Journal of Engineering Mathematics最新文献

We consider the model of Mindlin–Timoshenko for a multi-structure composed of an elastic plate surrounded by a thin layer of uniform thickness. From the viewpoint of numerical simulation, the treatment of the behavior of this structure is difficult because of the presence of the thin coating. In order to overcome this difficulty, we use the asymptotic expansion method to identify an approximate model that does not involve the thin layer geometrically but which accounts for its effect through new approximate boundary conditions. These conditions are set on the junction interface between the two sub-structures and depend on the thickness and the physical characteristics of the thin layer. Moreover, we give optimal error estimates between the exact and the approximate solutions of the considered transmission problem, which validate this approximation.

We present a numerical approach to address mass transport problems in multiphase systems, where a diffusing species concentration may exhibit discontinuities across phase boundaries. The approach employs a fixed structured grid, non-conforming with the probably complex or even evolving phase interfaces, in the same spirit as in numerous works in the literature focused on the dynamics of multiphase flows containing solid particles, immiscible fluids, elastic embedded structures, etc. The distinctive feature of the proposition is that in the transport equation, solved over the entire domain, the discontinuities are captured by including a distribution of source-dipoles along the phase boundaries. Moreover, the magnitude of the discontinuities and the source-dipole field strength do not need to be predetermined but are found as parts of the solution by a compatibility condition on the composite concentration field. A numerical implementation based on the finite element method is presented and examples are discussed demonstrating the validity of the approach. In addition, several types of multiphase mass transport problems are discussed, and simple examples are also presented, where it could find application.

In this article, we’ll show how to solve the time-fractional seventh-order Lax’s Korteweg–de Vries and Kaup–Kupershmidt equations analytically using the homotopy perturbation approach, the Adomian decomposition method, and the Elzaki transformation. The KdV equation is a general integrable equation with an inverse scattering transform-based solution that arises in a variety of physical applications, including surface water waves, internal waves in a density stratified fluid, plasma waves, Rossby waves, and magma flow. Fractional derivative is described in the Caputo sense. The solutions to fractional partial differential equation is computed using convergent series. The numerical computations and graphical representations of the analytical results obtained using the homotopy perturbation and decomposition techniques. Moreover, plots that are simple to grasp are used to compare the integer order and fractional-order solutions. After only a few iterations, we may easily obtain numerical results that provide us better approximations. The exact solutions and the derived solutions were observed to be very similar. The suggested methods have also acquired the highest level of accuracy. The most prevalent and convergent techniques for resolving nonlinear fractional-order partial differential issues are the applied techniques.

Tahir et al. (J Stat Comput Simul 88(14):2775–2798, 2018) introduced the inverse Nadarajah–Haghighi distribution (INHD) and demonstrated its ability to model positive real data sets with decreasing and upside-down bathtub hazard rate shapes. This article focuses on the inference of unknown parameters using a generalized Type-II hybrid censoring scheme (GT-II HCS) for the INHD in the presence of competing risks. The maximum likelihood (ML) and Bayes approaches are used to estimate the model parameters. Based on the squared error loss function, we compute Bayes estimates using Markov Chain Monte Carlo (MCMC) by applying Metropolis-Hasting (M-H) algorithm. Furthermore, the asymptotic confidence intervals, bootstrap confidence intervals (BCIs) and the highest posterior density (HPD) credible intervals are constructed. Using real data sets and simulation studies, we examined the introduced methods of inference with different sample sizes.

This paper proposes a probabilistic model that explains the phenomenon of cracking localization (CL) in RC beams with addition of steel fibers. Quantification of the CL is defined as the ratio between the total number of cracks and the number of significantly wide cracks. The model considers both the fibers and conventional reinforcement ratios, as well as the steel stress hardening and the location of the rebars in the cross-section. The fiber distribution in the concrete mix is considered random while the conventional reinforcement—as deterministic. A cumulative function of the total steel distribution, and a binomial probability function are proposed for a newly defined variable that represents the distribution of the fibers effectiveness along the beam. The model was validated with available data from flexural experiments showing good agreement of the model’s prediction with the reported results. The model shows that the cracking localization level in beams is more pronounced in beams with low reinforcement ratios and relatively large fibers content and enables its quantification.

