A new model for thin plates with rapidly varying thickness. III. Comparison of different scalings. (English) Zbl 0605.73048

Kohn, Robert V.; Vogelius, Michael

Q. Appl. Math. 44, 35-48 (1986).

This paper continues a series of papers on bending of plates with varying thickness [see parts II and I, ibid. 43, 1-22 (1985; Zbl 0565.73046) and Int. J. Solids Struct. 20, 333-350 (1984; Zbl 0532.73055)]. There are three different regimes: slow variation, variation on the same scale as the mean thickness and fast variation. After a brief review of the three models the case is investigated when the thickness is a function of a single variable. For a general thickness function the results are less complete. The conclusions have implications for structural optimization.

Reviewer: W.Schnell

MSC:

74K20	Plates
74P99	Optimization problems in solid mechanics

Keywords:

symmetric plates; set of dual variational principles; bending; varying thickness; slow variation; same scale as the mean thickness; fast variation

Citations:

Zbl 0565.73046; Zbl 0532.73055