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. Numerical method for shape optimization using tspline based. In this work, an explicit boundary topology optimization using sbmfm is presented with an effective boundary. 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. Author links open overlay panel zoohwan hah sungkie youn. Youn 2012 introduced the splinebased meshfree method sbmfm. Siam journal on numerical analysis society for industrial. Therefore, we have what is known as a meshfree or meshless method. 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.
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. Because of the inherent properties of splines, that is, nurbs nonuniform rational b. Websplinebased meshfree finite element approximation for plaplacian. 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. However, the finiteelement based shape design sensitivity analysis and optimization have experienced some bottleneck problems such as design parameterization and design remodeling during optimization. Siam journal on scientific computing siam society for. In this paper, as a remedy for these problems, an isogeometricbased. Topology optimization based on splinebased meshfree method. A meshfree approach for transient heat conduction analysis of. Bspline quasiinterpolation based numerical methods for.
The spline based meshfree method sbmfm is a new class of meshfree method based on isogeometric analysis. A linearly conforming point interpolation method lcpim for threedimensional elasticity problems. The key aspect of the method is that any derivative is stated as neighboring nodal values based on bspline interpolants. The use of mq was first developed by hardy 7 in 1971 as an interpolation method for modeling the earths gravitational field. Abstract a meshfree radial point interpolation method rpim is developed for stress analysis of three.
An nsided polygonal smoothed finite element method nsfem for solid mechanics. There are two methods that can be used in scattered data interpolation i. The weighted extended bspline webspline based meshfree finite element method is used to compute the first eigenpair. Many authors have improved the work of shepard by proposing many new ideas on the extension of the original method. However, the finiteelementbased shape design sensitivity analysis and optimization have experienced some bottleneck problems such as design parameterization and design remodeling during optimization. Evaluation of coupled finite elementmeshfree method for a. Eulerian analysis of bulk metal forming processes based on spline based meshfree method. An adaptive isogeometric analysis meshfree collocation method for. Topology optimization based on splinebased meshfree. In this study, the femeshfree method is extended to the free and. In this study, the fe meshfree method is extended to the free and forced. Abstract aim of the present chapter is to provide an indepth presentation and. Numerical method for shape optimization using tspline.
In the 1990s a new class of meshfree methods emerged based on the galerkin method. The key aspect of the method is that any derivative is stated as neighboring nodal values based on b spline interpolants. Pdf a moving kriging interpolation meshfree method based. Eulerian analysis of bulk metal forming processes based on spline. The free vibration analysis of cracked thin plates via a quasiconvex coupled isogeometricmeshfree method is presented. Eulerian analysis of bulk metal forming processes based on. While their two disadvantages limit their application to fullscale crashworthiness simulation of railway vehicles. To improve the computational efficiency, a new coupled femmeshfree method elementfree galerkin method efgm has been proposed for automotive crashworthiness simulation recently. 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.
The tension method controls the stiffness of the surface according to the character of the modeled phenomenon. This meshfree method is based on the quartic 4th order spline. 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. 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. Minimization techniques for pxlaplacian problem using. We beginby examining weak enforcement of such conditions for bspline basis functions, with application. For instance, one of the simplest meshfree methods is shepards global surface scheme. The reproducing conditions for bspline basis functions are rationally proposed. Mfree2d is designed for 2d stress and strain analysis. 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. 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. Splinebased meshfree method sbmfm is originated from the isogeometric analysis iga which integrates design and analysis through nonuniform rational bspline nurbs basis functions.
In this method, any governing equations are discretized by bspline approximation which is implemented as a generalized fd technique using local bspline collocation scheme. Free vibration analysis of cracked thin plates by quasi. In this paper, a new bspline based boundary method is developed as a complete. This approach is based on the splinebased meshfree method. A consistently coupled isogeometricmeshfree method with arbitrary order monomial reproducibility is presented. Discontinuous radial basis function approximations for. Mar 28, 2010 numerical methods for shape design sensitivity analysis and optimization have been developed for several decades. In this work, an extension has been performed on the analysis basis of spline based meshfree method sbmfm to stabilize its solution. The accuracy of the method improves if we add more data sites. A spectrum analysis of galerkin meshfree method was presented. Uhvhdufk dwwhqwlrq vlqfh v and various meshfree methods have been developed with a wide range of applications 17. Splinebased meshfree method with extended basis request pdf. Bspline quasiinterpolation based numerical methods for some.
As the rpim shape functions have the kronecker delta. International journal for numerical methods in engineering, 72. 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. 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.
