Shape Optimal Design of Membrane Wrinkling Minimization Using NURBS Curves

This study concerns a shape optimum design to minimize wrinkle intensity of a membrane under an area constraint. The membrane shape is modeled by non-uniform rational B-spline (NURBS) curves and the curve-passing points are adopted as design variables. The membrane wrinkle intensity is evaluated through the wrinkle-mode deformation energy proposed by one of the authors. Where, the total strain energy in a wrinkled membrane evaluated by the tension field theory is effectively decomposed into elastic strain energy and apparent wrinkle-mode deformation energy by applying a projection matrix. The latter only depends on the deformation caused by wrinkling, and is utilized as an objective function. As a numerical example, the optimization is applied to a typical square membrane design problem to demonstrate the effect of the shape optimization on the wrinkle reduction. The wrinkle-mode deformation energy decreases to 10% of the original design for only 5% reduction of the membrane area. Additionally, a high convergence property is achieved regardless of direct implementation of the nonlinear finite element analysis during the optimization.