A three dimensional computational investigation on the influence of essential boundary condition imposition in NURBS isogeometric finite element analysis.

*(Chinese. English summary)*Zbl 1265.74085Summary: Isogeometric analysis provides a perfect unification of functions based on non-uniform rational B-spline (NURBS) used for computer aided geometric design and the finite element analysis. The geometric modeling error is significantly reduced and the solution accuracy is improved. Nevertheless, the NURBS-basis functions commonly are not interpolation functions, and, consequently, to directly impose the essential boundary conditions on the control points may yield noticeable solution errors. In this work, the interpolation property of NURBS-basis functions is discussed in detail, and, after that, a penalty formulation yielding improved solution accuracy and convergence behavior is proposed to enforce the essential boundary conditions in the isogeometric analysis of three-dimensional elasticity problems. Numerical results demonstrate that the approach of direct boundary condition enforcement on the control variables produces much larger solution errors as well as lower displacement and strain energy convergence rates, while the proposed method is capable of achieving optimal convergence rates simultaneously with superior accuracy.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |