Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

A novel meshfree approach based on the finite pointset method for linear elasticity problems

Abstract: In this work a promising novel meshfree numerical formulation with improved accuracy based on the finite pointset method (FPM) is reported and implemented for the first time for linear elasticity problems. This truly meshfree approach is applied in order to solve the governing partial differential equations, the Navier–Cauchy equations. The numerical results of some 2D and 3D classical and well-known benchmark examples using this formulation are reported and compared with a previous FPM formulation which demonstrate the improvement in accuracy, and finally, the numerical solution of a three-dimensional realistic example is reported which suggest that the presented FPM approach is promising and feasible for this kind of problems in solid mechanics.

RBF-based meshless modeling of strain localization and fracture

Abstract: This work attempts to contribute further knowledge and understanding in the discipline of computational science in general and numerical modeling of discontinuity problems in particular. Of particular interest is numerical simulation of dynamic strain localization and fracture problems. The distinguishing feature in this study is the employment of neural-networks-(RBF)-based meshfree methods, which differentiates the present approach from many other computational approaches for numerical simulation of strain localization and fracture mechanics. As a result, new meshfree methods based on RBF networks, namely moving RBF-based meshless methods, have been devised and developed for solving PDEs. Unlike the conventional RBF methods, the present moving RBF is locally supported and yields sparse, banded resultant matrices, and better condition numbers. The shape functions of the new method satisfy the Kroneckerdelta property, which facilitates the imposition of the essential boundary conditions. In addition, the method is applicable to arbitrary domain and scattered nodes. To capture the characteristics of discontinuous problems, the method is further improved by special techniques including coordinate mapping and local partition of unity enrichment. Results of simulation of strain localization and fracture, presented in the latter chapters of the thesis, indicate that the proposed meshless methods have been successfully applied to model such problems.

Nonlinear Meshfree Analysis Program (NMAP) Version 1.0 (User's Manual)

Abstract: : As a part of the meshfree method development for fragment-impact modeling, an enhanced semi-Lagrangian reproducing kernel particle method formulation for modeling large material deformation and damage mechanisms was developed. The formulation includes a microcrack-informed damage model (MIDM) for improved material failure modeling. The MIDM is based on multiscale homogenization using the energy bridging theory pertinent to fragment penetration modeling of concrete materials. Enhanced kernel contact algorithms to model multi-body contact applicable to penetration problems were also developed. The computational formulations and numerical algorithms for these new meshfree method developments were implemented into the parallel Nonlinear Meshfree Analysis Program (NMAP) code. This report provides user instructions for building and running a model in NMAP. The report, together with previously published technical reports, also provides a general overview of the theoretical foundation of the newly developed meshfree formulation for fragment-impact modeling.