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Cellular structures consist of foams, honeycombs, and lattices. Lattices have many outstanding properties over foams and honeycombs, such as lightweight, high strength, absorbing energy, and reducing vibration, which has been extensively studied and concerned. Because of excellent properties, lattice structures have been widely used in aviation, bio-engineering, automation, and other industrial fields. In particular, the application of additive manufacturing (AM) technology used for fabricating lattice structures has pushed the development of designing lattice structures to a new stage and made a breakthrough progress. By searching a large number of research literature, the primary work of this paper reviews the lattice structures. First, based on the introductions about lattices of literature, the definition and classification of lattice structures are concluded. Lattice structures are divided into two general categories in this paper: uniform and non-uniform. Second, the performance and application of lattice structures are introduced in detail. In addition, the fabricating methods of lattice structures, i.e., traditional processing and additive manufacturing, are evaluated. Third, for uniform lattice structures, the main concern during design is to develop highly functional unit cells, which in this paper is summarized as three different methods, i.e., geometric unit cell based, mathematical algorithm generated, and topology optimization. Forth, non-uniform lattice structures are reviewed from two aspects of gradient and topology optimization. These methods include Voronoi-tessellation, size gradient method (SGM), size matching and scaling (SMS), and homogenization, optimization, and construction (HOC). Finally, the future development of lattice structures is prospected from different aspects.

Dynamics of two-dimensional flow past a rigid flat plate with a trailing closed flexible filament acting as a deformable afterbody are investigated numerically by an immersed boundary-lattice Boltzmann method for the fluid flow and a finite element method for the filament motion. The effects of Reynolds number ($Re$) and length ratio ($Lr$) on the flow patterns and dynamics of the rigid-flexible coupling system are studied. Based on our numerical results, five typical state modes have been identified in $Lr\\unicode{x2013}Re$ plane in terms of the filament shape and corresponding dynamics, i.e. static deformation, micro-vibration, multi-frequency flapping, periodic flapping and chaotic flapping modes, respectively. Benefiting from the passive flow control by using the flexible filament as a deformable afterbody, the coupled system may enjoy a significant drag reduction (up to $22\\,\\%$) compared with bare plate scenarios ($Lr=1$). Maximum drag reduction achieved at $L_{c,{min}} \\in [1.8, 2]$ is often accompanied by the onset of the system state transition. The flow characteristic and its relation to the change in hydrodynamic drag are further explored in order to reveal the underlying mechanisms of the counterintuitive dynamical behaviour of the coupled system. The scaling laws for the form drag and the friction drag, which arise from the pressure and viscous effects, respectively, are proposed to estimate the overall drag acting on the system. The results obtained in the present study may shed some light on understanding the dynamical behaviour of rigid-flexible coupling systems.

The dynamics of viscous fluid flow over a circular flexible plate are studied numerically by an immersed boundary–lattice Boltzmann method for the fluid flow and a finite-element method for the plate motion. When the plate is clamped at its centre and placed in a uniform flow, it deforms by the flow-induced forces exerted on its surface. A series of distinct deformation modes of the plate are found in terms of the azimuthal fold number from axial symmetry to multifold deformation patterns. The developing process of deformation modes is analysed and both steady and unsteady states of the fluid–structure system are identified. The drag reduction due to the plate deformation and the elastic potential energy of the flexible plate are investigated. Theoretical analysis is performed to elucidate the deformation characteristics. The results obtained in this study provide physical insight into the understanding of the mechanisms on the dynamics of the fluid–structure system.

Given its intriguing band structure and unique tunable bandgap, AB-stacked bilayer graphene has great potentials in the applications of high-end electronics, optoelectronics and semiconductors. The epitaxial growth of AB-stacked single-crystal bilayer graphene films requires a strict AB-stacked lattice, identical orientations and seamless stitching of bilayer graphene islands. However, the particles inevitably present on the metal surface that produced during high temperature growth would induce random orientations, twisted stacking islands, and uncontrollable multilayers, which is a great challenge to overcome. Here, we propose a heat-resisting-box assisted strategy to produce nearly pure AB-stacked bilayer graphene single-crystal films on Cu/Ni (111) foils. With our technique, the particles on the Cu/Ni (111) surface are effectively eliminated, which greatly minimizes the occurrence of randomly twisted islands and uncontrollable multilayers. The as-grown AB-stacked bilayer graphene films show > 99% alignment and > 99% AB stacking order. Our work provides a promising method towards the growth of pure AB-stacked bilayer graphene single crystals and would accelerate its device applications.

