Application of stress smoothing methods to a finite element pile driving analysis

In finite element analysis of pile driving, the nodes of the finite element mesh are the most important locations for output stresses. Especially at the pile-soil interface, it is essential to obtain accurate nodal stresses. Several global and local stress smoothing methods available in the literature were reviewed and examined. Global methods are found to be computationally expensive, so results obtained from several local stress smoothing methods are compared. It is shown that accurate nodal stresses can be obtained by approximating the stress distribution inside four-element patches by a polynomial with order equal to the order of the shape functions. Equally good results can be obtained by approximating the stress distribution inside each element by a bilinear surface. When a method taking into account both equilibrium and boundary conditions was applied, a set of ill-conditioned matrices was produced for the four-element patches. Such methods are therefore not recommended.