Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory

Graphene-polymer nano-composites are one of the most applicable engineering nanostructures with superior mechanical properties. In the present study, a finite element (FE) approach based on the size dependent nonlocal elasticity theory is developed for buckling analysis of nano-scaled multi-layered graphene sheets (MLGSs) embedded in polymer matrix. The van der Waals (vdW) interactions between the graphene layers and graphene-polymer are simulated as a set of linear springs using the Lennard-Jones potential model. The governing stability equations for nonlocal classical orthotropic plates together with the weighted residual formulation are employed to explicitly obtain stiffness and buckling matrices for a multi-layered super element of MLGS. The accuracy of the current finite element analysis (FEA) is approved through a comparison with molecular dynamics (MD) and analytical solutions available in the literature. Effects of nonlocal parameter, dimensions, vdW interactions, elastic foundation, mode numbers and boundary conditions on critical in-plane loads are investigated for different types of MLGS. It is found that buckling loads of MLGS are generally of two types namely In-Phase (INPH) and Out-of-Phase (OPH) loads. The INPH loads are independent of interlayer vdW interactions while the OPH loads depend on vdW interactions. It is seen that the decreasing effect of nonlocal parameter on the OPH buckling loads dwindles as the interlayer vdW interactions become stronger. Also, it is found that the small scale and polymer substrate have noticeable effects on the buckling loads of embedded MLGS.     

Joint replenishment model with substitution

When products are coupled to the same cycle, the joint replenishment model (JRM) is used to determine optimal inventory levels, where the amount to order (for each item) is designed to minimize the joint holding and ordering costs based on a given demand. JRM studies assume that there is no substitution between items. However, this assumption is unrealistic in some settings where substitution cannot be ignored. This paper combines the separate works on substitution and joint replenishment and proposes a solution procedure for solving the joint replenishment model with substitution (JRMS) for two products within the framework of the classical economic order quantity model. We determine the optimal order quantities for each product taking into consideration substitution between them so that demand is partially met and the total cost associated with the delivery, holding, and shortage of the products is minimized. We also provide an extensive scenario analysis and draw insights. In particular, we shed some light on the role of substitution in reducing the fixed cost. We show that JRMS can result in substantial cost savings compared to the ordinary JRM.     

Some curvature properties of Cartan spaces with mth root metrics

In this paper, we define some non-Riemannian curvature properties for Cartan spaces. We consider a Cartan space with the mth root metric. We prove that every mth root Cartan space of isotropic Landsberg curvature, or isotropic mean Landsberg curvature, or isotropic mean Berwald curvature reduces to a Landsberg, weakly Landsberg, and weakly Berwald spaces, respectively. Then we show that the mth root Cartan space of almost vanishing H-curvature satisfies H?=?0.     

A generalizaton of Hardy’s uncertainty principle on compact extensions of \mathbb R ^n

Let \(K\) be a compact subgroup of automorphisms of \(\mathbb R ^n\) . We prove in this paper a generalization of Hardy’s uncertainty principle on the semi-direct product \(K\ltimes \mathbb R ^n\) , and we solve the sharpness problem. As a consequence, a complete analogue of classical Hardy’s theorem is obtained. The representation theory and the Plancherel formula play an important role in the proofs.     

Reserve stock models: Deterioration and preventive replenishment

Reserve stocks are needed in a wide spectrum of industries from strategic oil reserves to tactical (machine buffer) reserves in manufacturing. One important aspect under-looked in research is the effect of deterioration, where a reserve stock, held for a long time, may be depleted gradually due to factors such as spoilage, evaporation, and leakage. We consider the common framework of a reserve stock that is utilized only when a supply interruption occurs. Supply outage occurs randomly and infrequently, and its duration is random. During the down time the reserve is depleted by demand, diverted from its main supply. We develop optimal stocking policies, for a reserve stock which deteriorates exponentially. These policies balance typical economic costs of ordering, holding, and shortage, as well as additional costs of deterioration and preventive measures. Our main results are showing that (i) deterioration significantly increases cost (up to 5%) and (ii) a preventive replenishment policy, with periodic restocking, can offset some of these additional costs. One side contribution is refining a classical reserve stock model (Hansmann, 1962).     

Multi-variable Hermite matrix polynomials: Properties and applications

In this paper, the multi-variable Hermite matrix polynomials are introduced by algebraic decomposition of exponential operators. Their properties are established using operational methods. The matrix forms of the Chebyshev and truncated polynomials of two variable are also introduced, which are further used to derive certain operational representations and expansion formulae.     

Exact boundary controllability of vibrating non-classical Euler–Bernoulli micro-scale beams

This study investigates the exact controllability problem for a vibrating non-classical Euler–Bernoulli micro-beam whose governing partial differential equation (PDE) of motion is derived based on the non-classical continuum mechanics. In this paper, it is proved that via boundary controls, it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time. This control objective is achieved based on the PDE model of the system which causes that spillover instabilities do not occur.     

Viscosity iterative scheme for generalized mixed equilibrium problems and nonexpansive semigroups

In this paper, we propose a new general iterative scheme based on the viscosity approximation method for finding a common element of the set of solutions of the generalized mixed equilibrium problem and the set of all common fixed points of a finite family of nonexpansive semigroups. Then, we prove the strong convergence of the iterative scheme to find a unique solution of the variational inequality that is the optimality condition for the minimization problem. Our results extend and improve some recent results of Cianciaruso et al. (J. Optim. Theory Appl. 146:491–509, 2010), Kamraksa and Wangkeeree (J. Glob. Optim. 51:689–714, 2011), and many others.     

On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）

In this paper,we consider the family of generalized Petersen graphs P(n,4).We prove that the metric dimension of P(n,4) is 3 when n ≡ 0(mod 4),and is 4 when n = 4k + 3(k is even).For n ≡ 1,2(mod 4) and n = 4k + 3(k is odd),we prove that the metric dimension of P(n,4) is bounded above by 4.This shows that each graph of the family of generalized Petersen graphs P(n,4)has constant metric dimension.     

Numerical Simulation of a Turbulent FSI Benchmark Case

In an effort to expand the capabilities of a validated simulation environment for fluid-structure interaction to turbulent flows, we present the simulation of a turbulent FSI benchmark case with large displacements in a simplified two-dimensional unsteady RANS setup. We find a fair agreement to experimental data that encourages further refinement of our approach and future three-dimensional simulations with eddy-resolving schemes. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)