Postbuckling behavior of uniformly compressed circular arches with clamped ends

Summary This communication presents a relatively simple formula for the prediction of the initial postbuckling behavior (in the sense of Koiter) of hingeless elastic circular arches of uniform crosssection subjected to a uniform external gas pressure. Calculations are performed on the basis of an asymptotic method which contains elements of the techniques of analysis used by Budiansky and Hutchinson, and Chien.

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Zusammenfassung Diese Mittelung befaßt sich mit dem nachkritischen Verhalten (im Sinne von Koiter) des unter dem Gasdruck stehenden, eingespannten, elastischen Kreisbogenträgers. Eine verhältnismäßig einfache, genaue Berechnungsformel für die anfängliche nachkritische Belastung wird mittels eines Störungsverfahrens abgeleitet.

     

Steel arches subjected to blast loading: A non-discretisation analysis approach

An innovative numerical non-discretisation semi-analytical methodology for the non-linear dynamic analysis of circular steel arch members subjected to blast loading is presented in this paper. The steel arch has a singly-symmetric cross-section with both elastic and plastic domains to account for the spread of yielding, while it is restrained at its two ends by translational springs in both the horizontal and vertical directions as well as counterpart rotational springs which simulate semi-rigid connections. The rate-dependent effects of the steel material due to rapid dynamic loading, as well as geometric non-linearities and material non-linearities are taken into account in the analysis. The effect of the included angle on the dynamic behaviour of a circular steel arch is investigated comprehensively, while the proposed methodology is validated against ABAQUS finite elements, for which the results show that the developed formulation is accurate in capturing the behaviour of the steel arch member subjected to blast loading, providing an efficacious formulation for further structural design and evaluation.     

In-plane postbuckling of rings subjected to a constant-directional pressure load

Summary The results obtained in this communication characterize the initial postbifurcation behavior of thin elastic rings subjected to a constant-directional and normal uniform external pressure. They complement the calculated postcritical values presented by Budiansky and Sills in previous publications.

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Zusammenfassung Diese Mitteilung befaßt sich mit dem Verhalten der Kreisringe nach den Verzweigungen des Gleichgewichts. Zwei Fälle des Drucklastverhaltens werden untersucht, nämlich: 1) die Elementarlasten behalten ihre Richtung auch während und nach dem Ausknicken des Ringes und 2) die Elementarlasten stehen fortwährend senkrecht auf den zugeordneten Ringelementen (Gasdruck). Die Ergebnisse ergänzen die von Budiansky und Sills angegebenen nachkritischen Werte.

     

Deformation of rigidly clamped specimens of acrylic plastics subjected to one-sided cyclic heating

The effect of one-sided rapid cyclic heating on the deformation of rigidly clamped specimens of acrylic plastics has been investigated. It is shown that as the temperature drop increases, so does the bending deformation (concave toward the heated surface) of the unclamped specimens; the greatest temperature change during thermal cycling is concentrated in an active surface layer not more than 1.6 mm thick and is accompanied by the development of tensile stresses in that layer. The characteristics of the reversibility of the deformation upon subsequent annealing are examined.Riga Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 85–90, January–February, 1976.     

Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces

A study on the buckling and dynamic stability of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces is performed in this research. The static and dynamic governing equations of the nanobeam are established with Galerkin method and under Euler–Bernoulli hypothesis. The buckling, post-buckling and nonlinear dynamic stability character of the nanobeam is presented. The quasi-elastic method, Leibnitz’s rule, Runge–Kutta method and the incremental harmonic balanced method are employed for obtaining the buckling voltage, post-buckling characteristics and the boundaries of the principal instability region of the dynamic system. Effects of the electrostatic load, van der Waals force, creep quantity, inner damping, geometric nonlinearity and other factors on the post-buckling and the principal region of instability are investigated.     

Dispersion of normal waves in a linearly orthotropic circular cylinder with a clamped lateral surface

We propose a method of obtaining the dispersion equation for normal waves in an orthotropic cylinder from the boundary conditions on the rigidly clamped boundary using a system of exponential particular solutions of the three-dimensional equations of its stationary wave motions. We compute the real and imaginary branches of the dispersion spectrum for a waveguide made of monocrystalline strontium sulfate. On figure. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 96–99.     

Influence of load position on the stability of shallow arches

The influence of load position of lhe snap-through instability of shallow, circular, elastic arches is investigated. Results are obtained for pinned, clamped, and clamped-pinned end conditions. The worst load position is seen to depend on the arch rise.

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Zusammenfassung Der Eifluss der Kraftlage auf die Durchschgsinstabilität von flachen, elastischen Kreisbögen wird untersucht. Es sind Ergebnisse erhalten worden für Bögen mit gelenkigen eingespannten, und gelenkig-eingespannten Lagern. Die ungünstigste Kraftlage hängt von der Bogenhöhe ab.

     

Effect of a supporting rod on the integrity of a circular plate subjected to local heating

The authors examine the thermal field, subcritical stress state, and loss of stability in a circular plate reinforced along its boundary. The plate is subjected to axially symmetric heating by sources distributed over a region of the plate. The determination of critical parameters leads to the discovery of eigenvalues for a type-II Fredholm integral equation. It is shown that in the system under consideration both global and local failures of stability may occur. The effect of mechanical and thermal characteristics of the system on its thermal stress state and on the magnitude of the critical parameters is investigated.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 1–4, 1989.     

