This approach is based on the spline based meshfree method. To improve the computational efficiency, a new coupled femmeshfree method elementfree galerkin method efgm has been proposed for automotive crashworthiness simulation recently. A spectrum analysis of galerkin meshfree method pinkang xie, dongdong wang department of civil engineering, xiamen university. An efficient radial basis function meshfree local petrov. Hanjie zhang 1, 2,junzhao wu 1, 2,dongdong wang 1, 2, 1. A spectrum analysis of galerkin meshfree method was presented.
A moving kriging interpolation meshfree method based on. The reproducing conditions for bspline basis functions are rationally proposed. Meshfree automatically fills the computation domain with the point cloud. The method is then compared against the method is then compared against the finite element method on a test case of unidirectional fully developed incompressible fluid. Meshfree methods, numerical integration, computational electromagnetics. This method yields high accuracy and convergence rate without necessitating extra nodes or dofs. Splinebased meshfree method sbmfm is originated from the isogeometric analysis iga which. Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Although the adoption of a meshfree formulation would seem to hold the answer, the current stateoftheart in node based formulations suffers from a lack of stability andor consistency for. Eulerian analysis of bulk metal forming processes based on spline based meshfree method. Tspline based xiga for fracture analysis of orthotropic media. Mfree2d is designed for 2d stress and strain analysis. Mesh free methods are a respons to the limitations of finite element methods. Oct 21, 2011 kansas method, which is a domaintype meshless method, was developed by kansa in 1990 6 by directly collocating rbfs, especially multiquadric approximations mq.
We also discuss another approach to the cubic bspline quasiinterpolation based method, where we achieve fourth order of accuracy in space. Topology optimization based on splinebased meshfree method. A moving kriging interpolation mki meshfree method based on naturally stabilized nodal integration nsni scheme is presented to study static, free vibration and buckling behaviors of isotropic reissnermindlin plates. Chen, and mark botkinb acenter for computer aided design and department of mechanical engineering college of engineering, the university of iowa, iowa city, ia 52242. The main aim of this work is to consider a meshfree algorithm for solving burgers equation with the quartic bspline quasiinterpolation. The point of this method was to build an analysis domain by trimming operations so that the boundaries are represented by trimming curves only in a single nurbs patch in twodimensional cases.
The method combines the strengths of isogeometric analysis and meshfree methods. An adaptive isogeometric analysis meshfree collocation method for. Continuumbased design sensitivity analysis and optimization using meshfree method kyung k. The current reliance on legacy meshbased finite element software for such analysis instead leads to excessive manual mesh construction and modification. Kim and young proposed the splinebased meshfree method, where the approximation function is defined based on a background eulerian nurbs mesh and then trimmed by the boundary that is represented. Gradient strains are directly computed at nodes similar to the direct nodal integration dni. Youn 2012 introduced the spline based meshfree method sbmfm.
This meshfree method is based on the quartic 4th order spline. A moving kriging interpolation mki meshfree method based on naturally stabilized nodal integration nsni scheme is presented to study static, free vibration and buckling behaviors of isotropic. Femeshfree quad4 element with modified radial point. We perform some numerical experiments to demonstrate the efficiency of the webspline. The present coupled method preserve smoothing transition between. This formulation employs the consistently coupled isogeometricmeshfree strategy where a mixed basis vector of the convex bsplines is used to impose the consistency conditions throughout the whole problem domain. Spline based meshfree method sbmfm is originated from the isogeometric analysis iga which integrates design and analysis through nonuniform rational b spline nurbs basis functions. The partitionofunity method based on fe meshfree quad4 element synthesizes the respective advantages of meshfree and finite element methods by exploiting composite shape functions to obtain highorder global approximations. The spline based meshfree method sbmfm is a new class of meshfree method based on isogeometric analysis. Among different meshfree methods one of the most frequently used meshfree method is the galerkin type of meshfree method using the moving least square or reproducing kernel approximation 1, 2.
The quartic splines weight function is given as follows. Uhvhdufk dwwhqwlrq vlqfh v and various meshfree methods have been developed with a wide range of applications 17. A key challenge while employing bspline basis functions in. Free vibration analysis of cracked thin plates by quasiconvex coupled isogeometricmeshfree method.
Mesh free methods eindhoven university of technology. Korea atomic energy research institute, dukjin, yuseong, daejeon, 305. Siam journal on scientific computing society for industrial. A meshless method based on radial basis and spline interpolation for 2d and 3d inhomogeneous. Quasiinterpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the illconditioning problem resulting from using the. Tspline based xiga for fracture analysis of orthotropic media s. Meshfree approximation methods with matlab interdisciplinary. Some applications of these methods can be found in 2531. The main idea behind the introduced approach is to use collocation in local domains containing of sets of regular or scattered nodes and approximating the solution by bspline basis functions. For instance, one of the simplest meshfree methods is shepards global surface scheme.
