Multi-scale methods

In this paper four multiple scale methods are proposed. The meshless hierar chical partition of unity is used as a multiple scale basis. The multiple s cale analysis with the introduction of a dilation parameter to perform mult iresolution analysis is discussed. The multiple field based on a I-D gradie nt plasticity theory with material length scale is also proposed to remove the mesh dependency difficulty in softening/localization problems. A non-lo cal (smoothing) particle integration procedure with its multiple scale anal ysis are then developed. These techniques are described in the context of t he reproducing kernel particle method. Results are presented for elastic-pl astic one-dimensional problems and 2-D large deformation strain localizatio n problems to illustrate the effectiveness of these methods. Copyright (C) 2000 John Wiley & Sons, Ltd.