A non-parametric solution to shape identification problem of free-form shells for desired deformation mode

• A shape identification method is presented for controlling the static deformation modes of free-form shells.
• Stiffness control can also be achieved by defining the displacements of the loading points to the desired values
• It is a non-parametric shape optimization method that does not require any design variable parameterization.
• Mesh smoothing is simultaneously implemented in the shape updating process.

A shape identification method of free-form shells is presented for controlling the static deformation mode to the desired one. This problem is formulated as a parameter-free shape optimization problem, in which a squared displacements error norm on the prescribed region is employed as an objective functional. The shape sensitivity, called shape gradient function, is theoretically derived using the adjoint variable method and the formula of the material derivative, and then applied to a gradient method with Laplacian smoother for shells to determine the smooth optimal shape. Several calculated examples are presented to verify the validity and practical utility of the proposed method.