A study on the stress gradient reconstruction in finite elements problems with application of radial basis function networks

The recovery of the stress gradient in finite elements problems is a widely discussed topic with many applications in the design process. The stress gradient is related to the second derivative (Hessian) of the nodal displacements and numerical techniques are required for its calculation. Particular difficulties are encountered in the reconstruction of the stress gradient in the boundary regions of the domain. This is of particular concern in most applications, especially in mechanical components, where the maximum values of stresses are often located in these regions and the stress gradient has a strong influence on the fatigue life of the component. This paper presents a comparison between some already published, partially modified, recovery techniques and a different approach based on radial basis function networks. The aim of the paper is to compare the performances of the different approaches for a number of element types with particular focus on the boundary regions. Some examples of mechanical interest are considered.