On the use of mixed basis function degrees within a convective isogeometric element formulation

Abstract

AbstractSolving linear elasticity problems using standard finite element methods, different locking phenomena can occur. In order to counteract these effects, mixed methods or formulations using higher approximation orders can be employed, for instance. As a consequence, this leads to an increased computational effort. Hence, a selective elevation of orders in decisive directions within a purely displacement‐based element formulation is proposed in this contribution. Within isogeometric analysis (IGA), the geometry is discretized using non‐uniform rational B‐splines (NURBS), which simultaneously represent the basis functions for the analysis. Due to the fact that the geometry can be preserved exactly during analysis, this can increase the accuracy of results. In this contribution, convective basis systems that are aligned with the local geometry are employed combined with selective order elevation. The required convective basis systems are interpolated from those determined in each control point.