Stability of cylindrical shells made of a particulate composite with nonlinear elastic matrix and damaged inclusions

The bifurcation instability problem for cylindrical shells made of particulate composites with nonlinear elastic matrix and damaged inclusions is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 80–91, August 2007.     

Equations of attainable set dynamics,part 1: Integral funnel equations

In control theory, there is growing interest in the evolution of sets, especially attainable sets at timet. This is caused due to their applications to control under uncertainty, optimal control, and differential games. Recently, a new mathematical theory for attainable set evolution was developed. It is based on the concept of approximate localization, instead of differentiation. Here, we give a generalization of this theory.     

Existence results for second order impulsive functional differential inclusions

In this paper, the existence of solution on a compact interval to second order impulsive functional differential inclusions is investigated. Several new results are obtained by using suitable fixed point theorem.     

On Systems of Boundary Value Problems for Differential Inclusions

Herein we consider the existence of solutions to second-order, two-point boundary value problems （BVPs） for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.     

Existence of solutions of semilinear stochastic delay evolution inclusions in a Hilbert space

In this paper the existence of mild solutions of a class of semilinear stochastic evolution inclusions with delays in a Hilbert space is studied. The results are obtained by using a fixed point theorem for condensing map due to Martelli. The result is illustrated with an example.     

Open channel turbulent flow over hemispherical ribs

This paper reports an experimental investigation of open channel turbulent flow over hemispherical ribs. A row of ribs consists of hemispheres closely placed to one another in the spanwise direction and cover the entire span of the channel. The pitch-to-height ratio is varied to achieve the so-called d-type, intermediate and k-type roughness. The Reynolds numbers based on water depth, h, and momentum thickness, θ, of the approach flow are respectively, Re_h = 28,100 and Re_θ = 1800. A particle image velocimetry is used to obtain detailed velocity measurements in and above the cavity. Streamlines, mean velocity and time-averaged turbulent statistics are used to study the effects of pitch-to-height ratio on the flow characteristics and also to document similarities and differences between the present work and prior studies over two-dimensional transverse rods. It was observed that interaction between the outer flow and the shear layers generated by ribs is strongest for k-type and least for d-type ribs. The results also show that hemispherical ribs are less effective in augmenting flow resistance compared to two-dimensional transverse ribs. The levels of the Reynolds stresses and budget terms increase with increasing pitch-to-height ratio inside the roughness sublayer.     

Effective elastic properties of doubly periodic array of inclusions of various shapes by the boundary element method

A rectangular cell of known boundary conditions is cut out from a medium containing the doubly periodic array of inclusions. The stress and strain relationship of the rectangular cell is obtained by using the classical boundary element methods. By matching the boundary condition requirements, the effective elastic properties of the doubly periodic array of inclusions can then be calculated. Numerical examples from the sub-domain boundary element method and the single domain boundary element method are compared and discussed. However, the present method cannot be readily extended to domains having circular or curved boundary parts.     

New exact results for the effective electric, elastic, piezoelectric and other properties of composite ellipsoid assemblages

In this paper we present a unified treatment of composite ellipsoid assemblages in the setting of uncoupled phenomena like conductivity and elasticity and coupled phenomena like thermoelectricity and piezomagnetoelectricity. The building block of this microgeometry is a confocal ellipsoidal particle consisting of a (possibly void) core and a coating. All space is filled up with such units which have different sizes but possess the same aspect ratios. The confocal ellipsoids may have the same orientation in space or may be randomly oriented. The resulting microgeometry simulates two-phase composites in which the reinforcing components are short fibers or elongated particles. Our main interest is in obtaining information of an exact nature on the effective moduli of this microgeometry whose effective tensor symmetry structure depends on the packing mode of the coated ellipsoids. This information will sometimes be complete like the full effective thermoelectric tensor of an assemblage which contains aligned ellipsoids in which the coating is isotropic and the core is arbitrarily anisotropic. In the majority of the cases however the maximum achievable exact information will be only partial and will appear in the form of certain exact relations between the effective moduli of the microgeometry. These exact relations are obtained from exact solutions for the fields in the microstructure for a certain set of loading conditions. In all the considered cases an isotropic coating can be combined with a fully arbitrary core. This covers the most important physical case of anisotropic fibers in an isotropic matrix. Allowing anisotropy in the coating requires the fulfillment of certain constraint conditions between its moduli. Even though in this case the presence of such constraint conditions may render the anisotropic coating material hypothetical, the value of the derived solutions remains since they still provide benchmark comparisons for approximate and numerical treatments. The remarkable feature of the general analysis which covers all treated uncoupled and coupled phenomena is that it is developed solely on the basis of potential solutions of the conduction problem in the same microgeometry.     

Three-dimensional micromechanical modeling of voided polymeric materials

A three-dimensional micromechanical unit cell model for particle-filled materials is presented. The cell model is based on a Voronoi tessellation of particles arranged on a body-centered cubic (BCC) array. The three-dimensionality of the present cell model enables the study of several deformation modes, including uniaxial, plane strain and simple shear deformations, as well as arbitrary principal stress states.The unit cell model is applied to studies on the micromechanical and macromechanical behavior of rubber-toughened polycarbonate. Different load cases are examined, including plane strain deformation, simple shear deformation and principal stress states. For a constant macroscopic strain rate, the different load cases show that the macroscopic flow strength of the blend decreases with an increase in void volume fraction, as expected. The main mechanism for plastic deformation is broad shear banding across inter-particle ligaments. The distributed nature of plastic straining acts to reduce the amount of macroscopic strain softening in the blend as the initial void volume fraction is increased. In the case of plane strain deformation, the plastic flow is observed to initiate across inter-particle ligaments in the direction of constraint. This particular mode of deformation could not have been captured using a two-dimensional, plane strain idealization of cylindrical voids in a matrix.The potential for localized crazing and/or cavitation in the matrix is addressed. It is observed that the introduction of voids acts to relieve hydrostatic stress in the matrix material, compared to the homopolymer. It is also seen that the predicted peak hydrostatic stress in the matrix is higher under plane strain deformation than under triaxial tension (with equal lateral stresses), for the same macroscopic stress triaxiality.The effect of void volume fraction on the macroscopic uniaxial tension behavior of the different blends is examined using a Considère construction for dilatant materials. The natural draw ratio was predicted to decrease with an increase in void volume fraction.     

Existence and exact controllability of fractional evolution inclusions with damping

The aim of this paper is to deal with the existence of mild solutions and exact controllability for a class of fractional evolution inclusions with damping (FEID, for short) in Banach spaces. Firstly, we provide the representation of mild solutions for FEID by applying the method of Laplace transform and the theory of (α,κ)‐regularized families of operators. Next, we are concerned with the existence and exact controllability of FEID under some suitable sufficient conditions by using the method of measure of noncompactness and an appropraite fixed point theorem. Finally, an application to nonlinear partial differential equations with temporal fractional derivatives is presented to illustrate the effectiveness of our main results. Copyright © 2017 John Wiley & Sons, Ltd.