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This paper reports the first attempt to extend a novel localized boundary knot method to the 2D and 3D acoustic problems with complicated geometry. The solution of original partial differential equation with inhomogeneous term is firstly described as a sum of a particular solution and a homogeneous one. Secondly, the Chebyshev interpolation technique is applied to the approximation of particular solution. The interpolation approach adopts the Chebyshev-Gauss-Lobatto nodes to offer the spectral convergence and high accuracy. And then the numeircal solution of homogeneous equation is obtained by applying the localized boundary knot method with non-singular general solutions. As a localized meshless method, the localized boundary knot method in conjunction with the interpolation technique is very simple mathematically, accurate numerically, and particularly feasible for large-scale computation in a complicated geometry. Numerical experiments including 2D and 3D models verify the performance of the proposed method for solving inhomogeneous Helmholtz-type equations.

This paper presents a local non-singular knot method (LNKM) to accurately solve the large-scale acoustic problems in complicated geometries. The LNKM is a domain-type meshless collocation method, which relies only on scattered nodes. Firstly, a series of subdomains corresponding to every nodes can be searched based on the Euclidean distance between nodes. To each subdomain, a small linear system can be yielded by using the non-singular general solutions of Helmholtz-type equations. Secondly, the unknown variables at every nodes can be explicitly expressed by the function values at their corresponding supporting nodes. Finally, a large sparse system of linear equations is formed and solved to obtain the numerical solutions of physical quantities at every nodes. The proposed LNKM is mathematically simple, numerically accurate, and more applicable to the large-scale computation. Four numerical examples conform its effectiveness and accuracy for the large-scale computation of Helmholtz-type equations in complicated geometries.

A new space–time meshless method is proposed for solving the nonhomogeneous convection–diffusion equations with variable coefficients. From the perspective of the space–time distance, the space–time radial basis function in a space and time scale framework is presented and then is employed to discretize the time-dependent parabolic partial differential equations. The present meshless scheme is a truly meshless method which requires neither domain or boundary discretization, and can be easily used for 1D, 2D, and 3D problems. Furthermore, the proposed new methodology does not require the discretization of the temporal derivatives, and therefore is very simple mathematically, relatively fast computationally, and easy to program. Numerical examples conform the effectiveness and accuracy of the proposed method.

In this paper, the molecular dynamics simulations are utilized to study the cooling rate effect and to understand the relationship among the local atomic structure, free volume, and mechanical property in Cu50Zr50 metallic glass. The radial distribution function, bond pair analysis technique, and Voronoi tessellation are performed to characterize the structure evolution and local atomic configurations during the cooling process. The results demonstrate that a faster cooling rate results in a higher glass transition temperature and less amount of icosahedra-like clusters. It has been recognized that the concentration of free volumes presents a strong evidence of upward trends as the cooling rate increases. The analyses for the free volume and Voronoi polyhedron indicate that icosahedral-like clusters show a lower free volumes as compared with the rest clusters, revealing that well-developed icosahedra-like clusters in Cu50Zr50 make the system densely packed and lower free volume structure. In addition, the simulated alloy obtained at a lower cooling rate exhibits a higher yield strength and elastic modulus, all of which may attribute to the structure with more densely icosahedral-like clusters and less free volumes.

In this article, the virtual boundary element method (VBEM) in conjunction with conjugate gradient algorithm (CGA) is employed to treat three-dimensional inverse problems of steady-state heat condu...

Al-based glassy alloys (metallic glasses) have been of great scientific and technological interest as a high specific strength and high corrosion resistant materials. However, the low glass-forming ability (GFA) is still a choke point that greatly influences the applications. In order to further comprehend the glass formation mechanism and investigate the possibility of enhancing the GFA, it is important to obtain the definite information on the atomic scale glassy structures in correlation with properties and to study the composition dependence of crystallization and properties of Al-based metallic glasses. The purpose of this paper is to summarize the structure characteristics and crystallization behavior in conjunction with alloy component in Al-based metallic glasses and to investigate the possibility of synthesizing an Al-based bulk metallic glass with better engineering performances. This may assist to learn the structural features systematically and understand the development and current status for Al-based metallic glasses.

In the present work, we investigate the isothermal annealing process of Cu64Zr36 metallic glass (MG) by means of molecular dynamics (MD) simulations, and characterize the compression properties under different temperatures and compressive rates. The pair distribution functions, the bond-orientational order, and the cluster-type index method are modeled and analyzed to characterize changes in the structure. Results of the modeling and analysis reveal that the MgZn2-type Laves, MgCu2-type Laves and five-fold local symmetry structures can be formed during the isothermal holding at 950 K. Study on the compression properties shows that at a fixed strain rate, the yield strength and yield drop all increase with decreasing temperature. At a fixed temperature, however, the increase of the strain rate leads to a noticeable increase in the yield strength at 600 K, but has little effect on yield strength at 10 K. Moreover, the modeling and analysis of the structure at a temperature of 10 K and strain-rate of 5 × 107 s−1 demonstrate that the order-disorder transformation initiates the shear band.

Metallic glasses (amorphous alloys) have grown from a singular observation to an expansive class of alloys with a broad range of scientific interests. Their unique properties require a robust understanding on the structures at the atomic level while alloys in this class have a similar outlook on the microstructure. In this review, we went through the history of the majority studies on the structure models of metallic glasses, and summarized their historical contributions to the understanding of the structure metallic glasses and the relationship between their structures and properties.