Existence and regularity of solutions for an evolution model of perfectly plastic plates. (English) Zbl 1412.74013
Summary: We continue the study of a dynamic evolution model for perfectly plastic plates, recently derived in [the second author and M. G. Mora, Math. Models Methods Appl. Sci. 26, No. 10, 1825–1864 (2016; Zbl 1346.74015)] from three-dimensional Prandtl-Reuss plasticity. We extend the previous existence result by introducing non-zero external forces in the model, and we discuss the regularity of the solutions thus obtained. In particular, we show that the first derivatives with respect to space of the stress tensor are locally square integrable.
MSC:
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
| 74K20 | Plates |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
Keywords:
dynamic evolution; perfect plasticity; Prandtl-Reuss plasticity; thin plates; functions of bounded deformation; functions of bounded HessianCitations:
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