A strain smoothing method in finite nelements for structural analysis

This thesis further developments strain smoothing techniques in finite elementmethods for structural analysis. Two methods are investigated and analyzed both theoretically and numerically. The first is a smoothed finite element method (SFEM) where an assumed strain field is derived from a smoothed operator of the compatible strain field via smoothing cells in the element.The second is a nodally smoothed finite element method (N-SFEM),where an assumed strain field is evaluated using the strain smoothing in neighbouring domains connected with nodes.For the SFEM, 2D, 3D, plate and shell problems are studied in details. Twoissues based on a selective integration and a stabilization approach for volumetric locking are considered. It is also shown that the SFEM in 2D with asingle smoothing cell is equivalent to a quasi-equilibrium model.For the N-SFEM, a priori error estimation is established and the convergence is confirmed numerically by benchmark problems. In addition, a quasi-equilibrium model is obtained and as a result a dual analysis is very promising to estimate an upper bound of the global error in finite elements.It is also expected that two present approaches are being incorporated withthe extended finite element methods to improve the discontinuous solution offracture mechanics.