In this study, bending, free vibration, and buckling response of functionally graded porous micro-plates are investigated using the classical and first-order shear deformation plate theories. The ...Navier solution technique is utilized to obtain analytical solutions to simply supported rectangular plates. A power-law distribution is used to model the variation of two material constituents through the plate thickness. Three different porosity distributions are considered and assumed to take forms of cosine functions. The microstructure-dependent size effects are captured using the modified couple stress theory. Numerical results of bending, free vibration, and buckling are presented to determined the effects of constituent material variation, microstructure-dependent size effects, and porosity distributions on the mechanical response of functionally graded porous micro-plates.
•Analytical modelling of pin-lug progressive contact.•Curved beam model of the lug solved by Castigliano’s theorem.•Definition of enhanced load factor accounting for initial clearance and lug ...geometry.•Contact extent evaluation in terms of load factor.•Comparison between numerical and analytical forecasts.
A preliminary analytical model of a pinned connection is carried out. The lug is idealized in terms of a curved beam, and the presence of an initial clearance between the pin and the lug is accounted for. This model rationalizes the nonlinear and linear mechanical responses of the structure; a coefficient summarizing the effect of the load, Young’s modulus, and initial clearance, is derived; this coefficient is kindred to that computed according to the theory of elasticity. An enhanced load factor that accounts for the lug geometry is proposed. Two loci of local maximum stress occur. One point is the stress at the centre of the pin-lug contact, whereas the other point falls laterally along the lug bore border. While the central stress is forecast by the analytical model with reasonable accuracy, the analytical stress computed laterally is too approximate to be employed in engineering applications. Despite this drawback, a better understanding of the load transfer mechanism within the pinned connection is achieved, by particularly rationalizing the nonlinear, progressive character of the pin-lug contact, and the usefulness of the load factor.
Abstract
We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz along the direction of advection. It is ...characterized by the kinetic coefficients—the advection velocity, diffusion coefficient and the reaction kernel, quantifying the aggregation rates. We analyze a simplified model with mass-independent advection velocity, diffusion coefficient, and reaction rates. We also examine a model with mass-dependent coefficients arising in the context of aggregation with sedimentation. For the quasi-stationary case and simplified model, we obtain an exact solution for the spatially dependent agglomerate densities. For the case of mass-dependent coefficients we report a new conservation law and develop a scaling theory for the densities. For the numerical efficiency we exploit the low-rank approximation technique; this dramatically increases the computational speed and allows simulations of very large systems. The numerical results are in excellent agreement with the predictions of our theory.
•Inextensional vibrations are studied through strain gradient elasticity.•First work on inextensional modes of spherical shell using strain gradient theory.•Formulae for inextensional vibration ...frequencies are derived.
We study inextensional vibrations of the spherical shell using strain gradient elasticity theory under Kirchhoff-Love hypotheses. For admissibility of the inextensional deformations the shell is punctured by making a tiny hole. The shell is assumed to be made of linearly elastic, homogeneous, and isotropic material. The closed form expression for the frequencies of inextensional modes of vibration of spherical caps of various polar angles and that of nearly complete spherical shell are derived using Rayleigh's method. Towards this, the displacement and velocity fields are obtained by setting the membrane strains to zero. Further, to facilitate the existence of inextensional vibrations, boundaries are assumed to be traction free. The frequencies are computed for the positive and negative signs in the strain gradient term of the constitutive law. The computed frequencies, employing negative sign are found to be higher than those computed using classical elasticity theory. The opposite effect is seen when the frequencies are computed with the positive sign. Further, the frequencies are found to saturate when the positive sign is used in the constitutive law. Parametric studies viz. variation in frequencies with the circumferential wavenumbers for different values of length scale parameter, variation in frequencies with circumferential wavenumbers for different values of polar angles and a given length scale parameter, variation of frequency with increasing polar angle for a given circumferential wavenumber, variation of saturation wavenumber with increasing polar angle, and increasing length scale parameter are carried out. The frequencies of nearly a spherical shell with increasing circumferential wavenumber are also computed.
