From the finite element analysis to the isogeometric analysis in an object oriented computing environment

During the last decades, the finite element method has become the most powerful tool for structural analysis massively used in practical engineering. However, recently the isogeometric analysis has been introduced as a viable alternative to the standard, polynomial-based finite element analysis. Moreover, it has been shown that it may outperform the classical finite element method in many aspects. This paper presents how the isogeometric analysis can be integrated within an object oriented finite element environment. The class hierarchy and corresponding methods are designed in such a way, that most of the existing functionality of the finite element code is reused. The missing data and algorithms are developed and implemented in such a way that the object oriented features, such as modularity, extensibility, maintainability, and robustness, are fully retained. The performance of the implemented isogeometric analysis methodology is presented on two- and three-dimensional examples.

Research highlights
► Isogeometric analysis has been integrated in object oriented FEM computing environment.
► Class hierarchy design is based on strict separation of interpolation, integration and analysis-specific functionality.
► Modularity and easy extensibility of the whole environment has been retained.
► Amount of modified and/or added code is rather limited mostly related to handling B-spline basis functions.