The damping efficiency of vertical porous baffles is investigated for a dynamically coupled fluid-vessel system. The system comprises of a two-dimensional vessel, with a rectangular cross-section, partially filled with fluid, undergoing rectilinear motions with porous baffles obstructing the fluid motion. The baffles pierce the surface of the fluid, thus the problem can be considered as separate fluid filled regions of the vessel, connected by infinitely thin porous baffles, at which transmission conditions based on Darcy’s law are applied. The fluid is assumed to be inviscid, incompressible and irrotational such that the flow in each region is governed by a velocity potential. The application of Darcy’s law at the baffles is significant as it makes the system non-conservative, and thus the resulting characteristic equation for the normal modes leads to damped modes coupled to the moving vessel. Numerical evaluations of the characteristic equation show that the lowest frequency mode typically has the smallest decay rate, and hence will persist longest in an experimental setup. The maximum decay rate of the lowest frequency mode occurs when the baffles split the vessel into identically sized regions.

The paper presents a fast and stable solver algorithm for structural problems. The point is the distance between the eigenvector of the constrained stiffness matrix and the unconstrained matrix. The coarse motions are close to the kernel of the unconstrained matrix. We use lower-frequency deformation modes to construct an iterative solver algorithm through domain decomposition expressing near-rigid-body motions, deflation algorithms, and two-level algorithms. We remove the coarse space from the solution space and hand over the iteration space to the fine space. Our solver is parallelized, and the solver thus has two sets of domain decomposition. One decomposition generates the coarse space, and the other is for parallelization. The basic framework of the solver is the parallel conjugate gradient (CG) method on the fine space. We use the CG method for the basic framework instead of the (simplest) domain decomposition method. We conducted benchmark tests using elastic static analysis for thin plate models. A comparison with the standard CG solver results shows the new solver’s high-speed performance and remarkable stability.

Coaxial magnetic gears have been investigated thoroughly in recent years. However, magnetic gears are prone to slippage that could be caused by overloading or acceleration of the drive. In the present work, the dynamical system of equations in coaxial magnetic gears was investigated in order to calculate the maximum operational characteristic of the drive. A non-dimensional condition was derived analytically that can determine the dynamical behaviour and whether the system will converge or diverge without the requirement of a numerical solution of the dynamical equation of the drive. A case study was performed where different values of acceleration and applied torque were considered. The convergence of the system was initially examined with the developed non-dimensional condition and then the equation was solved numerically in order to verify the prediction. The developed condition correctly predicted the behaviour of the drive in all cases. Finally, with the developed model the operational characteristics of a coaxial magnetic gear that yield a required transmission error can be calculated analytically. Therefore, with the developed model the maximum operational characteristics in coaxial magnetic gears can be determined analytically with a non-dimensional criterion without implementing iterative methods that would significantly increase the computational cost.

Shrinkage estimation in the gamma density using prior information is valuable in various fields, including finance, healthcare, and environmental science, where accurate parameter estimation is essential for decision-making and modeling. This manuscript considers the problem of estimation of (theta^{alpha }) in Gamma density G(1/θ, p) when the prior estimate or guessed value of the parameter (theta^{alpha }) is available in the form of point estimate (theta_{0}^{alpha }). Some families of estimators of (theta^{alpha }) are defined with its properties. Estimators developed by other authors are identified as particular members of the suggested families of shrinkage estimators. In particular, we have discussed the properties of the suggested families of estimators in an exponential distribution with known coefficient of variation. Numerical illustrations are also given in order to judge the merits of the proposed families of estimators over others.

Abstract

Carbon tax serves as a tool to discourage carbon dioxide ( (text {CO}_2) ) emissions, which are a root cause of climate change. A well-designed tax policy could reduce the risk of climate change, promote innovation in carbon-reducing technologies, and increase public revenue. In this research work, the model formulation is based on dynamic interactions among variables, namely the atmospheric concentration of (text {CO}_2) , human population, forestry biomass, and the levied carbon tax. We assume that the collected revenue is used to control anthropogenic emissions of (text {CO}_2) and fund reforestation/afforestation programs. We have derived sufficient conditions under which the considered dynamical variables settle to their equilibrium levels. The model analysis reveals that the atmospheric level of (text {CO}_2) decreases as the levied tax rate increases, indicating that the atmospheric (text {CO}_2) level can be reversed from its present state through the imposition of a carbon tax. Additionally, the formulated system undergoes Hopf-bifurcation concerning the growth of the levied tax and deforestation rate. Furthermore, through simulations, we have demonstrated that utilizing tax revenues for technologies that limit human-induced (text {CO}_2) emissions and reforestation/afforestation programs is a promising strategy for mitigating the increased levels of (text {CO}_2) .