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.     

Theoretical model for the transverse interference pattern of GRIN optical fiber using a laser sheet of light

A new technique (El-Ghandoor et al., Opt. Laser Technol. 31(7) (1999) 481–488) has been applied to study the shape of transverse interference fringes, instead of multiple beam Fizeau fringes (Marhic, Stein, Appl. Phys. Lett. 35 (1975) 1678–1682), from a GRIN optical fiber. In this technique, a laser light sheet is used to illuminate and pass directly through the optical fiber. Theoretical expressions are derived for the optical path differences of three groups of interference beams. The first one passes through the cladding, the core, and then the cladding once again; the second passes through the cladding only, and the third passes through the surrounding air. Theoretical expressions for the shape of transverse interference fringes formed across isotropic non-absorbing optical fibers are also calculated.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

Bifurcation Instability of sheet metal during spring-back

In automotive and home appliance industries, there are many complex-shaped sheet metal components which need to be fabricated in multiple stamping operations. For example, the manufacturing of an outer case of washing machine consists of stamping followed by a bending operation. After the first stage of the stamping process, a large amount of spring-back takes place, and therefore, it is difficult to proceed to the next stage of the bending process. In the stamping process of that kind of sheet component with low geometric constraint, the forming area is large compared to the forming depth. Therefore, the formed part is in an unstable state and is less geometrically constrained, which causes a large amount of spring-back. To investigate this phenomenon, finite element analyses are carried out. During a spring-back analysis after forming, bifurcation takes place and the finite element solution procedure using the Newton–Raphson scheme becomes unstable. To get a stable post-bifurcation solution, a bifurcation algorithm is introduced at the bifurcation point. The deformed shapes obtained from finite element analyses are in good agreement with the experimental data. From this study, it is shown that the bifurcation behaviour enlarges the spring-back and the degree of dimensional error. To obtain additional possible post-bifurcation solutions, non-bifurcation analyses using initial guesses obtained in a modal analysis are carried. For the initial guesses, lowed four eigenmodes are utilized. Finally, the post-bifurcation behaviour and spring-back amount are investigated for various process parameters including the forming depth, punch width and corner radius.     

Stochastic functional differential equations modelling materials with selective recall

We study a problem in stochastic functional differential equations which, in addition to a standard one-one-parameter noise term involves a random perturbation of the memory. This problem can also be regarded as a first order hyperbolic system of stochastic partial differential equations with given initial data and nonlocal boundary data. Existence and uniqueness of a solution is established and the generator of the associated Markov process is analyzed. Thereafter, for two model problems arising from first- and second-order integro-differential equations suggested by physical applications we establish asymptotic stability in probability of the associated stochastic processes.     

Effect of impinging plate geometry on the self-excitation of subsonic impinging jets

In the generation of discrete tones by subsonic impinging jets, there exists a difference of opinion as how the feedback is achieved, i.e., the path of the feedback acoustic waves is whether inside the jet or outside the jet? The only available model (Tam and Ahuja model) for the prediction of an average subsonic jet impingement tone frequency assumes that the upstream part of the feedback loop is closed by an upstream propagating neutral wave of the jet. But, there is no information about the plate geometry in the model. The present study aims at understanding the effect of the plate geometry (size and co-axial hole in the plate) on the self-excitation process of subsonic impinging jets and the path of the acoustic feedback to the nozzle exit. The present results show that there is no effect of plate diameter on the frequency of the self-excitation. A new type of tones is generated for plates with co-axial hole (hole diameter is equal to nozzle exit diameter) for Mach numbers 0.9 and 0.95, in addition to the axisymmetric and helical mode tones observed for plates without co-axial hole. The stability results show that the Strouhal number of the least dispersive upstream propagating neutral waves match with the average Strouhal number of the new tones observed in the present experiments. The present study extends the validity of the model of Tam and Ahuja to a plate with co-axial hole (annular plate) and by doing so, we indirectly confirmed that the major acoustic feedback path to the nozzle exit is inside the jet.     

Diffusion of chemically reactive species in a porous medium over a stretching sheet

Solutions for a class of nonlinear second-order differential equations, arising in diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet, are obtained. Furthermore, using the Brouwer fixed point theorem, existence results are established. Moreover, the exact analytical solutions (for some special cases) are obtained. The results obtained for the diffusion characteristics reveal many interesting behaviors that warrant further study of the effects of reaction rate on the transfer of chemically reactive species.     

Signal intensity enhancement of μ-LIF by using ultra-thin laser sheet illumination and aqueous mixture with ethanol/methanol for micro-channel applications

Measurement of concentration distributions of suspended particles in a micro-channel is one of the most crucial necessities in the area of Lab-on-a-chip to be used for various bio-chemical applications. One most feasible way to measure the concentration field in the micro-channel is using μ-LIF (micro-scale laser-induced fluorescence) method. However, an accurate concentration field at a given cross-plane in a micro-channel has not been successfully achieved so far due to various limitations in the light illumination and fluorescence signal detection. The present study demonstrates a novel method to provide an ultra-thin laser sheet beam having 5 μm thickness using a micro-focus laser line generator. The laser sheet beam illuminates an exact plane of concentration measurement field to increase the signal-to-noise ratio and considerably reduce the depth uncertainty.Nile Blue A was used as fluorescent dye for the present LIF measurement. The enhancement of the fluorescent intensity signals was performed by a solvent mixture of water (95%) and ethanol (EtOH)/methanol (MeOH) (5%) mixture. To reduce the rms errors resulting from the CCD electronic noise and other sources, an expansion of grid size was attempted from 1×1 to 3×3 or 5×5 pixel data windows and the pertinent signal-to-noise level has been noticeably increased accordingly.     

考虑钢板剥离影响的加固混凝土梁抗剪承载力研究

通过对U形钢板的作用分析，提出钢板剥离对U形钢板加固混凝土梁的抗剪承载力有影响，对规范中的抗剪承载力计算式，应引入考虑钢板剥离影响的修正系数K，系数K是关于粘贴强度的函数。通过两组共14个粘贴U形钢板加固混凝土梁的有限元模型的数值仿真，并对分析结果进行数值拟合，推导了系数K的具体计算式，提出了考虑钢板剥离影响的加固混凝土梁的抗剪承载力计算式。最后通过4根梁实体模型的剪切破坏试验，验证了所提出计算式的合理性。     

坡面流及土壤侵蚀动力学（II）——————土壤侵蚀

介绍了坡面土壤侵蚀的基本特征和主要类型, 综述了坡面土壤侵蚀动力学过程和预报模型等方面的研究进展, 包括土壤表层结皮、雨滴溅蚀、片流侵蚀、细沟侵蚀、坡面流输沙、土壤侵蚀界限坡度, 以及土壤侵蚀预报模型等. 并简要讨论了土壤侵蚀动力学研究的发展趋势.