Topic
Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
Papers published on a yearly basis
Papers
More filters
01 Jan 2003
TL;DR: This chapter reviews octree-based discretization techniques for the generation of open covers for the Galerkin-based and the point collocation-based method of finite spheres.
Abstract: Publisher Summary The capability to automatically solve boundary value problems on complex domains leads to the widespread use of finite element techniques. However, problems associated with the generation of a “good quality” mesh has resulted in the development of the so-called “meshfree methods” that offer an alternative to the finite element methods by circumventing the problem of mesh generation. They also offer greater flexibility in the choice of approximation spaces and nonGalerkin weighted residual schemes. This chapter reviews octree-based discretization techniques for the generation of open covers for the Galerkin-based and the point collocation-based method of finite spheres. The method of finite spheres is a truly meshfree numerical technique developed for the solution of boundary value problems on complex domains. In this method, the computational domain is subordinate to the open cover generated by the spherical subdomains.
01 Jan 2016
TL;DR: In this paper, a meshless natural neighbor Galerkin method for bending and vibration analysis of plates and laminates is presented, which has distinct advantages of geometric flexibility of meshless method.
Abstract: In the present work a meshless natural neighbor Galerkin method for the bending and vibration analysis of plates and laminates is presented. The method has distinct advantages of geometric flexibility of meshless method. The compact support and the connectivity between the nodes forming the compact support are performed dynamically at the run time using the natural neighbor concept. By this method the nodal connectivity is imposed through nodal sets with reduced size, reducing significantly the computational effort in construction of the shape functions. Smooth non-polynomial type interpolation functions are used for the approximation of inplane and out of plane primary variables. The use of non-polynomial type interpolants has distinct advantage that the order of interpolation can be easily elevated through a degree elevation algorithm, thereby making them suitable also for higher order shear deformation theories. The evaluation of the integrals is made by use of Gaussian quadrature defined on background integration cells. The plate formulation is based on first order shear deformation plate theory. The application of natural neighbor Galerkin method formulation has been made for the bending and free vibration analysis of plates and laminates. Numerical examples are presented to demonstrate the efficacy of the present numerical method in calculating deflections, stresses and natural frequencies in comparison to the Finite element method, analytical methods and other meshless methods available in the literature.
01 Jan 2011
TL;DR: This work shows how to combine the advantages of RBF and RK approximations to yield a local approximation that is better conditioned than that of the radial basis collocation method, while at the same time offers a higher rate of convergence that that of Galerkin type reproducing kernel method.
Abstract: Meshfree methods have been formulated based on Galerkin type weak formulation and collocation type strong formulation. The approximation functions commonly used in the Galerkin based meshfree methods are the moving least-squares (MLS) and reproducing kernel (RK) approximations, while the radial basis functions (RBFs) are usually employed in the strong form collocation method. Galerkin type formulation in conjunction with approximation functions with polynomial reproducibility yields algebraic convergence. Alternatively, strong form collocation method with RBF approximation offers exponential convergence, however the method is suffered from ill-conditioning due to its "nonlocal" approximation. In this work, we discuss stability issues related to nodal integration of Galerkin type meshfree method and ill-conditioning of the radial basis collocation method. We show how to combine the advantages of RBF and RK approximations to yield a local approximation that is better conditioned than that of the radial basis collocation method, while at the same time offers a higher rate of convergence that that of Galerkin type reproducing kernel method.
TL;DR: In this article , a mesh-free procedure based on the finite pointset methods for thermo-elastic problems with moving heat sources, which are present in welding processes, is presented.
Abstract: This manuscript presents the development and application of a meshfree procedure based on the finite pointset methods for thermo-elastic problems with moving heat sources, which are present in welding processes. The meshfree nature of this formulation gives the advantage of dealing with geometrical distortions and even fragmentations without the need of using computationally expensive remeshing approaches with a very simple implementation. A description of the implementation of this method and the solutions of some numerical examples are presented in order to show the potential of this formulation for dealing with thermoelasticity problems with moving heat sources and to introduce promising future fields of application.