Isogeometric Analysis as a New FEM Formulation - Simple Problems of Steady State Thermal Analysis

Abstract

The subject of this article concerns Isogeometric Analysis as a new formulation within Finite Element Method. Motivation for this new approach was presented together with theoretical foundations of the method. The main subject of the paper is numerical implementation of the method in the Matlab environment. Special focus was put on the new concept of element and new geometry data interpretation in terms of analysis. Object oriented programming was utilized to produce more universal tool for future investigations. Several examples for Poisson's partial differential equation solution were presented. The h-refinement was utilized to show method convergence. Steady state thermal analysis was performed with temperatures and heat flux as boundary conditions. Quick geometry data transfer and mesh refinement from Rhino software with Grasshopper plug-in was also prepared and described in the paper. Finally, authors’ conclusions concerning new method were presented and comparison between FEM and IGA was made on the basis of the studied examples.