Development of Smoothed Finite Element Method (SFEM)

Abstract

To overcome shortcomings of the finite element method (FEM), this thesis focuses on formulating and developing five new FEM models, including four smoothed FEM (S-FEM) models and one alpha-FEM model by combining the existing standard FEM and the strain smoothing technique. The results of the research showed four crucial contributions: (1) Five new numerical methods are promising to provide more feasible options for numerical methods, especially for methods using triangular and tetrahedral elements; (2) S-FEM models give more the freedom and convenience in constructing shape functions, and also in using distorted elements and n-sided polygonal elements; (3) NS-FEM which possesses interesting properties of an equilibrium FEM model is promising to provide a much simpler tool to estimate the quality of the solution (global error, bounds of solutions, etc) by combining itself with FEM; (4) alpha-FEM has a very meaningful contribution in providing more the reference benchmark solutions wi