Modeling problems of steeply inclined cableway subjected to moving load

Problems of structural modeling of multi-span bicable ropeway systems due to significant inclination of a track are discussed in this paper with reference to the vibration analysis. The analytical continuous model of a cableway is formulated in a form which enables to describe in-plane vibrations of steeply inclined carrying cable subjected to traveling passenger carriers modeled by moving pendulums. The nonlinear interaction between carrying cable and moving carriers is taken into account in the moving load definition. Effects of a steep track slope are discussed on the basis of equations of motion of the system. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Buckling and vibration of cross-ply laminated circular cylindrical panels

Summary The free vibration problem of a thin cross-ply composite laminated circular cylindrical panel subjected to arbitrary combinations of axial and circumferential initial compressions is studied. The equations of motion are derived, in the framework of the Donnell-type theory, in terms of the panel middle surface displacements components. Closed form solutions are obtained, for simply-supported panels, and numerical results for both antisymmetric and unsymmetric laminated cross-ply panels are presented.

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Résumé On étudie le problème de libre vibration d'une coque cylindrique ouverte, composée de fines lamelles croisées, soumise aux combinaisons arbitraires des compressions initiales de la circonférence et de l'axe. Les équations de vibrations dérivent, en accord avec la théorie de Donnell, des composantes de déplacement de la surface moyenne de la coque ouverte. On obtient des solutions exactes pour les coques cylindriques ouvertes posées librement et on présente des résultats numériques pour les coques cylindriques ouvertes composées de fines lamelles croisées antisymétriques et non symétriques.

     

The vibration and stability of non-homogeneous orthotropic conical shells with clamped edges subjected to uniform external pressures

In this paper an analytical procedure is given to study the free vibration and stability characteristics of homogeneous and non-homogeneous orthotropic truncated and complete conical shells with clamped edges under uniform external pressures. The non-homogeneous orthotropic material properties of conical shells vary continuously in the thickness direction. The governing equations according to the Donnell’s theory are solved by Galerkin’s method and critical hydrostatic and lateral pressures and fundamental natural frequencies have been found analytically. The appropriate formulas for homogeneous orthotropic and isotropic conical shells and for cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Several examples are presented to show the accuracy and efficiency of the formulation. The closed-form solutions are verified by accurate different solutions. Finally, the influences of the non-homogeneity, orthotropy and the variations of conical shells characteristics on the critical lateral and hydrostatic pressures and natural frequencies are investigated, when Young’s moduli and density vary together and separately. The results obtained for homogeneous cases are compared with their counterparts in the literature.     

A two-dimensional layerwise-differential quadrature static analysis of thick laminated composite circular arches

In this paper, a high accuracy and rapid convergence hybrid approach is developed for two-dimensional static analyses of circular arches with different boundary conditions. The method essentially consists of a layerwise technique in the thickness direction in conjunction with differential quadrature method (DQM) in the axial direction. Hence, the high accuracy and fast convergence of DQM with generality of layerwise formulations for modeling the transverse deformations of arbitrary laminated composite thick arches are combined. This results in superior accuracy with fewer degrees of freedom than conventional finite element method (FEM) or finite difference method (FDM). The convergence behavior of the method is shown and to verify its accuracy, the results are compared with those obtained based on the first order shear deformation Reissner–Naghdi type shell theory and also higher order shear deformation theory. The effects of opening angles, ply angle, boundary conditions, and thickness-to-length ratio on the stress and displacement components are studied.     

Bending of glass-reinforced plastic beams subjected to a pulsed distributed load created by electromagnetic fields

The behavior of glass-reinforced plastic beams subjected to the action of a pulsed-distributed load is examined. The use of an electrodynamic apparatus producing a powerful magnetic field is described. Procedures for making strain-gauge measurements and recording the forces are outlined. The applicability of the Timoshenko theory to the dynamic bending of glass-reinforced plastic beams is demonstrated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 868–873, September–October, 1974.     

A frequency criterion for doubly clamped beam-type N/MEMS subjected to the van der Waals attraction

In general, the vibration frequency of electrically actuated nano/micro-beams under suddenly applied DC voltage is decreased with an increase of the input voltage. However, this descending behavior may be changed, if the initial gap between the movable and fixed electrodes is increased or a large axial compressive residual stress is applied to the system. Accurate determination of the threshold of this frequency behavior change under the van der Waals (vdW) attraction is the objective of the present paper. To this end, a geometric non-linear Euler–Bernoulli electro-mechanical beam model which accounts for the effect of axial residual stresses and the vdW attraction is considered. The oscillatory behavior of the system is studied semi-analytically through the homotopy analysis method (HAM). Employing the HAM solutions, the threshold of the frequency behavior change of the system is obtained. It is found that there exist linear relationships between the normalized parameters of the problem at this threshold. Using this important finding, a frequency criterion for doubly clamped beam-type N/MEMS is introduced. The present findings agree excellently with available experimental and other existing results in the literature as well as those obtained by three-dimensional finite element simulations carried out in COMSOL Multiphysics commercial software.     

Buckling of an annular plate under tensile point loading

In this paper, we address the stability of an elastic thin annular plate stretched by two point loads that are located on the outer boundary. A roller support is considered on the outer boundary while the inner edge of the plate is free. Muskhelishvili’s theory of complex potentials has been applied to obtain a solution of the plane problem in the form of a power series. The buckling problem has been solved using the Rayleigh–Ritz method, based on the energy criterion. The critical Euler force and the respective buckling mode have been computed. Dependence between the critical force and the relative orifice size has been illustrated. Analysis of the results has shown that a symmetric buckling mode takes place for a sufficiently large hole, with the greatest deflection observed around the hole along the force line. However, an antisymmetric buckling mode occurs for relatively small holes, with the greatest deflection being along a line that is orthogonal to the force line.