Analysis of Compression Stress of a Filler and Bending of a Sandwich Panel under Multipoint Loading

The distribution of transverse stresses in the midlayer of a composite sandwich panel under multipoint loading is investigated. The stresses averaged across the thickness of a soft filler are estimated using a discrete model. Finite expressions for the compression of the filler along the length of the panel are derived by means of superposition of the local effects from the bending of face layers under an infinite system of transverse point forces constant across the panel thickness. The effects of compression and transverse extension of the filler, in the case of a high distribution frequency of these forces, i.e., when the distance between the forces is comparable to the panel thickness, are revealed. Compression of the panel by two systems of forces applied symmetrically or nonsymmetrically to the upper and lower faces is considered. The bending characteristics in the cases of loading with point forces and piecewise distributed loads are compared. The formulas obtained are used to determine the length of a small region on the panel surface for which the local effects from the distributed pressure and the point force are equivalent. The corresponding estimates are obtained in a closed form. The analysis, carried out with varied parameters of the structure, allows us to elucidate the peculiarities of the effect of discontinuous loads on the design characteristics in the local zones, using finite expressions derived by the operational method.     

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.     

Deformation of a composite plate on an elastic foundation by local loads

Bending of an elastic annular composite plate with a light filler lying on an elastic foundation is considered. The plate is subjected to local loads. To describe the kinematics of the package, asymmetric across its thickness, the hypotheses of broken normal is accepted. The reaction of foundation is described based on the Winkler model. A system of equilibrium equations is constructed, and its exact solution in displacements is found. Numerical solutions for a metal-polymer sandwich plate are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 109–120, January–February, 2007.     

Waves of Transverse Stresses under a Plane Impact on the Surface of a Sandwich Panel (Acoustic Approximation)

The wave process arising in a sandwich panel with a free back surface under the action of a short-term dynamic load on the front surface of the upper layer (plane deformation) is investigated. The calculation procedure for displacements, rates, and stresses under a rectangular short-time pulse, whose duration does not exceed the double time of wave travel within a layer, is based on the representation of the solution to the one-dimensional wave equation in terms of characteristics. The transmission and reflection coefficients of the pressure pulses on the contact surfaces of layers with different physical properties are determined. The expressions for tensile stresses in the panel face layers and filler, which are responsible for the material failure by spalling, are presented. The stresses in relation to the geometry and dynamic parameters of the sandwich structure are analyzed. In the case of a symmetric panel structure, the stress pattern in the midlayer and on its contact boundaries is given, which takes into account the branching and superposition of pulses.     

Stability problem of a circular sandwich ring under uniform external pressure

The solution of the stability problem of a circular sandwich ring under uniform external pressure is given in a refined statement. The need to determinate the precritical stresses in load-bearing layers in the refined statement with regard to the transverse compression of the core is established, which is the basis for the detection of the mixed flexural buckling forms (BFs) with more than two half-waves along the circumferential coordinate (n>2). It is found that sandwich structures with a determining parameter of transverse compression corresponding to the limit of transition from the mixed BFs to synphasic ones are the most efficient from the weight viewpoint. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 317–328, May–June, 2000.     

Exponential stabilization of a flexible structure with a local interior control and under the presence of a boundary infinite memory

In this paper, we deal with the interior stabilization problem of a flexible structure governed by a hyperbolic partial differential equation coupled to two ordinary differential equations. Contrary to the previous works on the system, the boundary control is subject to the presence of an infinite memory term. In order to deal with such a nonlocal term, the minimal state approach is invoked. Specifically, a localized interior control is proposed in order to compensate the infinite memory effect. Thereafter, reasonable assumptions on the memory kernel are evoked so that the closed-loop system is shown to be well-posed thanks to semigroups theory of linear operators. Furthermore, the resolvent method is used to establish the exponential stability of the system.     

Elastic solutions of a functionally graded cantilever beam with different modulus in tension and compression under bending loads

This paper considers a functionally graded cantilever beam with different modulus in tension and compression. The beam is subjected to bending loads, including pure bending, shear force at the free end and uniform pressure on the upper lateral, respectively. Its modulus values in tension and compression both change with the thickness coordinate as arbitrary functions, which could bring the beam a broader range of applications in engineering. The problem is treated as a plane stress case and described by Airy stress function. By using semi-inverse method, the elastic solutions for the beam are obtained, which can be easily degenerated into the ones for homogeneous beams. An example is finally presented to show the effect of nonhomogeneous materials with different modulus on the elastic field in a cantilever beam.     

Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads

The finite element dynamic response of an unsymmetric composite laminated orthotropic beam, subjected to moving loads, has been studied. One-dimensional finite element based on classical lamination theory, first-order shear deformation theory, and higher-order shear deformation theory having 16, 20 and 24 degrees of freedom, respectively, are developed to study the effects of extension, bending, and transverse shear deformation. The theories also account for the Poisson effect, thus, the lateral strains and curvatures can be expressed in terms of the axial and transverse strains and curvatures and the characteristic couplings (bend–stretch, shear–stretch and bend–twist couplings) are not lost. The dynamic response of symmetric cross-ply and unsymmetric angle-ply laminated beams under the action of a moving load have been compared to the results of an isotropic simple beam. The formulation also has been applied to the static and free vibration analysis.     

Small ball probabilities for a Wiener process under weighted sup-norms,with an application to the supremum of bessel local times

LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup_0<11(t ^–p R(t)) and sup _t 0(e ^–1 R(t)), withp[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process.     

On the stress distribution in a rectangular thick plate of a composite material with curved structure under forced vibration

The stress distribution in a rectangular plate of a multilayer composite material with a periodically curved structure under forced vibration is studied. It is assumed that the plate is hinge supported at opposite sides. The investigation is carried out within the exact three-dimensional linear theory of elasticity. The mechanical relationships of the plate material are described by the continuum theory of Akbarov and Guz'. The numerical results obtained by the finite element method show that even in low-frequency dynamic loading of the plate the extreme values of stresses, which appear as a result of the curving in the plate structure, considerably exceed those in the corresponding static loading.Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 447–454, July–August, 1999.