Design and implementation of a new spherical super element in structural analysis

Finite Element Method (FEM) has proved to be a powerful tool for the analysis of mechanical problems such as finding natural frequency and deformation of structures. Design and implementation of super elements with a purpose in reduction of computational time along with accuracy is one of the challenges facing engineers in the past decade. In this study a newly spherical super element is designed and implemented to some problems. This element is generated in such a way that the user can select as many numbers of nodes as desired. Proper formulation is presented to generate the shape function for each node in this element. Some examples of static and vibration analysis using this element are performed and results are comparable with high accuracy and less computational time with findings of commercial finite element packages, analytical and experimental methods. This element can be used to analyze hollow spherical structures such as biological cells, ball bearings and pressure vessels.