbitrarily shaped cavities, with free-edge boundary conditions, that are periodically repeated in a thin elastic plate. The solution is found using a specially developed boundary element method coupled with an array Green’s function. The computational code is tested against the solution obtained using multipoles which applies only to circular geometries but is shown to give very good agreement. The code is also validated using energy balance equations which includes the evanescent modes. A number of cavity shapes are investigated and results are compared against circular cavities with equivalent volumes.     

The natural vibrations of rectangular plates reinforced by orthogonal ribs

A technique is proposed to determine the fundamental frequencies of vibrations of rectangular plates strengthened by an orthogonal system of ribs. The necessity of allowing for the discrete arrangement of ribs is demonstrated by numerical examples. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 117–122, July, 2000.