A numerical method to optimize the design of a space inflatable membrane reflector

A numerical method is proposed to optimize the design of a space inflatable membrane reflector. The initial geometry is expressed by polynomial series weighted by a set of shape parameters. The problem is formulated as a minimization of a cost function representing the difference between the effective shape of the reflector and a perfect parabolic surface. The minimization is performed using the Nelder–Mead method or downhill simplex method. The cost function is computed at each vertex of a simplex defined in the space of optimization parameters by solving direct problem thanks to a finite element method. The finite element model handles geometrical non-linearities and takes into account phenomena like membrane wrinkling and torus buckling which may affect the reflector shape when inflated.

► A numerical method to optimize a space inflatable membrane reflector is presented.
► Parameterization of the initial shape is proposed.
► Finite element analysis has been performed using the conjugate gradient algorithm.
► It allows to consider automatically wrinkling if its occurs.