New planar velocity fields for upper bound limit analysi

A generalised framework has recently been proposed for derivation of kinematically admissible velocity fields in 3- dimensional upper bound limit analysis in Tresca s material using coordinate transformations. In many cases the approach allows the local dissipation of plastic work to be derived in closed form. The original framework was restricted to orthogonal coordinate systems. However, the present paper extends the approach to allow for variations in plane or radial velocity fields in a direction normal to the field. This important extension allows applications to horizontal loading of circular foundations, or vertical loading of non-circular (e.g. square) foundations