Date: 15 May 2012

Upper Bound Theorem

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Abstract

Plastic limit analysis is a convenient tool to find approximate solutions of boundary value problems. In general, this analysis is based on two principles associated with the lower bound and upper bound theorems. The latter is used in the present monograph to estimate the limit load for welded structures with and with no crack. A proof of the upper bound theorem for a wide class of material models has been given by Hill (1956). The only reliable output of upper bound solutions is the load required to initiate the process of plastic deformation. Any upper bound limit load is higher than or equal to the actual load. This statement becomes more complicated in the case of multiple load parameters. Upper bound solutions are not unique and their accuracy significantly depends on the kinematically admissible velocity field chosen.