Showing papers by "YuanTong Gu published in 2003"
TL;DR: In this article, a mesh free weak-strong (MWS) form method is proposed based on a combined formulation of both the strong-form and the local weak-form, which only needs the local numerical integration, is only used for nodes on or near the natural boundaries.
Abstract: A novel meshfree weak–strong (MWS) form method is proposed based on a combined formulation of both the strong-form and the local weak-form. In the MWS method, the problem domain and its boundary is represented by a set of distributed points or nodes. The strong form or the collocation method is used for all nodes whose local quadrature domains do not intersect with natural (Neumann) boundaries. Therefore, no numerical integration is required for these nodes. The local weak-form, which needs the local numerical integration, is only used for nodes on or near the natural boundaries. The locally supported radial point interpolation method and the moving least squares approximation are used to construct the meshfree shape functions. The final system matrix will be sparse and banded for computational efficiency. Numerical examples of two-dimensional solids are presented to demonstrate the efficiency, stability, accuracy and convergence of the proposed meshfree method.
126 citations
TL;DR: The radial point interpolation method (RPIM) based on local supported radial basis function (RBF) and the Galerkin weak form has been developed and successfully applied to many engineering problems as discussed by the authors.
Abstract: The radial point interpolation method (RPIM) based on local supported radial basis function (RBF) and the Galerkin weak form has been developed and successfully applied to many engineering problems. Recently, a new meshfree method was proposed based on the universal moving Kriging interpolation. This paper studies the difference between the meshfree shape functions created based on the point interpolation and the Kriging interpolation. It is found that both the two methods yield the same shape function as long as the same radial basis function or semivariogram is adopted for interpolation. Although the two methods lead to the same shape function, the theorem in Kriging formulation may provide an alternative theoretical support for the RPIM. Some common semivariograms used in Kriging may also be incorporated in the RPIM. In addition, in order to satisfy the conformability requirements, a penalty technique is introduced in this paper to form a conforming Kriging, which can pass the standard patch test exactly.
97 citations
TL;DR: In this paper, a boundary radial point interpolation method (BRPIM) is presented for solving boundary value problems of two-dimensional solid mechanics, where the boundary of a problem domain is represented by a set of properly scattered nodes.
Abstract: In this paper, a boundary-type meshfree method, the boundary radial point interpolation method (BRPIM), is presented for solving boundary value problems of two-dimensional solid mechanics. In the BRPIM, the boundary of a problem domain is represented by a set of properly scattered nodes. A technique is proposed to construct shape functions using radial functions as basis functions. The shape functions so formulated are proven to possess both delta function property and partitions of unity property. Boundary conditions can be easily implemented as in the conventional Boundary Element Method (BEM). The Boundary Integral Equation (BIE) for 2-D elastostatics is discretized using the radial basis point interpolation. Some important parameters on the performance of the BRPIM are investigated thoroughly. Validity and efficiency of the present BRPIM are demonstrated through a number of numerical examples.
93 citations
TL;DR: In this paper, a mesh-free radial point interpolation method (RPIM) is presented for the analysis of piezoelectric structures, in which the fundamental electrostatic equations governing piezolectric media are solved numerically without mesh generation.
Abstract: 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.
73 citations
TL;DR: Hybrid boundary point interpolation methods (HBPIM and HBRPIM) are presented for solving boundary value problems of two-dimensional solids in this article, where the boundary of a problem domain is represented by properly scattered nodes.
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.
46 citations
TL;DR: It is shown that PIM with the present MTA is very effective in constructing shape functions, and most importantly, PIM shape functions possess Kronecker delta function properties.
45 citations
01 Jan 2003
TL;DR: A proof-of-conccpt prOLOtype of Web Service is developed here to validate and demonstrate the MineML specification, a XML-based uniform encoding for generic mineral and mining data handling.
Abstract: In recent years, the mineral applications dealing with more complex data in distri buted e nvironment have grown rapidly. Many .mineral and mining organization!> have to orgunizc inte!.nally and g12bally d~stributed manufacturing and experiment sites, which share die roles of databases and other multi-service s like s(lftwareprogi1J.ni~. Thus, therc are-comi-n.erCial -ana technical pressures pushing the mineral .