TY - JOUR A2 - Mucchi, Emiliano AU - Shimoda, Masatoshi AU - Liu, Yang PY - 2015 DA - 2015/08/24 TI - Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem SP - 471646 VL - 2015 AB - We present a node-based free-form optimization method for designing forms of thin-walled structures in order to control vibration displacements or mode at a prescribed frequency. A squared displacement error norm is introduced at the prescribed surface as the objective functional to control the vibration displacements to target values in a frequency response problem. It is assumed that the thin-walled structure is varied in the normal direction to the surface and the thickness is constant. A nonparametric shape optimization problem is formulated, and the shape gradient function is theoretically derived using the material derivative method and the adjoint variable method. The shape gradient function obtained is applied to the surface of the thin-walled structure as a fictitious traction force to vary the form. With this free-form optimization method, an optimum thin-walled structure with a smooth free-form surface can be obtained without any shape parameterization. The calculated results show the effectiveness of the proposed method for the optimal free-form design of thin-walled structures with vibration mode control. SN - 1070-9622 UR - https://doi.org/10.1155/2015/471646 DO - 10.1155/2015/471646 JF - Shock and Vibration PB - Hindawi Publishing Corporation KW - ER -