The fully developed turbulent Boussinesq convection is known to form large-scale rolls, often termed the ‘large-scale circulation’ (LSC). It is an interesting question how such a large-scale flow is created, in particular in systems when the energy input occurs at small scales, when inverse cascade is required in order to transfer energy into the large-scale modes. Here, the small-scale driving is introduced through stochastic, randomly distributed heat source (say radiational). The mean flow equations are...

Stokes flow in a lid-driven cavity under the effect of an inclined magnetic field is studied. The radial basis function (RBF) approximation is employed to the magnetohydrodynamic (MHD) equations which include Navier–Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetics through Ohm’s law with the Stokes approximation. Numerical results are obtained for the moderate Hartmann number (0 ≤ M ≤ 80) and different angles of a magnetic field (0 ≤ α ≤ π). It...

In the low-frequency range, the acoustical behaviour of enclosed spaces is strongly influenced by excited acoustic modes resulting in a spatial irregularity of a steady-state sound field. In the paper, this problem has been examined theoretically and numerically for a system of coupled spaces with complex-valued conditions on boundary surfaces. Using a modal expansion method, an analytic formula for the Green's function was derived allowing to predict the interior sound field for a pure-tone excitation....

In the paper the calculation of ultrasonic field generated by the transmitting transducer and the pulse-echo amplitude received after beam reflection at the defect in tested material is presented. The focus of the authors is directed on the specific transducer – defect configurations where the common methods of determination of ultrasonic beam trajectory fails. The developed analytical model is based on well-established principles of elastodynamic theory and forms the basis for computer program for simulation...

The thermoplastic polymers present amorphous or semi-crystalline structures which are very important factors in describing volumetric shrinkage. The thermoplastic materials are commonly used for production of daily life products, industrial or as the prototypes. Different techniques of manufacturing polymer structures are considered like: injection molding, extrusion, milling, additive manufacturing (AM). AM is a very fast developing field in the manufacturing and research. Unfortunately, components or prototypes made using the thermoplastic semi-crystalline materials in 3D techniques...

Maximization of the critical force of cracked columns, subjected to generalized follower force is discussed in the paper. The crack is assumed to be formed according to the opening and sliding modes and is modeled by a localized loss of stiffness. Influence of the crack stiffness and its localization on the value of the critical force is analyzed. The optimization process is based on the multimodal approach. The localization of crack with the critical force...

The paper presents numerical simulations of single- and multi-step shear stress relaxations of isotropic magnetorheological elastomer (MRE) using fractional derivative Maxwell and Kelvin–Voigt viscoelastic models. The isotropic MRE has been fabricated by filling micro-sized carbonyl iron particles in silicone rubber. Fractional derivative Maxwell and Kelvin–Voigt viscoelastic models were used to fit the experimental data of the isotropic MRE measured by single- and multi-step relaxation tests at different constant strains and external magnetic fields. The fractional...

An implicit constitutive relation is proposed for elastic bodies, when the gradient of the displacement is assumed to be very small, and as a result the strains are small. The resulting constitutive relation is a non-linear relationship between the linearized strain and the stress. The model is used to fit data for rock and concrete. Some boundary value problems are studied within the context of homogeneous deformations, and also a problem with inhomogeneous deformations is...

Basing on the consistent couple stress theory (CCST), we develop a unified size-dependent shear deformation theory to analyze the free vibration characteristics of simply supported, porous functionally graded (FG) piezoelectric microplates which resting on the Winkler–Pasternak foundation are subjected to electric voltages. Various CCST-based shear deformation theories can be reproduced by incorporating their corresponding shape functions, which characterize the through-thickness distributions of the shear deformations, into the unified size-dependent theory. The reproduced CCST-based plate theories...

The paper is devoted to an axisymmetric bending problem of a generalized circular sandwich plate with continuous variation of mechanical properties in the thickness direction of the core. The plate is clamped and carries a concentrated force in its center. The improved shear deformation theory of the normal straight line to the neutral surface is elaborated. The deformation of this normal straight line is graphically presented for the exemplary sandwich structures of the plate. Two...

