This research deals on how to maximize the targeting natural frequency of a plate by attaching a beam stiffener. The goal is to find out the beam attaching position on a plate to maximize its fundamental natural frequency.
The shape optimization technique is used to describe the movement of beam element in a plate. The shape optimization is an inclusive FEM-based structural optimization technique using the shape, rotation, length of a structure and the connections between structures as design variables. The translation and rotation of a beam can be expressed as shape base vectors describing the variation of beam nodes. Then the optimal combinations of shape base vectors maximizing the natural frequency of the plate while satisfying the constraints can be found via optimization algorithms such as feasible direction methods and linear programing.
In this thesis the optimal position and the rotation angle of a beam stiffener on a plate is obtained with the shape optimization technique. The initial position of the beam stiffener is directly related on the computational loads. When the initial position is selected as the element which has the highest natural frequency sensitivity to its thickness, the optimum stiffener attaching position can be found most easily.
