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首页> 外文期刊>SIAM Journal on Mathematical Analysis >Boundary homogenization and reduction of dimension in a Kirchhoff-Love plate
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Boundary homogenization and reduction of dimension in a Kirchhoff-Love plate

机译：Kirchhoff-Love板的边界均匀化和尺寸减小

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摘要

We investigate the asymptotic behavior, as e tends to 0(+), of the transverse displacement of a Kirchhoff-Love plate composed of two domains Omega(+)(epsilon) boolean OR Omega(-)(epsilon) subset of R-2 depending on e in the following way. The set Omega(+)(epsilon) is a union of fine teeth, having small cross section of size epsilon and constant height, epsilon-periodically distributed on the upper side of a horizontal thin strip with vanishing height he, as e tends to 0(+). The structure is clamped on the top of the teeth, with a free boundary elsewhere, and subjected to a transverse load. As e tends to 0(+), we obtain a "continuum" bending model of rods in the limit domain of the comb, while the limit displacement is independent of the vertical variable in the rescaled (with respect to h(epsilon)) strip. We show that the displacement in the strip is equal to the displacement on the base of the teeth if h(epsilon) epsilon(4). However, if the strip is thin enough (i.e., h(epsilon) similar or equal to epsilon(4)), we show that microscopic oscillations of the displacement in the strip, between the basis of the teeth, may produce a limit average field different from that on the base of the teeth; i.e., a discontinuity in the transmission condition may appear in the limit model.
机译：我们调查e趋于0（+）的Kirchhoff-Love板的横向位移的渐近行为，该板由R-2的两个域Omega（+）（epsilon）布尔值或Omega（-）（epsilon）子集组成通过以下方式取决于e。集合Omega（+）（epsilon）是细齿的结合，具有小截面的epsilon和恒定的高度，ε周期性地分布在水平细条的上侧，高度e逐渐消失，e趋于0 （+）。该结构被夹紧在牙齿的顶部，在其他位置具有自由边界，并承受横向载荷。当e趋于0（+）时，我们在梳子的极限域中获得杆的“连续”弯曲模型，而极限位移与重新缩放后的（相对于h（ε））带中的垂直变量无关。我们证明，如果h（epsilon） epsilon（4），则带材中的位移等于齿根的位移。但是，如果条带足够薄（即h（epsilon）近似或等于epsilon（4）），则表明在齿根之间，条带中的位移的微观振荡可能会产生极限平均场与牙齿的牙齿不同;即，传输条件的不连续性可能会出现在极限模型中。

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