Splinebased meshfree method sbmfm is originated from the isogeometric analysis iga which integrates design and analysis through nonuniform rational bspline nurbs basis functions. This first method called the diffuse element method dem, pioneered by nayroles et al. Abstract a meshfree radial point interpolation method rpim is developed for stress analysis of three. The classical approach is to use polynomials of degree 3, called cubic splines, which can achieve the continuity of the first derivative, but not that of second derivative.
Kim and young proposed the splinebased meshfree method, where the approximation function is defined based on a background eulerian nurbs mesh and then trimmed by the boundary that is. Analysis of laminated composite plates based on thbrkpm. Numerical methods for shape design sensitivity analysis and optimization have been developed for several decades. More importantly, a seamless link between meshfree methods and isogeometric analysis can be easily. The performance of this weight function proved that the quartic 4th order spline gains the highest accuracy. We also discuss another approach to the cubic b spline quasiinterpolation based method, where we achieve fourth order of accuracy in space. Adaptive splinebased finite element method with application. Jul 25, 2006 2009 a bridging transition technique for the combination of meshfree method with finite element method in 2d solids and structures. An nsided polygonal smoothed finite element method nsfem for solid mechanics. Discontinuous radial basis function approximations for.
There are two methods that can be used in scattered data interpolation i. Bspline method web method absorbs the regularity problem as the degree of the bsplines is. However, the finiteelementbased shape design sensitivity analysis and optimization have experienced some bottleneck problems such as design parameterization and design remodeling during optimization. In the sbmfm, the domain boundaries are represented by trimming curves only. A meshfree quasiinterpolation method for solving burgers. Department of civil engineering, xiamen university, xiamen 361005, china 2. Rengui yuab, renhong wanga, and chungang zhua school of m athematical sciences, dalian u niversity of t echnology, dalian 116024, chinaa department of m athematics, shangqiu n ormal college, shangqiu 476000, chinab.
A linearly conforming point interpolation method lcpim for threedimensional elasticity problems. Numerical method for shape optimization using tspline. The free vibration analysis of cracked thin plates via a quasiconvex coupled isogeometricmeshfree method is presented. Problems involving with moving discontinuities such as crack propagation can be analyzed by these methods without the requirement of remeshing or rearranging of the nodal points. Meshfree approximation methods with matlab gregory e. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. The coupled thbrkpm method blends the advantages of the isogeometric analysis and. Minimization techniques for pxlaplacian problem using web. In the 1990s a new class of meshfree methods emerged based on the galerkin method. Construction of new cubic bezierlike triangular patches with. Abstract a meshfree radial point interpolation method rpim is developed for stress analysis of threedimensional 3d solids, based on the galerkin weak form formulation using 3d meshfree shape functions constructed using radial basis functions rbfs. Pdf a moving kriging interpolation meshfree method based. Websplinebased meshfree finite element approximation for plaplacian.
The potential weakness of the sbmfm is its numerical instability from using regular grid background mesh. A meshfree approach for transient heat conduction analysis. A meshfree method typically requires only the speci. The point interpolation method pim 16 based on gaussian and multiquadric radial basis functions are applied. In this study, the fe meshfree method is extended to the free and forced. Minimization techniques for pxlaplacian problem using webspline based meshfree method. Siam journal on numerical analysis society for industrial.
The accuracy of the method improves if we add more data sites. Meshfree approximation with matlab pdf free download. A consistently coupled isogeometricmeshfree method with arbitrary order monomial reproducibility is presented. Free vibration analysis of cracked thin plates by quasi. In this work, an extension has been performed on the analysis basis of spline based meshfree method sbmfm to stabilize its solution. In this method the system matrix is sparse and banded. Siam journal on scientific computing siam society for. Bspline based boundary conditions in the material point method. The tension method controls the stiffness of the surface according to the character of the modeled phenomenon.
Because of the inherent properties of splines, that is, nurbs nonuniform rational b. This paper compares the finite element method fem, as the one of the most important numerical methods, and the meshfree method radial point interpolation method rpim, as newly developed numerical technique, for solving several electrostatic problems. Kim and young proposed the spline based meshfree method, where the approximation function is defined based on a background eulerian nurbs mesh and then trimmed by the boundary that is represented. International journal for numerical methods in engineering, 72. May 20, 2017 spline based meshfree method sbmfm is originated from the isogeometric analysis iga which integrates design and analysis through nonuniform rational b spline nurbs basis functions. Apr 04, 2017 in this method, any governing equations are discretized by b spline approximation which is implemented as a generalized fd technique using local b spline collocation scheme. In this paper, as a remedy for these problems, an isogeometricbased. Meshless methods mms provide an alternative to the fem. In this method, any governing equations are discretized by bspline approximation which is implemented as a generalized fd technique using local bspline collocation scheme. However, the finiteelement based shape design sensitivity analysis and optimization have experienced some bottleneck problems such as design parameterization and design remodeling during optimization.
