| 英文摘要 |
"This research is based on the iso-geometric analysis (IGA) method, which uses non-uniform rational B-splines (NURBS) as a shape function multiplied by control values to approximate physical fields. The NURBS function is a combination of B-splines and weights. In computer-aided design, NURBS can accurately describe geometric shapes, such as circles, because of introducing the weights which are used to describe irrational functions. Therefore, weights are one of the key variables in making NURBS more flexible in describing geometry. In general, the finite element method approximates physical fields by solving physical quantities at discrete points, while in IGA method, the weights are fixed as geometric weights and the control values are used as variables for solving physical problems. However, geometric fields are not necessarily related to physical fields. Therefore, in this research, we introduce the optimization method, which treat both control values and weights as nodal variables, to obtain better physical solution. The weights are calculated using least squares and non-linear iterative methods to allow a more complete reconstruction of the physical field. In addition, when dealing with irrational essential boundary conditions, we use curve fitting to fit the irrational boundary conditions and calculate the boundary weights to minimize the boundary error. Finally, the results of the weight calculation are tested against the two-dimensional Poisson's equation and the optimization of iso-geometric analysis method is applied to the steady-state heat transfer problem. The optimization results show that a more accurate approximate solution can be obtained with fewer discrete points." |
本站僅提供期刊文獻檢索。
