A new sensitivity analysis method for membrane wrinkling is presented. The wrinkling phenomenon is modeled by the tension filed theory with a projection technique. In the technique, the total strain energy in wrinkled membranes is effectively decomposed into elastic energy and zero-strain energy parts using a projection matrix. The zero-strain energy part depends on only the zero-energy deformation caused by wrinkling, and is utilized for a quantifier of degree of membrane wrinkling at a

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... l point. The wrinkle quantity of the discretized membrane element is obtained by the integral of the zero-strain energy over each element. The total wrinkle quantity of whole membrane is also obtained by the summation of the elemental wrinkle quantities. The sensitivity of the total wrinkle quantity is derived with respect to displacement vector and also design parameter. The latter is given by the semi-analytical differentiation method (SDM). The proposed sensitivity analysis method is applied to a shape design problem for wrinkle reduction of a square membrane to demonstrate its effectiveness.