Yield Condition and Optimum Pointwise Reinforcement for Fracturing Continua

摘要

The nonlinear program which governs the provision of optimum pointwise reinforcement in a plastic fracturing continuum under a predetermined stress field is formulated and solved. Tensors which represent excess pointwise capacity are developed for the two- and three-dimensional cases, including skew reinforcement, and it is from these that capacity is minimized. Basic tensor invariants are combined with the Kuhn-Tucker optimality conditions to yield the governing equations, which in some cases can be solved directly. The formulation can be employed with positive, negative or mixed stress fields.