Developability conditions for prestress optimization of a curved surface Original Research Article

Developability conditions are presented for prestressed curved surfaces to be reduced to plane sheets by relaxing the stresses. Those conditions are applied to an optimization problem for minimizing the deviation of stresses from the target values. Two formulations based on the displacements defined by the local and global coordinates of finite elements are presented. It is shown that the numbers of constraints by those formulations are same if triangular elements are used, and there is an upper bound in the number of the elements in a cutting sheet. Performances of the two formulations are compared in the numerical examples, and the local formulation is shown to lead to more accurate estimation of stresses that are actually generated by connecting and stretching the plane sheets.