The paper addresses the classical problem of optimal truss design
where cross-sectional areas and the positions of joints are
simultaneously optimized. Several approaches are discussed from a
general point of view. In particular we focus on the difference
between simultaneous and alternating optimization of geometry and
topology. We recall a rigorously mathematical approach based on the
implicit programming technique which considers the classical single
load minimum compliance problem subject to a volume constraint. This
approach is refined leading to three new problem formulations which
can be treated by methods of Mathematical Programming. In particular
these formulations cover the effect of melting end nodes, i.e.,
vanishing potential bars due to changes in the geometry. In one of
these new problem formulations the objective function is a polynomial
of degree three and the constraints are bilinear or just sign constraints.
Since heuristics is avoided, certain optimality properties can be
proved for resulting structures. The paper closes with two numerical
test examples.