Isogeometric Modeling for Finite Element Analysis: B-Spline Finite Element Development with Rotational Degrees of Freedom

摘要

During the design process, it is often necessary to perform various structural analyses in order to check the suitability of a design which is not yet finalized. Conventionally, this is done by translating the design geometry defined in Computer-Aided Design (CAD) software into a Finite Element (FE) mesh, then the structural analysis is performed. Considering that the mesh generation may represent about 80 percent of the total overall analysis time, and it is repeatedly required whenever the design changes, these steps of translations adversely affect the overall design process. We address isogeometric modeling for more efficient finite element analysis by employing the finite elements' interpolation functions in exactly the same manner as the B-Spline basis functions in the CAD geometry. This eliminates the need for mesh generation or translations by keeping the geometrical information in one CAD representation. One particular issue is the definition of rotational degrees of freedom, which are essential and very common in many structural finite element analyses but may not be easily modeled for points in CAD. We show that the rotational degrees of freedom can be modeled in the isogeometric analysis scheme by employing nodal points on the geometry corresponding to the control points.