Meccanica

The classical analysis of bending of a circular plate subjected to transverse loading often neglects the effect of the radial component of the reaction force. This paper analyzes this effect for a moderately thick circular plate with roller constraint. A nonclassical axisymmetric bending problem of a circular Mindlin plate is studied for a concentrated force and uniformly distributed loading. The governing equation is derived based on the incremental deformation theory of elasticity. With the aid of Bessel functions, explicit expressions for small- and large-scale transverse deflections and section rotation are obtained. Singular behavior at the plate center is discussed in detail. Two possible hypotheses at the plate center are analyzed, and they give rise to different singularities of the deflection, rotation, and stresses at the plate center. When neglecting the radial reaction force component, our model reduces to the classical circular Mindlin plate theory. Obtained results are useful in the safety design of circular plates under complicated loading.

Typically, the cantilever non-uniform gravity-loaded Euler–Bernoulli beams are numerically modeled as the governing equation for free vibration analysis does not yield an exact solution. We show that, for certain polynomial variations of the mass and stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation for gravity-loaded beams. An inverse problem approach is used to find an infinite number of such beams, with various mass and stiffness distributions, which share the same fundamental frequency. The derived distributions are demonstrated as test functions for a p-version finite element method. The functions can also be used to design gravity-loaded cantilever beams having a pre-specified fundamental natural frequency. Examples of such beams with rectangular cross section are presented. The bounds for the pre-specified fundamental frequency and its variation for beams of different lengths are also studied. In presence of uncertainty, this flexural stiffness is treated as a spatial random field. For known probability distributions of the natural frequencies, the corresponding distribution of this field is found analytically. This analytical solution can serve as a benchmark solution for different statistical simulation tools to find the probabilistic nature of the stiffness distribution for known probability distributions of the frequencies.

Gear drive units are important components of technical systems (TS) and need to be of high quality. Planetary gear units are very compact and efficient mechanical power transformers, but further increase of operating quality level requires the application and development of the new design methodology. The subject of this contribution is presentation of Reliability for design as the new approach of reliability modelling suitable for the new design methodology application, especially for planetary gear units using various kinds of experimental and exploitation data. The methodology follows V-model for TS design which is in this work adapted for gear units design and for presentation of the new methodology based on property based design, axiomatic design and robust design methodology. To this end, the procedure for total reliability of TS decomposition, and methodology for elementary reliability for design of structure components calculation is developed and presented. The reliability for design is established in reverse form of reliability for maintenance which presents common perception of the “reliability” term. This approach is intended to provide further increase of planetary gear unit’s quality and efficient usability of gear unit component resources. The design directions are oriented to providing equal level of elementary reliability of components.

This paper focuses on the cavitation effect on nonlinear elastoplastic deformation rectangular aluminum plate subjected to underwater explosion loading. Cavitation is a phenomenon that may be occurred for plates in the process of underwater explosion forming. The total pressure of the explosion becomes zero at the cavitation time, so that the governing equations of motion will be different before and after the cavitation. As a result, in terms of analysis and design, the cavitation time is significant in studying the behavior of a rectangular plate at underwater explosive loading. Based on Hamilton principle and variation method the nonlinear equations of motion of an underwater rectangular plate subjected to explosive loading are obtained. Exact linear dynamic response of plate is derived by employing the eigen function and nonlinear dynamic response of plate is derived by employing the finite difference method (FDM). The linear and nonlinear work hardening material modeling is considered to define the elastoplastic stress–strain relations. Return mapping algorithm is applied to calculate the stress and strain in any steps of loading. Then, the displacement, velocity and generated stress of plate during cavitation time are calculated. Using von Mises yield criterion, one can distinguishes the cavitation with in elastic or plastic regimes. By recognizing the time of cavitation in the range of elastic or plastic, the displacement and velocity field of plate are determined in duration of explosive loading. Results show that the cavitation time is on the order of 5–10 μs. Depending on amount of charge mass and stand-off, the cavitation time may occur in elastic or plastic regime. The results obtained of linear exact solution considering the linear work hardening material modeling are compared to results obtained of FDM considering the linear and nonlinear work hardening material modeling.

