TY - JOUR
T1 - A new model for thin plates with rapidly varying thickness
AU - Kohn, Robert V.
AU - Vogelius, Michael
N1 - Funding Information:
tThe numerical work reported in Section 7 was supported by the Computer Science Center of the University of Maryland, U.S.A. tSupported in part by NSF research grant MCS-8201308. §Supported in part by NSF research grant MCS 78-02920. Current address: Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, U.S.A.
PY - 1984
Y1 - 1984
N2 - We study the bending of a thin plate with rapidly varying thickness, for example one with rib-like stiffeners or perforated by small holes. We obtain a fourth-order equation for the midplanc displacement, using an asymptotic analysis based on three-dimensional linear elasticity. The coefficients of this equation represent the constitutive law relating bending moments to midplane curvature; they are explicitly determined by the plate geometry. Our analysis distinguishes between three different cases, in which the thickness varies on a length scale longer than, on the order of, or shorter than the mean thickness.
AB - We study the bending of a thin plate with rapidly varying thickness, for example one with rib-like stiffeners or perforated by small holes. We obtain a fourth-order equation for the midplanc displacement, using an asymptotic analysis based on three-dimensional linear elasticity. The coefficients of this equation represent the constitutive law relating bending moments to midplane curvature; they are explicitly determined by the plate geometry. Our analysis distinguishes between three different cases, in which the thickness varies on a length scale longer than, on the order of, or shorter than the mean thickness.
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U2 - 10.1016/0020-7683(84)90044-1
DO - 10.1016/0020-7683(84)90044-1
M3 - Article
AN - SCOPUS:0021156618
VL - 20
SP - 333
EP - 350
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
SN - 0020-7683
IS - 4
ER -