YuanTong Gu

A point interpolation method for two‐dimensional solids

A Point Interpolation Method (PIM) is presented for stress analysis for two-dimensional solids. In the PIM, the problem domain is represented by properly scattered points. A technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points. The PIM equations are then derived using variational principles. In the PIM, the essential boundary conditions can be implemented with ease as in the conventional Finite Element Methods. The present PIM has been coded in FORTRAN. The validity and efficiency of the present PIM formulation are demonstrated through example problems. It is found that the present PIM is very easy to implement, and very flexible for obtained displacements and stresses of desired accuracy in solids. As the elements are not used for meshing the problem domain, the present PIM opens new avenue to develop adaptive analysis codes for stress analysis in solids and structures.

A local point interpolation method for static and dynamic analysis of thin beams

The Local Point Interpolation Method (LPIM) is a newly developed truly meshless method, based on the idea of Meshless Local Petrov-Galerkin (MLPG) approach. In this paper, a new LPIM formulation is proposed to deal with 4th order boundary-value and initial-value problems for static and dynamic analysis (stability, free vibration and forced vibration) of beams. Local weak forms are developed using weighted residual method locally. In order to introduce the derivatives of the field variable into the interpolation scheme, a technique is proposed to construct polynomial interpolation with Kronecker delta function property, based only on a group of arbitrarily distributed points. Because the shape functions so-obtained possess delta function property, the essential boundary conditions can be implemented with ease as in the conventional Finite Element Method (FEM). The validity and efficiency of the present LPIM formulation are demonstrated through numerical examples of beams under various loads and boundary conditions.

Meshfree methods and their comparisons

In recent years, one of the hottest topics in computational mechanics is the meshfree or meshless method. Increasing number of researchers are devoting themselves to the research of the meshfree methods, and a group of meshfree methods have been proposed and used to solve the ordinary differential equations (ODEs) or the partial differential equations (PDE). In the meantime, meshfree methods are being applied to a growing number of practical engineering problems. In this paper, a detailed discussion will be provided on the development of meshfree methods. First, categories of meshfree methods are introduced. Second, the methods for constructing meshfree shape functions are discussed, and the interpolation qualities of them are also studied using the surface fitting. Third, several typical meshfree methods are introduced and compared with each others in terms of their accuracy, convergence and effectivity. Finally, the major technical issues in meshfree methods are discussed, and the future development of meshfree methods is addressed.

Boundary meshfree methods based on the boundary point interpolation methods

A group of meshfree methods based on Boundary Integral Equation have been developed in order to overcome drawbacks in the conversional boundary element method (BEM) that requires boundary elements in constructing shape functions. In this paper, the radial basis point interpolation is firstly used to formulate the boundary radial point interpolation method (BRPIM). Two boundary meshfree methods: the boundary point interpolation method (BPIM) using the polynomial PIM and the BRPIM, are then examined in detail. The numerical implementations of these two methods are studied to address several technical issues, including the size of the compact support domain, the convergence, the performance, and so on. These two boundary-type meshfree methods are also compared with the Boundary Node Method and the conventional BEM in terms of both efficiency and performance. Several numerical examples of 2D elastostatics are analyzed using BPIM and BRPIM. It is found that BPIM and BRPIM are very easy to implement, and very robust for obtaining numerical solutions for problems of computational mechanics with very good accuracy. Key issues related the future development of boundary meshfree methods are also discussed.

Graphene-like Two-Dimensional Ionic Boron with Double Dirac Cones at Ambient Condition

Recently, partially ionic boron (γ-B28) has been predicted and observed in pure boron, in bulk phase and controlled by pressure [ Nature 2009 , 457 , 863 ]. By using ab initio evolutionary structure search, we report the prediction of ionic boron at a reduced dimension and ambient pressure, namely, the two-dimensional (2D) ionic boron. This 2D boron structure consists of graphene-like plane and B2 atom pairs with the P6/mmm space group and six atoms in the unit cell and has lower energy than the previously reported α-sheet structure and its analogues. Its dynamical and thermal stability are confirmed by the phonon-spectrum and ab initio molecular dynamics simulation. In addition, this phase exhibits double Dirac cones with massless Dirac Fermions due to the significant charge transfer between the graphene-like plane and B2 pair that enhances the energetic stability of the P6/mmm boron. A Fermi velocity (vf) as high as 2.3 × 10(6) m/s, which is even higher than that of graphene (0.82 × 10(6) m/s), is predicted for the P6/mmm boron. The present work is the first report of the 2D ionic boron at atmospheric pressure. The unique electronic structure renders the 2D ionic boron a promising 2D material for applications in nanoelectronics.

