Keywords: isogeometric analysis, structural analysis, object oriented environment.

The finite element method (FEM) is probably the most widespread analysis tool for the structural analysis. During the last decades, the FEM has matured to such a state that it is ubiquitously used in practical engineering. Since the finite element analysis (FEA) is based (not only) on the spatial discretization of the underlying domain, an important prerequisite for the successful application of the FEM is a proper mesh of the geometric representation of that domain. This links the FEM closely to computer aided design (CAD) handling the geometric description of the domain. The common situation in engineering practice is that the design is encapsulated in the CAD system, data from which the mesh is generated that inputs in the FEA. This is now considered a major bottleneck in computer aided engineering (CAE). The root cause is that CAD and FEA evolved independently since their origin and each one works with different geometric representations. The geometric model from the CAD often contains ambiguities (gaps, overlaps) and levels of detail (small features) which are inappropriate for the FEA. Therefore the model must first be fixed yielding an analysis suitable geometry (ASG) which is then subjected to discretization into a finite element mesh. However, the mesh produced is usually only an approximation (typically piecewise polynomial) of the actual geometry, which can lead to accuracy problems. This is further amplified by the fact that most FEAs are still performed with low-order elements, for which the geometric errors are the largest.

The above problems are more or less addressed by the so-called isogeometric analysis (IGA), which is nowadays attracting significant focus as to a viable alternative to the standard, polynomial-based FEA. The IGA builds upon the concept of isoparametric elements, in which the same basis functions are used to approximate the geometry and the solution on a single finite element. The IGA, as its name suggests, goes one step further as it employs the same functions for the description of the geometry and for the approximation of the solution space on that geometry. This implies that once the ASG is constructed from the initial CAD geometry, its isogeometric mesh encapsulates the exact geometry no matter how coarse the mesh actually is. As a consequence, the analysis process can be refined to any level without altering the geometry in any way and without accessing the CAD geometry.

The aim of this paper is to present how the IGA concept may be implemented into an inherent object oriented finite element environment. The class hierarchy and corresponding methods are designed in such a way, that most of the existing functionality is reused. The missing data and algorithms, namely those providing the support for handling isogeometric basis functions, forming the isogeometric mesh, application of appropriate numerical integration scheme, and the assignment of boundary conditions are developed and implemented in such a way that the object oriented features, such as modularity, extensibility, maintainability, and robustness, are fully retained. The functionality of the implementation and the performance of the IGA is presented for a simple two-dimensional example.

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