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**Basis reduction for the shakedown problem for bounded kinematic hardening material.**
*(English)*
Zbl 1011.74009

Summary: Limit and shakedown analysis are effective methods for assessing the load carrying capacity of a given structure. The elasto-plastic behavior of the structure subjected to loads varying in a given load domain is characterized by the shakedown load factor, defined as the maximum factor which satisfies the sufficient condition stated in the corresponding static shakedown theorem. The finite element discretization of the problem may lead to very large convex optimization. For the effective solution a basis reduction method has been developed that makes use of the special problem structure for perfectly plastic material. The paper proposes a modified basis reduction method for direct application to the two-surface plasticity model of bounded kinematic hardening material. The considered numerical examples show an enlargement of the load carrying capacity due to bounded hardening.

### MSC:

74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |

74P10 | Optimization of other properties in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |