B-Spline meshing for high-order finite element analyses of multi-physics problems

Abstract

Multi-physics problems often involve differential equations of higher-order, which cannot be solved with standard finite
element methods. B-splines as finite element basis functions provide the required continuity and smoothness. However, the mesh
generation for arbitrarily shaped domains is non-intuitively and traditional techniques often lead to distorted elements.
Here a strategy is presented to design isoparametric B-spline based meshes for curves, surfaces, and volumes. The error of the
homeomorphic transformation into curved boundaries is estimated. For selected two and three-dimensional shapes, the knot
vectors and the control points are calculated.
Exemplarily, a finite element analysis of a helical structure subjected to a chemo-mechanical deformation with phase decomposition
is performed.