New Numerical Method for Two-Dimensional Partially Wrinkled Membranes

Based on the introduction of a nonnegative adjustable parameter into Poisson's ratio, a new numerical method is proposed to solve numerically the partially wrinkled membrane problems with arbitrary complex shapes. Three fundamental issues in this new method are addressed. First, a nonnegative adjustable parameter is introduced into the constitutive law, automatically representing unwrinkled (taut) and wrinkled states of a membrane. Second, a parametric variational principle is developed for the new membrane model. Third, by the variational principle, the original membrane problem is converted to a nonlinear mathematical programming problem. The variational principle and the mathematical programming formulation lay a foundation for efficient numerical analysis of wrinkled membrane structures using finite element discretization. Three typical examples are given to show the effectiveness of this method.