A coupled element free Galerkin/boundary element method for stress analysis of two-dimensional solids

Element Free Galerkin (EFG) method is a newly developed meshless method for solving partial differential equations using Moving Least Squares interpolants. It is, however, computationally expensive for many problems. A coupled EFG/Boundary Element (BE) method is proposed in this paper to improve the solution efficiency. A procedure is developed for the coupled EFG/BE method so that the continuity and compatibility are preserved on the interface of the two domains where the EFG and BE methods are applied. The present coupled EFG/BE method has been coded in FORTRAN. The validity and efficiency of the EFG/BE method are demonstrated through a number of examples. It is found that the present method can take the full advantages of both EFG and BE methods. It is very easy to implement, and very flexible for computing displacements and stresses of desired accuracy in solids with or without infinite domains.

A review of biomass burning: Emissions and impacts on air quality, health and climate in China.

Biomass burning (BB) is a significant air pollution source, with global, regional and local impacts on air quality, public health and climate. Worldwide an extensive range of studies has been conducted on almost all the aspects of BB, including its specific types, on quantification of emissions and on assessing its various impacts. China is one of the countries where the significance of BB has been recognized, and a lot of research efforts devoted to investigate it, however, so far no systematic reviews were conducted to synthesize the information which has been emerging. Therefore the aim of this work was to comprehensively review most of the studies published on this topic in China, including literature concerning field measurements, laboratory studies and the impacts of BB indoors and outdoors in China. In addition, this review provides insights into the role of wildfire and anthropogenic BB on air quality and health globally. Further, we attempted to provide a basis for formulation of policies and regulations by policy makers in China.

A radial point interpolation method for simulation of two-dimensional piezoelectric structures

A meshfree, radial point interpolation method (RPIM) is presented for the analysis of piezoelectric structures, in which the fundamental electrostatic equations governing piezoelectric media are solved numerically without mesh generation. In the present method, the problem domain is represented by a set of scattered nodes and the field variable is interpolated using the values of nodes in its support domain based on the radial basis functions with polynomial reproduction. The shape functions so constructed possess a delta function property, and hence the essential boundary conditions can be implemented with ease as in the conventional finite element method (FEM). The method is successfully applied to determine deflections or electric potentials of a bimorph beam and mode shapes and natural frequencies of transducers. The present results agree well with those of experiments as well as the FEM by ABAQUS. Some shape parameters are also investigated thoroughly for the future convenience of applying the RPIM for smart materials and structures without the use of elements.

Application of meshless local Petrov-Galerkin (MLPG) approach to simulation of incompressible flow

ABSTRACT The meshless local Petrov-Galerkin (MLPG) method is an effective local mesh-free method for solving partial differential equations using moving least-squares (MLS) approximation and local weak form. In this article, the MLPG formulation is used with some modifications to simulate the incompressible flow within an irregular domain with scattered nodal distribution. The governing equations are taken in terms of vorticity–stream functions. It is found that the results agree very well with the available results in the literature. The numerical examples show that the MLPG method is a very promising method for computational fluid dynamics (CFD) problems, as the requirement for a global mesh is removed.

Hybrid boundary point interpolation methods and their coupling with the element free Galerkin method

Abstract Hybrid boundary point interpolation methods (HBPIM and HBRPIM) are presented for solving boundary value problems of two-dimensional solids. In HBPIM and HBRPIM, the boundary of a problem domain is represented by properly scattered nodes. The point interpolation methods are used to construct shape functions with Kronecker delta function properties based on arbitrary distributed boundary nodes. Boundary conditions can be implemented with ease as in the conventional boundary element method. In HBPIM and HBRPIM, the ‘stiffness’ matrices so obtained are symmetric. This property of symmetry can be an added advantage in coupling the HBPIM and HBRPIM with other established meshfree methods. A novel coupled element free Galerkin (EFG)/HBPIM (or HBRPIM) method for 2D solids is then developed. The compatibility condition on the interface boundary is introduced into the variational formulations of HBPIM, HBRPIM and EFG using the Lagrange multiplier method. Coupled system equations are derived based on the variational formulation. The validity and efficiency of the present HBPIM, HBRPIM and coupled methods are demonstrated through the numerical examples. It is found that presented methods are very efficient for solving problems of computational mechanics.