A new model for thin plates with rapidly varying thickness.

*(English)*Zbl 0532.73055Summary: 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 midplane 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.

##### MSC:

74K20 | Plates |