Recent Advances in Meshfree Methods

J. S. Chen
Professor
Department of Civil & Environmental Engineering
University of California, Los Angeles

Date:  Tuesday, October 7, 2003
Time:  3:30 p.m.
Place:  W183 Nebraska Hall

In recent years, a new class of numerical methods, collectively called the meshfree method, has been developed as a generalization of finite element methods for computational mechanics. Meshfree methods employ new approximation theories that allow the construction of shape functions and domain discretization without the need of an explicit mesh. This unique property provides meshfree methods with considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, multiple-scale phenomena, and large material distortion and structural deformation. The most significant advantage in meshfree methods is the flexibility in customizing approximation functions for desired smoothness, accuracy, or special characteristics of particular engineering and scientific problems. Adaptivity formulation and multiple scale solution strategies can also be implemented with relative ease.

The objective of presentation is to provide introduction to the fundamental theory and recent advances in meshfree methods. New developments to address boundary conditions, domain integration, stability, dispersion, and adaptivity computation will be discussed. Applications to metal forming processes, elastomeric materials and devices, magnetostrictive particle-reinforced composites, plate and shell structures, modeling of damage and fragmentation processes, and mesoscale modeling and multiscale homogenization of stressed grain growth will be demonstrated.