Web-Spline IGA Based Support Position Optimization for Natural Frequency Maximization of the Curved Beam

This work presents a novel optimization framework for finding the optimal support position of the curved beam to maximize its natural frequency. In order to solve this challenging but quite practical problem, the proposed framework makes full use of the advantage related to the isogeometric analysis (IGA) in combination with web-splines. To be specific, IGA, employing non-uniform rational B-spline (NURBS) basis functions for the interpolation of both the structural geometry and physical field, has natural advantages in the curved beam analysis, such as the exact expression for the smooth geometry, and the guarantee for the high-order continuity of physical fields. Whereas, the displacement constraint at the support position (excepting both ends) could not be accurately imposed by using IGA, due to the lack of interpolation properties of NURBS basis functions. But this Dirichlet boundary imposition problem can be solved very well by adopting the concept of web-splines, in which the interpolation functions are simply multiplied by a weight function vanishing on the fixed position. Also, the support position can be freely changed with the variation of the weight function. So, the framework combining the IGA with web-splines are developed in this work to implement the curved beam’s support optimization design. Numerical example considering the natural frequency maximization problem of a typical curved beam is investigated to show the superiority of the proposed method.