Three different approaches are formulated to obtain the bounds of the effective elastic moduli of nanoparticle-reinforced composites based on the CSA and the interface stress model. It is found that the effective bulk modulus can be obtained by all three different approaches but the effective shear modulus can be obtained only by the energy approach. The bounds of the effective bulk modulus coincide and depend only on the interface bulk modulus, while those of the...

For 2-dimensional problems in peridynamics, the transfer functions of boundary traction are constructed. The peridynamic motion equation introducing the boundary traction is improved and used to solve some typical 2-dimensional deformation and fracture problems, including the uniaxial tension and pure bending of plate, and fracture of a plate with the small circular hole or central crack. The acquired numerical solutions are close to the analytical solutions of elasticity and numerical solutions given by the finite...

The present article deals with the propagation of inhomogeneous waves in an orthotropic medium based on Eringen’s nonlocal thermoelasticity. For chosen directions of propagation and a real finite inhomogeneity parameter, a complex slowness vector is specified to define the propagation of inhomogeneous incident wave. Then the reflection, transmission of plane waves at a plane interface between two nonlocal orthotropic thermoelastic halfspaces are discussed. In this incidence, horizontal slowness determines the slowness vectors for all reflected,...

Structural Health Monitoring (SHM) is a fast-developing, interdisciplinary field of research having its roots in vibroacoustics and non-destructive testing and evaluation. Fast development of the area is due to the fact that SHM is heavily stimulated by the engineering problems of maintenance and safe operation of technical infrastructure. The use of SHM is slowly becoming a standard in high-cost, modern infrastructure. Therefore, the possibility of application should always be on the horizon of any related...

Three different theoretical models for the analysis of movements of granular media caused by the gravity forces only are critically discused. In each of them the motion is treated as a purely kinematical problem. It has been shown that in application to varoius practical problems, they lead to different displacements patterns (e.g. funnel or mass flow, formation of shear bands or a flow without such bands). Examples of applicaion illustrate the discussion.

Two severe plastic deformation (SPD) processing techniques, namely equal-channel angular pressing (ECAP) and cyclic extrusion-compression (CEC), are investigated by using the finite element method. The major aspect examined is the non-uniformity of the accumulated, equivalent plastic strain after processing with the use of different shapes of the die. The quantitative effect of several parameters on the plastic flow is determined. It is found that the diameter ratio of the chambers and narrower channel in the...

The paper presents the simulations of texture evolution of the AZ31B Mg alloy subjected to equal channel angular pressing (ECAP) and rotary swaging (RS) processes. It is shown that using the crystal plasticity (CP) parameters obtained by curve fitting conducted on simple mechanical tests with the aid of the evolutionary algorithm, it is possible to correctly predict the texture evolution in both processes. The influence of the initial texture as well as the CP parameters...

In this work, the axiomatic model of dynamics is developed corresponding to the classical model of Newton’s dynamics. The key elements of the model are the ability to distinguish isolated systems, and their subsequent division into a selected body (material particle) and its surroundings (attractor). The material particle (usually assumed to be small relative to surroundings), and the attractor are the axiomatic model’s primary concepts. The only fundamental state parameter of the model is acceleration...

The paper delivers a full justification of the Cherkaev–Lurie–Milton theorem in application to the elasticity problem of in-plane loaded plates, 2D periodic elastic composites, elasticity of thin plates subjected to transverse loads as well as in-plane periodic thin plates in bending. The theorem is treated as natural extension of Michell’s result on 2D elasticity and the Gauss–Bonnet formula applied to the deflection surface of a thin plate subject to bending.

We consider a one-dimensional two-temperatures thermoelastic model. The corresponding variational problem leads to a coupled system which is written in terms of the mechanical velocity, the temperature speed and the inductive temperature. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are proved and the linear convergence of the approximations is deduced under suitable additional regularity...