Abstract
In this paper, we present a shape optimization method for plate springs, which is based on the free-form optimization method for the shape design of shell structures we have developed. With the free-form optimization method, an optimum shell with smooth free-form surface can be obtained without any shape parameterization, In order to apply this method to the design of plate springs, we introduce a squared displacements error norm at the loaded points as the objective functional to control the displacements to the desired ones. It is assumed that the shell was varied in the normal direction to the surface and the thickness is constant. A non-parametric shape optimization problem without a volume constraint is formulated, and the shape gradient function is theoretically derived using the material derivative method. The shape gradient function is applied to the shell surface as the pseudo traction force to change the form. The calculated results show the effectiveness of the proposed method for the optimal free-form design of the plate springs.
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