Dual basis functions for isogeometric solid mechanics

Abstract eng:
The main paradigm of isogeometric analysis is the use of a common set of basis functions for design and analysis. Thus, the basis functions of a Computer-Aided-Design (CAD) application are used for the analysis with the Finite-Element-Method (FEM). In this work the basis functions of Non-Uniform Rational B-splines (NURBS), which is the prevailing geometry definition in CAD industry, are used. The defining characteristic of dual basis functions is that the integral of their product with their associated standard basis functions yields the Kronecker delta property with respect to indices. In the case of NURBS the definition of dual basis functions is non-trivial and several possibilities exist. This work shows and compares different approaches for the dual basis functions. They are applied within the isogeometric mortar method, which is used to couple non-conforming NURBS meshes. An outlook on further applications is given.

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