Search results for "Meshless"
showing 10 items of 51 documents
Mesoscopic aspects of the computational homogenization with meshless modeling for masonry material
2020
The multiscale homogenization scheme is becoming a diffused tool for the analysis of heterogeneous materials as masonry since it allows dealing with the complexity of formulating closed-form constitutive laws by retrieving the material response from the solution of a unit cell (UC) boundary value problem (BVP). The robustness of multiscale simulations depends on the robustness of the nested macroscopic and mesoscopic models. In this study, specific attention is paid to the meshless solution of the UC BVP under plane stress conditions, comparing performances related to the application of linear displacement or periodic boundary conditions (BCs). The effect of the geometry of the UC is also i…
Numerical Investigations of an Implicit Leapfrog Time-Domain Meshless Method
2014
Numerical solution of partial differential equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes in time. A predefined grid in the problem domain and a stability step size restriction need. Recently, the authors have reformulated the meshless framework based on smoothed particle hydrodynamics, in order to be applied for time domain electromagnetic simulation. Despite the good spatial properties, the numerical explicit time integration introduces, also in a meshless context, a severe constraint. In this paper, at first, the stability condition is addressed in a general way by allowing the time step inc…
Exponential convergence andH-c multiquadric collocation method for partial differential equations
2003
The radial basis function (RBF) collocation method uses global shape functions to interpolate and collocatethe approximate solution of PDEs. It is a truly meshless method as compared to some of the so-calledmeshless or element-free finite element methods. For the multiquadric and Gaussian RBFs, there are twoways to make the solution converge—either by refining the mesh size
A numerical meshless particle method in solving the magnetoencephalography forward problem
2012
In this paper, a numerical meshless particle method is presented in order to solve the magnetoencephalography forward problem for analyzing the complex activation patterns in the human brain. The forward problem is devoted to compute the scalp potential and magnetic field distribution generated by a set of current sources representing the neural activity, and in this paper, it has been approached by means of the smoothed particle hydrodynamics method suitably handled. The Poisson equation generated by the quasi-stationary Maxwell’s curl equations, by assuming Neumann boundary conditions has been considered, and the current sources have been simulated by current dipoles. The adopted meshless…
A 3D Meshless Approach for Transient Electromagnetic PDEs
2012
A full wave three dimensional meshless approach for electromagnetic transient simulations is presented. The smoothed particle hydrodynamic (SPH) method is used by considering the particles as interpolation points, arbitrarily placed in the computational domain. Maxwell’s equations in time domain with the assigned boundary and initial conditions are numerically solved by means of the proposed method. The computational tool is assessed and, for the first time, a 3D test problem is simulated in order to validate the proposed approach.
Numerical Simulation of Friction Stir Welding by Natural Element Methods
2008
In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods (FEM) encounter several difficulties. While Lagrangian simulations suffer from mesh distortion, Eulerian or Arbitrary Lagrangian Eulerian (ALE) ones still have difficulties due to the treatment of convective terms, the treatment of the advancing pin, and many others. Meshless methods somewhat alleviate these problems, allowing for an updated Lagrangian framework in the simulation. Accuracy is not affected by mesh distortion (and hence the name mes…
Unconditionally stable meshless integration of time-domain Maxwell’s curl equations
2015
Grid based methods coupled with an explicit approach for the evolution in time are traditionally adopted in solving PDEs in computational electromagnetics. The discretization in space with a grid covering the problem domain and a stability step size restriction, must be accepted. Evidence is given that efforts need for overcoming these heavy constraints. The connectivity laws among the points scattered in the problem domain can be avoided by using meshless methods. Among these, the smoothed particle electromagnetics, gives an interesting answer to the problem, overcoming the limit of the grid generation. In the original formulation an explicit integration scheme is used providing, spatial a…
Meshless Simulation of Friction Stir Welding
2007
This paper encompasses our first efforts towards the numerical simulation of friction stir welding by employing a Lagrangian approach. To this end, we have employed a meshless method, namely the Natural Element Method (NEM). Friction Stir welding is a welding process where the union between the work pieces is achieved through the extremely high deformation imposed by a rotating pin, which moves between the two pieces. This extremely high strain is the main responsible of the difficulties associated with the numerical simulation of this forming process. Eulerian and Arbitrary Lagrangian-Eulerian (ALE) frameworks encounter difficulties in some aspects of the simulation. For instance, these ap…
A preliminary comparison between finite element and meshless simulations of extrusion
2009
In this paper the extrusion process of a cross-shaped profile was investigated. In particular, the study was focused on the distortion of extruding profiles when the workpiece and die axis are not aligned. The process was simulated using the finite element method (FEM) and the natural element method (NEM), both implemented in an updated-Lagrangian formulation, in order to avoid the burden associated with the description of free surfaces in ALE or Eulerian formulations. Furthermore, an experimental equipment was developed in order to obtain reliable data in terms of deformed entity, required process load and calculated pressure. At the end, a comparison between the numerical predictions and …
A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges
2015
In this paper recent results on a leapfrog ADI meshless formulation are reported and some future challenges are addressed. The method benefits from the elimination of the meshing task from the pre-processing stage in space and it is unconditionally stable in time. Further improvements come from the ease of implementation, which makes computer codes very flexible in contrast to mesh based solver ones. The method requires only nodes at scattered locations and a function and its derivatives are approximated by means of a kernel representation. A perceived obstacle in the implicit formulation is in the second order differentiations which sometimes are eccesively sensitive to the node configurat…