Papers by Keyword: Meshless Methods

Abstract: Indentation in brittle solids involves many complex phenomena related to cleavage and contact, as well as intrinsic stress singularities, which are almost impossible to capture with traditional continuum approach and FEA at mesoscale. In case of a two-phase ceramic composite [1–3] the number of unknown material and interfacial constants, that have to be calibrated experimentally, increases rapidly [4, 5]. In this paper, nanoindentation in zirconia-toughened alumina (ZTA) is modelled using discrete (peridynamical) approach

Abstract: The paper deals with use of the meshless method for soil subsurface settlement analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG) – local weak formulation of the equilibrium equations. The main difference between meshless methods and the conventional finite element method (FEM) is that meshless shape functions are constructed using randomly scattered set of points without any relation between points. The Heaviside step function is test function used in the meshless implementation presented in the article. Heaviside test function makes weak formulation integral very simple, because only body integral in governing equation is due a body force.

Abstract: This paper for the first time explores the application of the meshless approach, structured on the Local Radial Basis Function Collocation Method (LRBFCM), for solving the freezing process with convection in the liquid phase for a metals-like material in a closed rectangular cavity. The enthalpy one-domain formulation is used to avoid inclusion of additional boundary conditions at the fluid-solid interface. To avoid numerical instabilities, the freezing of a pure substance is modeled by a narrow phase change interval. The fluid flow is solved by a local pressure-velocity coupling, based on the mass continuity violation [1-3], and the explicit time stepping is used to drive the system to the free boundary solution. The results are presented through temperature and streamfunction contours and the liquid-solid interface position at the steady state, as well as the time development of the average Nusselt number and the time development of the cavity average liquid fraction. Results are validated with already benchmarked melting example [3]. The paper represents first steps in solution of the Hebdich and Hunt experiment by an alternative numerical technique, different from the classical finite volume or finite element methods [4].

Abstract: This paper describes an overview of a new meshless solution procedure for calculation of one-domain coupled macroscopic heat, mass, momentum and species transfer problems as well as phase-field concepts of grain evolution. The solution procedure is defined on the macro [1] as well as on the micro levels [2] by a set of nodes which can be non-uniformly distributed. The domain and boundary of interest are divided into overlapping influence areas. On each of them, the fields are represented by the multiquadrics radial basis functions (RBF) collocation on a related sub-set of nodes. The time-stepping is performed in an explicit way. All governing equations are solved in their strong form, i.e. no integrations are performed. The polygonisation is not present and the formulation of the method is practically independent of the problem dimension. The solution can be easily and efficiently adapted in node redistribution and/or refinement sense, which is of utmost importance when coping with fields exhibiting sharp gradients. The concept and the results of the multiscale solidification modeling with the new approach are compared with the classical mesh-based [3] approach. The method turns out to be extremely simple to code and accurate, inclusion of the complicated physics can easily be looked over. The coding in 2D or 3D is almost identical.

Abstract: This work aims at introducing the concept of the numerical Green’s function (NGF) idea for elastostatic fracture mechanics using the boundary element-free method (BEFM). Unlike the local boundary integral equation method (LBIE), the BEFM only requires boundary interpolation. This method derives from the coupling of the boundary integral equation method and the orthogonal moving least-squares approximation scheme (OMLS). OMLS differs from standard MLS by using an orthogonal basis instead of only a linear independent one, which increases its accuracy and efficiency. Some illustrative examples are included in the end.