Small-amplitude homogenization of elastic plate equation

ABSTRACT

In this paper we explicitly calculate the first correction in the small-amplitude homogenization limit of a sequence of periodic tensors describing material properties in the Kirchhoff model for pure bending of a thin solid symmetric plate under a transverse load. We also discuss smooth dependence of H-limit on a parameter and calculate H-limit of a periodic sequence of tensors.

Keywords:

• Kirchhoff model of elastic plate
• small-amplitude homogenization
• H-limit of periodic sequence

Mathematics Subject Classification 2010:

• 35J30
• 74K20
• 74Q05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported in part by Croatian Science Foundation (Hrvatska Zaklada za Znanost) under projects 9780 WeConMApp and 8904 Homdirestroptcm.