Numerical method for shape optimization using tspline based. Eulerian analysis of bulk metal forming processes based on spline. Websplinebased meshfree finite element approximation for p. Splinebased meshfree method with extended basis request pdf. Bspline quasiinterpolation based numerical methods for some. Fujian provincial key laboratory of mathematical modeling and highperformance scientific computation, xiamen. Evaluation of coupled finite elementmeshfree method for a. Youn 2012 introduced the splinebased meshfree method sbmfm. As the rpim shape functions have the kronecker delta. Minimization techniques for pxlaplacian problem using.
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i. Approximation of the first eigenpair of the plaplace operator using. Exploiting the concept of trimmed surface analysis, kim and youn introduced the spline based meshfree method sbmfm h. The key aspect of the method is that any derivative is stated as neighboring nodal values based on b spline interpolants. The webspline method uses weighted extended bsplines on a regular grid as basis functions and does not require any mesh generation which eliminates a difficult, timeconsuming preprocessing step and accurate approximations are possible with relatively lowdimensional subspaces. Therefore, we have what is known as a meshfree or meshless method. While their two disadvantages limit their application to fullscale crashworthiness simulation of railway vehicles. Sbmfm utilizes trimming technique of cad system by representing the domain using nurbs curves. In this paper, an alternative meshfree approach is presented for transient heat conduction analysis of nonlinear functionally graded materials fgms. This can only be achieved if polynomials of degree 5 or higher are used. We beginby examining weak enforcement of such conditions for bspline basis functions, with application. A meshfree approach for transient heat conduction analysis of. In the sbmfm, the nonuniform rational b spline nurbs patch is employed as a background mesh and the boundaries of the analysis domain are explicitly defined by nurbs trimming curves on the nurbs patch. The regularized method creates a smooth, gradually changing surface with values that may lie outside the sample data range.
In this paper, a new bspline based boundary method is developed as a complete. A numerical method for solving kdv equation with multilevel bspline quasiinterpolation. A mixed reproducing point vector is proposed to construct a consistently coupled isogeometricmeshfree approximation. Eulerian analysis of bulk metal forming processes based on. Many authors have improved the work of shepard by proposing many new ideas on the extension of the original method. In this paper, as a remedy for these problems, an isogeometric based shape. A meshless method based on radial basis and spline interpolation. Mar 28, 2010 numerical methods for shape design sensitivity analysis and optimization have been developed for several decades. Pdf a new class of stabilized websplinebased meshfree. Bspline quasiinterpolation based numerical methods for.
Although the adoption of a meshfree formulation would seem to hold the answer, the current stateoftheart in nodebased formulations suffers from a lack of stability andor consistency for. Evaluation of coupled finite elementmeshfree method for a robust fullscale crashworthiness simulation of railway vehicles show all authors. In this study, the femeshfree method is extended to the free and. Abstract aim of the present chapter is to provide an indepth presentation and. Pdf minimization techniques for pxlaplacian problem using. The use of mq was first developed by hardy 7 in 1971 as an interpolation method for modeling the earths gravitational field. Author links open overlay panel zoohwan hah sungkie youn. Atluri and zhu, in 1998, had originated the meshless local petrovgalerkin mlpg method, based on local weak form that requires only local background cells for. In this work, an explicit boundary topology optimization using sbmfm is presented with an effective boundary. Liu and his coworkers, based on meshfree technology for a quick demonstration of the software, please click here. Mfree2d is an adaptive stress analysis software package based on meshfree technology mfree2d is an adaptive stress analysis software package developed by prof.
A meshfree bspline finite element formulation for unilateral. Splinebased meshfree method with extended basis sciencedirect. The partitionofunity method based on femeshfree quad4 element synthesizes the respective advantages of meshfree and finite element methods by exploiting composite shape functions to obtain highorder global approximations. A recently developed meshfree method based on radial basis functions is the point interpolation meshless method proposed by wang and liu 15. The main idea behind the introduced approach is to use collocation in local domains containing of sets of regular or scattered nodes and approximating the solution by b spline basis functions. Meshfree methods antonio huerta2, ted belytschko1, sonia fern andezm endez 2, timon rabczuk1 1 department of mechanical engineering, northwestern university, 2145 sheridan road, evanston, il 60208, usa. Topology optimization based on splinebased meshfree.
The weighted extended bspline webspline based meshfree finite element method is used to compute the first eigenpair. The sbmfm uses spline basis functions for field variables and boundary representation. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Jun 12, 2012 the current reliance on legacy mesh based finite element software for such analysis instead leads to excessive manual mesh construction and modification. Siam journal on numerical analysis siam society for. This approach is based on the splinebased meshfree method. The key aspect of the method is that any derivative is stated as neighboring nodal values based on bspline interpolants. In this work, an explicit boundary topology optimization using sbmfm is presented with an.
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