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B- and strong stationarity for optimal control of static plasticity with hardening. (English) Zbl 1266.49013

Summary: Optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered. The control-to-state map is shown to be weakly directionally differentiable, and local optimal controls are proved to verify an optimality system of B-stationary type. For a modified problem, local minimizers are shown to even satisfy an optimality system of strongly stationary type.

MSC:

49J40 Variational inequalities
70Q05 Control of mechanical systems
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
35R45 Partial differential inequalities and systems of partial differential inequalities
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