Meshless Methods in Solid Mechanics

Finiteelementmethodhasbeenthedominanttechniqueincomputationalmech- icsinthepastdecades,andithasmadesigni?cantcontributionstothedevelopments in engineering and science. Nevertheless, FEM is not well suited to problems h- ing severe mesh distortion owing to extremely large deformations of materials, encountering moving discontinuities such as crack propagation along arbitrary and complex paths, involving considerable meshings and remeshings in structural optimization problems, or having multidomain of in?uence in multiphenomena physical problems. It is impossible to completely overcome those mesh-related dif?culties by a mesh-based method. The highly structured nature of ?nite e- ment approximations imposes severe penalties in seeking the solutions of those problems. Distinguishing with ?nite element, ?nite difference, and ?nite volume methods, meshless method discretizes the continuum body only with a set of nodal points andtheapproximationisconstructedentirelyintermsofnodes.Thereisnoneedof mesh or elements in this method. It does not possess the mesh-related dif?culties and provides an approach with more ?exibility in the applications in engineering and science. The meshless method started to capture the interest of a broader community of researchers only several years ago, and now it becomes a growing and evolving ?eld. It is showing that this is a very rich area to be explored, and has great promise for many very challenging computational problems. On the one hand, great advances of meshless methods have been achieved. On the other hand, there are many aspects of meshless methods that could bene?t from improvements. A broadercommunityofresearcherscanbringdiverseskillsandbackgroundstobear on the task of improving this method.