  An ongoing problem in the study of a classical many-body system is the
characterization of its equilibrium behaviour by theory or numerical
simulation. For purely repulsive particles, locating the melting line in the
pressure-temperature plane can be especially hard if the interparticle
potential has a softened core or contains some adjustable parameters. A method
is hereby presented that yields reliable melting-curve topologies with
negligible computational effort. It is obtained by combining the Lindemann
melting criterion with a description of the solid phase as an elastic
continuum. A number of examples are given in order to illustrate the scope of
the method and possible shortcomings. For a two-body repulsion of Gaussian
shape, the outcome of the present approach compares favourably with the more
accurate but also more computationally demanding self-consistent harmonic
approximation.
