2014 Volume 80 Issue 811 Pages SMM0039
In this paper, we present a shape identification method of free-form shells for controlling the static deformation mode to the desired one. It is assumed that the shell is varied in the out-of-plane direction to the surface and the thickness is constant. As an objective functional, a squared displacements error norm on the prescribed surface or at the loading points is utilized. A parameter-free shape optimization problem is formulated, and the shape sensitivity, called shape gradient function, is theoretically derived using the Lagrange multiplier method and the formula of the material derivative. The optimal shape is determined by the free-form shape optimization for shells, in which the derived each shape gradient function on the design surface is applied as the fictitious traction force to change the form. Several calculated examples show the effectiveness of the proposed method for the shape identification of free-form design of shell structures with a desired static deformation mode or required sriffness.
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C
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