  A design problem of finding an optimally stiff membrane structure by
selecting one-dimensional fiber reinforcements is formulated and solved. The
membrane model is derived in a novel manner from a particular three-dimensional
linear elastic orthotropic model by appropriate assumptions. The design problem
is given in the form of two minimization statements, reminiscent of a Nash
game. After finite element discretization, the separate treatment of each of
the two minimization statements follows from classical results and methods of
structural optimization: the stiffest orientation of reinforcing fibers
coincides with principal stresses and the separate selection of density of
fibers is a convex problem that can be solved by optimality criteria
iterations. Numerical solutions are shown for two particular configurations.
The first for a statically determined structure and the second for a statically
undetermined one. The latter shows related but non-unique solutions.
