Showing papers by "YuanTong Gu published in 2002"

A boundary point interpolation method for stress analysis of solids

Abstract: A boundary point interpolation method (BPIM) is proposed for solving boundary value problems of solid mechanics In the BPIM, the boundary of a problem domain is represented by properly scattered nodes The boundary integral equation (BIE) for 2-D elastostatics has been discretized using point interpolants based only on a group of arbitrarily distributed boundary points In the present BPIM formulation, the shape functions constructed using polynomial basis function in a curvilinear coordinate possess Dirac delta function property The boundary conditions can be implemented with ease as in the conventional boundary element method (BEM) The BPIM for 2-D elastostatics has been coded in FORTRAN, and used to obtain numerical results for stress analysis of two-dimensional solids

Point interpolation method based on local residual formulation using radial basis functions

Abstract: A local radial point interpolation method (LRPIM) based on local residual formulation is presented and applied to solid mechanics in this paper. In LRPIM, the trial function is constructed by the radial point interpolation method (PIM) and establishes discrete equations through a local residual formulation, which can be carried out nodes by nodes. Therefore, element connectivity for trial function and background mesh for integration is not necessary. Radial PIM is used for interpolation so that singularity in polynomial PIM may be avoided. Essential boundary conditions can be imposed by a straightforward and effective manner due to its Delta properties. Moreover, the approximation quality of the radial PIM is evaluated by the surface fitting of given functions. Numerical performance for this LRPIM method is further studied through several numerical examples of solid mechanics.

A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures

Abstract: A mesh free method called point interpolation method (PIM) is presented for static and mode-frequency analysis of two-dimensional piezoelectric structures. In the present method, the problem domain and its boundaries are represented by a set of properly scattered nodes. The displacements and the electric potential of a point are interpolated by the values of nodes in its local support domain using shape functions derived based on a point interpolation scheme. Techniques are discussed to surmount the singularity of the moment matrix. Variational principle together with linear constitutive piezoelectric equations is used to establish a set of system equations for arbitrary-shaped piezoelectric structures. These equations are assembled for all quadrature points and solved for displacements and electric potentials. A polynomial PIM program has been developed in MATLAB with matrix triangularization algorithm (MTA), which automatically performs a proper node enclosure and a proper basis selection. Examples are also presented to demonstrate the accuracy and stability of the present method and their results are compared with the conventional FEM results from ABAQUS as well as the analytical or experimental ones.

Comparisons of two meshfree local point interpolation methods for structural analyses

Abstract: As truly meshless methods, the local point interpolation method (LPIM) and the local radial point interpolation method (LR-PIM), are based on the point interpolations and local weak forms integrated in a local domain of very simple shape. LPIM and LR-PIM are examined and compared with each other. They are also compared with the established FEM and the meshless local Petrov-Galerkin (MLPG) method. The numerical implementations of these two methods are discussed in detail. Parameters that influence the performance of them are detailedly studied. The convergence and efficiency of them are thoroughly investigated. LPIM and LR-PIM formulations are developed for structural analyses of 2-D elasto-dynamic problems and 1-D Timoshenko beam problems in the first time. It is found that LPIM and LR-PIM are very easy to implement, and very efficient obtaining numerical solutions to problems of computational mechanics.

A Meshfree Weak-strong Form Method

Abstract: A novel meshfree weak-strong (MWS) form method is proposed based on a combined formulation of both the local weak form and the strong form. In the MWS method, the problem domain and its boundary is represented by a set of distributed nodes. The strong form or the collocation method is used for all internal nodes and the nodes on the essential boundaries. The local weak form (Petrov-Galerkin weak form) is used for nodes on or near the natural boundaries. The natural boundary conditions can then be easily imposed to produce stable and accurate solutions. The MWS method has advantages of both meshfree methods based on strong forms and weak forms. In the entire problem, only local integration meshes for nodes on or near the natural boundary are required.

Boundary Meshfree Methods Based On The Boundary Point Interpolation Methods

Abstract: A group of meshfree method based on Boundary Integral Equation (BIE) have been proposed and developed in order to overcome drawbacks in the conversional Boundary Element Method (BEM) that require boundary elements in constructing shape functions. In this paper, two boundary meshfree methods that use point interpolation methods (PIM), the Boundary Point Interpolation Method (BPIM) using the polynomial PIM and the Boundary Radial Point Interpolation Method (BRPIM) using the radial PIM, are reviewed and assessed. The numerical implementations of these two methods are examined and compared with each other on several technical issues in great details, including the size of the support domain, the convergence, the performance, and so on. These two boundary-type meshfree methods are also compared with the Boundary Node Method (BNM) and the conversional BEM in both efficiency and performance. Several numerical examples of 2-D elastostatics are analyzed using BPIM and BRPIM. It is found that the BPIM and BRPIM are very easy to implement, and very robust for obtaining numerical solutions for problems of computational mechanics. Key issues related the future development of boundary meshfree methods are also discussed.

Metal balancing from concentrator to multiple sources

Abstract: Mathematically sophisticated methods are now in common use for metal balancing of complex separation flow sheets at many concentrators. These balances usually entail minimisation of the sum of weighted squares of data adjustments subject to flow sheet constraints. The adjusted data provides numerical consistency across the complete flow sheet to facilitate performance calculations. A mine with multiple ore sources can be considered as a flow sheet with the end node comprising the concentrator and its products concentrate(s) and tailings. If the mass transfer and grade estimates for each ore source are sufficiently reliable, a similar metal balancing approach can be used for combined mine and concentrator data. Comparison of balanced and measured assays and mass movements provides useful guidance to security of marginal grade ore and possible dilution problems. This paper includes a summary of results from a case study based on a mine with multiple ore source.