TY - JOUR

T1 - NEW MODEL FOR THIN PLATES WITH RAPIDLY VARYING THICKNESS. II

T2 - A CONVERGENCE PROOF.

AU - Kohn, Robert V.

AU - Vogelius, Michael

PY - 1985

Y1 - 1985

N2 - In a recent paper the authors presented a model for thin plates with rapidly varying thickness, distinguishing between thickness variation on a length scale longer than, on the order of, or shorter than the mean thickness. They review the model here, and identify the case of long scale thickness variation as an asymptotic limit of the intermediate case, where the scales are comparable. They then present a convergence theorem for the intermediate case, showing that the model correctly represents the solution of the equations of linear elasticity on the three-dimensional plate domain, asymptotically as the mean thickness tends to zero.

AB - In a recent paper the authors presented a model for thin plates with rapidly varying thickness, distinguishing between thickness variation on a length scale longer than, on the order of, or shorter than the mean thickness. They review the model here, and identify the case of long scale thickness variation as an asymptotic limit of the intermediate case, where the scales are comparable. They then present a convergence theorem for the intermediate case, showing that the model correctly represents the solution of the equations of linear elasticity on the three-dimensional plate domain, asymptotically as the mean thickness tends to zero.

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U2 - 10.1090/qam/782253

DO - 10.1090/qam/782253

M3 - Article

AN - SCOPUS:0022052695

SN - 0033-569X

VL - 43

SP - 1

EP - 22

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

IS - 1

ER -