The limit analysis of indefinite plates resting on a continuous elastoplastic medium and subjected to a load distributed over a partial surface with a circular boundary yields the fundamental equation governing the problem. Minimum conditions are set and the solution that supplies the collapse load of the plate-soil system is found by variational calculus.

The free vibrations of circular cylindrical shells partiallyloaded by a distributed mass and rested on an elastic bed are studied in this paper. Both the mass-load and the elastic bed are assumed to be applied on limited arcs and with arbitrary distributions in circumferential direction,while they are considered to be uniformly distributed in longitudinaldirection on the entire shell length. Therefore, the problem is notaxisymmetric. The solution is obtained by using the development of theflexural mode shapes in a Fourier series, whose coefficients are determinedby rendering the Rayleigh quotient stationary, so a Galerkin equation isobtained. The proposed method is independent of the boundary conditionsat the shell ends. The results are satisfactorily compared to FEM results.Finally, the influence of the mass-load and of the bed stiffness on thenatural frequencies and mode shapes of a simply supported shell is shownand discussed.

A steady stagnation-point flow of an incompressible Maxwell fluid towards a linearly stretching sheet with active and passive controls of nanoparticles is studied numerically. The momentum equation of the Maxwell nanofluid is inserted with an external velocity term as a result of the flow approaches the stagnation point. Conventional energy equation is modified by incorporation of nanofluid Brownian and thermophoresis effects. The condition of zero normal flux of nanoparticles at the stretching surface is defined to impulse the particles away from the surface in combination with nonzero normal flux condition. A hydrodynamic slip velocity is also added to the initial condition as a component of the entrenched stretching velocity. The governing partial differential equations are then reduced into a system of ordinary differential equations by using similarity transformation. A classical shooting method is applied to solve the nonlinear coupled differential equations. The velocity, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, Nusselt number and Sherwood number are graphically presented to visualize the effects of particular parameters. Temperature distributions in passive control model are consistently lower than in the active control model. The magnitude of the reduced skin friction coefficient, Nusselt number and Sherwood number decrease as the hydrodynamic slip parameter increases while the Brownian parameter has negligible effect on the reduced heat transfer rate when nanoparticles are passively controlled at the surface. It is also found that the stagnation parameter contributes better heat transfer performance of the nanofluid under both active and passive controls of normal mass flux.

Asymptotic analysis of the flow passing over a small obstacle in the Hele-Shaw cell is performed. The results are based on the asymptotic formulas for Green’s and Neumann functions recently obtained by Maz’ya and Movchan. Theoretical results are illustrated by the numerical simulations.

A model based on molecular dynamics is suggested for description of the shape of nanobubble on the liquid-solid interface. The model results are in good agreement with the known experimental AFM measurements. Nanobubbles in water and in oil are studied. The evolution, moving and interactions of nanobubbles are considered. The influence of different external factors (temperature of the liquid, temperature of the substrate, the gradient of temperature, external pressure (depth of the liquid)) and internal characteristics (surface tension, density) on the nanobubbles evolution and behaviour is investigated.

Efficiency improvement in piston pumps and motors is a major task in pump development. Just a small improvement in efficiency can have a significant financial impact, particularly on large manufacturing plants employing many large-power pumps. According to the bibliography, effort has been concentrated in studding slipper swash plate leakage, forces, torques and slipper dynamics, but less attention has been given to the understanding the barrel dynamics and the inherent clearance between the barrel and the port plate. This paper clarifies the understanding of the complex barrel dynamics, pointing out how barrel-port plate film thickness depends on oil pressure and temperature. The paper demonstrates that mixed lubrication exist between the barrel face and the port plate under some of the conditions studied, proving that elastic metal to metal forces play an important role when studding barrel dynamics. According to the authors, more effort should be considered into properly designing the barrel sliding surface since both volumetric and mechanical efficiencies are very much dependent on this design. Fluid used hydraulic oil ISO 32.