Unsteady natural convection flow of viscous fluids in a circular cylinder, due to a generalized fractional thermal transport is analytically studied. The considered mathematical model is based on a ...new fractional differential constitutive equation of the thermal flux suitable to describe the thermal memory effects. To develop the mathematical model, the time-fractional Caputo-Fabrizio derivative is used. The generalized constitutive equation becomes equivalent to the classical Fourier's law for the zero value of the fractional order of derivative. Analytical solutions for the fluid temperature and velocity are determined using the Laplace and finite Hankel transforms. The influence of the memory parameter on heat transfer and fluid motion is discussed by numerical simulations and graphical illustrations.
This paper investigates the in-plane instability of functionally graded multilayer composite shallow arches reinforced with a low content of graphene platelets (GPLs) under a central point load. The ...GPL weight fraction, which is a constant within each individual GPL reinforced composite (GPLRC) layer, follows a layer-wise variation along the thickness direction. The effective Young’ modulus of the GPLRC is estimated by modified Halpin-Tsai micromechanics model. The virtual work principle is used to establish the nonlinear equilibrium equations for the FG-GPLRC arch fixed or pinned at both ends which are then solved analytically. A parametric study is conducted to examine the effects of distribution pattern, weight fraction, and size of GPL nanofillers and the geometrical parameters of the FG-GPLRC arch on its buckling and postbuckling behaviors. The conditions for multiple limit point buckling to occur in an FG-GPLRC pinned arch are also discussed. It is found that GPL nanofillers have a remarkable reinforcing effect on buckling and postbuckling performances of nanocomposite shallow arches.
The purpose of this paper is study the fractional-order dynamics of the oxygen diffusion through capillary to tissues under the influence of external forces considering the fractional operators of ...Liouville–Caputo and Caputo–Fabrizio. We apply the Laplace homotopy method for analytical and numerical results. Three cases are considered: first, when axial and radial forces acting on capillary, the second one when only radial force acting on capillary and finally when axial force acting on capillary. In order to validate the importance and application of the presented method with the old and new Caputo fractional order derivatives, we given some examples. The solutions obtained confirm that the Laplace homotopy method is a powerful an efficient technique for analytic treatment of a wide variety of diffusion equations in mathematical physics.
•Fundamental solutions for the oxygen diffusion equation are obtained.•We consider several cases for the effect of radial forces.•New complex dynamics are obtained with the application of several fractional-order derivatives.
A new strategy exploiting together the modified Riemann–Liouville fractional derivative rule and two kinds of fractional dual-function methods with the Mittag–Leffler function is presented to solve ...fractional nonlinear models. As an example, the space-time fractional Fokas-Lenells equation is solved by this strategy, some new exact analytical solutions including bright soliton, dark soliton, combined soliton and periodic solutions are found. The comparison of two kinds of fractional dual-function methods is also presented. These solutions exist under a constraint among parameters of nonlinear dispersion, nonlinearity and self-steepening perturbation. In order to further study the optical soliton transport and better understand the physical phenomenon behind the model, dynamical characteristics of analytical fractional soliton solutions including some graphics and analysis is provided. The role of the fractional-order parameter is studied.
Abstract
This paper investigates the new KP equation with variable coefficients of time ‘
t
’, broadly used to elucidate shallow water waves that arise in plasma physics, marine engineering, ocean ...physics, nonlinear sciences, and fluid dynamics. In 2020, Wazwaz 1 proposed two extensive KP equations with time-variable coefficients to obtain several soliton solutions and used Painlevé test to verify their integrability. In light of the research described above, we chose one of the integrated KP equations with time-variable coefficients to obtain multiple solitons, rogue waves, breather waves, lumps, and their interaction solutions relating to the suitable choice of time-dependent coefficients. For this KP equation, the multiple solitons and rogue waves up to fourth-order solutions, breather waves, and lump waves along with their interactions are achieved by employing Hirota's method. By taking advantage of
Wolfram Mathematica
, the time-dependent variable coefficient's effect on the newly established solutions can be observed through the three-dimensional wave profiles, corresponding contour plots. Some newly formed mathematical results and evolutionary dynamical behaviors of wave-wave interactions are shown in this work. The obtained results are often more advantageous for the analysis of shallow water waves in marine engineering, fluid dynamics, and dusty plasma, nonlinear sciences, and this approach has opened up a new way to explain the dynamical structures and properties of complex physical models. This study examines to be applicable in its influence on a wide-ranging class of nonlinear KP equations.
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