Applications of the MLPG Method in Engineering & Sciences: A Review 467

Abstract: A review is presented for analysis of problems in engineering & the sciences, with the use of the meshless local Petrov-Galerkin (MLPG) method. The success of the meshless methods lie in the local nature, as well as higher order continuity, of the trial function approximations, high adaptivity and a low cost to prepare input data for numerical analyses, since the creation of a finite element mesh is not required. There is a broad variety of meshless methods available to-day; however the focus is placed on the MLPG method, in this paper. The MLPG method is a fundamental base for the derivation of many meshless formulations, since the trial and test functions can be chosen from different functional spaces. In the last decade, a broad community of researchers and scientists contributed to the development and implementation of the MLPG method in a wide range of scientific disciplines. This paper first presents the basics and principles of the MLPG method, the mesh-less local approximation techniques for trial and test functions, applications to elas-ticity and elastodynamics, plasticity, fracture and crack analysis, heat transfer and fluid flow, coupled problems involving multiphase materials, and techniques for increasing the accuracy and computational effectiveness. Various applications to 2-D planar problems, axisymmetric problems, plates and shells or 3-D problems are included. An increased number of published papers in literature in the recent years can be considered as a measure of the growing research activity in the general scope of the MLPG method, and thus, several trends and ideas for future research interest are also outlined