In this paper, an alternative meshfree approach is presented for transient heat conduction analysis of nonlinear functionally graded materials fgms. In the sbmfm, the domain boundaries are represented by trimming curves only. The potential weakness of the sbmfm is its numerical instability from using regular grid background mesh. Pdf minimization techniques for pxlaplacian problem using. This can only be achieved if polynomials of degree 5 or higher are used. Construction of new cubic bezierlike triangular patches with. A meshless method based on radial basis and spline interpolation. Meshfree approximation methods with matlab gregory e. 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. Gradient strains are directly computed at nodes similar to the direct nodal integration dni. Fujian provincial key laboratory of mathematical modeling and highperformance scientific computation, xiamen. This approach is based on the spline based meshfree method. Bspline method web method absorbs the regularity problem as the degree of the bsplines is.
In this work, an explicit boundary topology optimization using sbmfm is presented with an. We perform some numerical experiments to demonstrate the efficiency of the webspline. Mesh free methods eindhoven university of technology. A numerical method for solving kdv equation with multilevel bspline quasiinterpolation. Websplinebased meshfree finite element approximation for p. Meshfree automatically fills the computation domain with the point cloud. A spectrum analysis of galerkin meshfree method pinkang xie, dongdong wang department of civil engineering, xiamen university. A meshfree quasiinterpolation method for solving burgers. The method combines the strengths of isogeometric analysis and meshfree methods. 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. Korea atomic energy research institute, dukjin, yuseong, daejeon, 305. 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. In this paper, as a remedy for these problems, an isogeometric based shape. Some applications of these methods can be found in 2531.
Mesh free methods are a respons to the limitations of finite element methods. An efficient radial basis function meshfree local petrov. The quartic splines weight function is given as follows. 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. Exploiting the concept of trimmed surface analysis, kim and youn introduced the spline based meshfree method sbmfm h. Continuumbased design sensitivity analysis and optimization using meshfree method kyung k. 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.
Pdf a new class of stabilized websplinebased meshfree. A meshless method based on radial basis and spline interpolation for 2d and 3d inhomogeneous. We also discuss another approach to the cubic bspline quasiinterpolation based method, where we achieve fourth order of accuracy in space. Evaluation of coupled finite elementmeshfree method for a robust fullscale crashworthiness simulation of railway vehicles show all authors.
A meshfree bspline finite element formulation for unilateral. 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. Free vibration analysis of cracked thin plates by quasiconvex coupled isogeometricmeshfree method. 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. Liu and his coworkers, based on meshfree technology for a quick demonstration of the software, please click here. A key challenge while employing bspline basis functions in.
Sbmfm utilizes trimming technique of cad system by representing the domain using nurbs curves. Jul 25, 2006 2009 a bridging transition technique for the combination of meshfree method with finite element method in 2d solids and structures. 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. Meshfree approximation with matlab pdf free download. This method yields high accuracy and convergence rate without necessitating extra nodes or dofs. Numerical methods for shape design sensitivity analysis and optimization have been developed for several decades. A recently developed meshfree method based on radial basis functions is the point interpolation meshless method proposed by wang and liu 15. 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.
A moving kriging interpolation meshfree method based on. Splinebased meshfree method sbmfm is originated from the isogeometric analysis iga which. 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. 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 meshfree method typically requires only the speci. Siam journal on scientific computing society for industrial. 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. More importantly, a seamless link between meshfree methods and isogeometric analysis can be easily. Hanjie zhang 1, 2,junzhao wu 1, 2,dongdong wang 1, 2, 1.
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. 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. Minimization techniques for pxlaplacian problem using web. The regularized method creates a smooth, gradually changing surface with values that may lie outside the sample data range.
The current reliance on legacy meshbased finite element software for such analysis instead leads to excessive manual mesh construction and modification. Meshfree approximation methods with matlab interdisciplinary. Tspline based xiga for fracture analysis of orthotropic media. A meshfree approach for transient heat conduction analysis. Department of civil engineering, xiamen university, xiamen 361005, china 2. A mixed reproducing point vector is proposed to construct a consistently coupled isogeometricmeshfree approximation.
Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Adaptive splinebased finite element method with application. Youn 2012 introduced the spline based meshfree method sbmfm. Siam journal on numerical analysis siam society for. 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 method is then compared against the finite element method on a test case of unidirectional fully developed incompressible fluid. Tspline based xiga for fracture analysis of orthotropic media s. This first method called the diffuse element method dem, pioneered by nayroles et al. Bspline based boundary conditions in the material point method. The present coupled method preserve smoothing transition between. The performance of this weight function proved that the quartic 4th order spline gains the highest accuracy. 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. 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.
The point interpolation method pim 16 based on gaussian and multiquadric radial basis functions are applied. 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. Meshless methods mms provide an alternative to the fem. The sbmfm uses spline basis functions for field variables and boundary representation. The main aim of this work is to consider a meshfree algorithm for solving burgers equation with the quartic bspline quasiinterpolation.
The coupled thbrkpm method blends the advantages of the isogeometric analysis and. Femeshfree quad4 element with modified radial point. 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. Pdf in this paper, we propose minimization techniques with webspline based meshfree finite element method for the solution of. 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. Meshfree methods, numerical integration, computational electromagnetics.
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