The distance spectral radius of a connected hypergraph is the largest eigenvalue of its distance matrix. In this paper, we determine the k -uniform hypertree with the minimal spectral radius among all k -uniform hypertrees with m edges and diameter d , where 3 ≤ d ≤ m - 1 .

Objective Free vibration characteristics of the trapezoidal lattice sandwich composite panels are investigated based on a novel equivalent plate model. Methods The equivalent shear modulus and the relative density of the graded lattice core are assumed to be thickness-dependent and these material properties are calculated based on the single-cell equivalence theory and the continuity assumption. Under the framework of the higher-order shear deformation theory (HSDT), the unknown displacement functions are expressed in terms of standard Fourier series and auxiliary functions to avoid discontinuities on the edges of lattice sandwich plate. Artificial spring technique is utilized to simulate arbitrary boundary conditions and the unknown coefficients in the displacement functions are obtained by Rayleigh–Ritz variational method. Results The accuracy of the present method can be verified by comparing the obtained results with FEM results and those from literature. On this basis, a detailed parametric study concerning the effect of boundary conditions, aspect ratio a / b , tilt angle θ , and lamination schemes on the vibration frequencies of the trapezoidal lattice sandwich plate is also performed.

Three kinds of Fe30Ni20Co20Cr20Mo3.5 high entropy alloy (HEA) coatings were prepared on the surface of a Q235 steel plate using plasma cladding and laser cladding. The microstructure, crystal structure, element distribution, microhardness, wear resistance, and corrosion resistance of the coatings were studied. The grain size of the high-speed laser cladding coating (HLC) was the smallest. The crystal structures of the plasma cladding coating (PC) and HLC were single face-centered cubic (FCC), while that of the deep laser cladding coating (DLC) was body-centered cubic (BCC). DLC had the best microhardness and wear resistance. The microhardness of PC, HLC, and DLC increased by 70%, 108%, and 109%, respectively, and the average friction coefficient decreased by 33%, 44%, and 51%, respectively, compared to Q235. HLC had the best corrosion resistance, with an annual corrosion rate of 0.66925 mm/a. The annual corrosion rate of PC and HLC was only 40% of Q235. The polarization curves of PC and HLC had obvious passivation regions with a width of up to 2 V. The corrosion types of PC were pitting corrosion and intergranular corrosion, that of HLC was general corrosion, and that of DLC was severe pitting corrosion.

The present work studied the microstructures of Cr19Fe22Co21Ni25Mo13 alloy, and tested the polarization properties in deaerated 1M nitric acid and 1M hydrochloric solutions at different temperatures. The alloy was processed by an argon atmosphere arc-melting. Results indicated that the microstructure of Cr19Fe22Co21Ni25Mo13 alloy was a dendritic one. The dendrites of Cr19Fe22Co21Ni25Mo13 alloy were an FCC structure, and the interdendrites of Cr19Fe22Co21Ni25Mo13 alloy were a eutectic structure with two phases of FCC and simple cubic (SC). The Cr19Fe22Co21Ni25Mo13 alloy had better corrosion resistance compared with commercial 304 stainless steel in both deaerated 1M HNO3 and 1M HCl solutions. The corrosion types of Cr19Fe22Co21Ni25Mo13 alloy in both of 1M HNO3 and 1M HCl solutions were uniform corrosion.

Porous microstructure is a common surface morphology that is widely used in antifouling, drag reduction, adsorption, and other applications. In this paper, the lattice gas automata (LGA) method was used to simulate the non-uniform electrochemical machining of porous structure at the mesoscopic level. In a cellular space, the metal and the electrolyte were separated into orderly grids, the migration of corrosive particles was determined by an electric field, and the influences of the concentration gradient and corrosion products were considered. It was found that different pore morphologies were formed due to the competition between dissolution and diffusion. When the voltage was low, diffusion was sufficient, and no deposit was formed at the bottom of the pore. The pore grew faster along the depth and attained a cylindrical shape with a large depth-to-diameter ratio. As the voltage increased, the dissolution rates in all directions were the same; therefore, the pore became approximately spherical. When the voltage continued to increase, corrosion products were not discharged in time due to the rapid dissolution rate. Consequently, a sedimentary layer was formed at the bottom of the pore and hindered further dissolution. In turn, a disc-shaped pore with secondary pores was formed. The obtained simulation results were verified by experimental findings. This study revealed the causes of different morphologies of pores, which has certain guiding significance for non-uniform electrochemical machining.

Recently, many authors investigated the existence of global attractors for different types of autonomous lattice dynamical systems. Within this work, we carefully study the existence of a uniform global attractor for a new class of first order non-autonomous lattice dynamical system in the Hilbert space l2l^{2}.