A NEW MODEL FOR THIN PLATES WITH RAPIDLY VARYING THICKNESS
A NEW MODEL FOR THIN PLATES WITH RAPIDLY VARYING THICKNESS
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DOI：
10.1016/0020-7683(84)90044-1
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发表时间：
1984-01-01
影响因子：
3.6
通讯作者：
VOGELIUS, M
中科院分区：
文献类型：
--
作者：
KOHN, RV;VOGELIUS, M
本文研究了具有快速变化厚度的薄板的弯曲问题，例如带有肋状加强筋或开有小孔的薄板。我们得到一个四阶方程的中平面位移，使用基于三维线弹性的渐近分析。该方程的系数表示将弯矩与中平面曲率相关联的本构律;它们由板的几何形状明确确定。我们的分析区分了三种不同的情况，其中厚度在长度尺度上比平均厚度长、大约或短。
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.