Esaim: Mathematical Modelling and Numerical Analysis on the Accuracy of Reissner–mindlin Plate Model for Stress Boundary Conditions *
Esaim: Mathematical Modelling and Numerical Analysis on the Accuracy of Reissner–mindlin Plate Model for Stress Boundary Conditions *
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通讯作者：
S. Zhang
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作者：
S. Zhang
对于具有应力边界条件的板，根据荷载的不同，Reissner-Mindlin板弯曲模型确定的变形可以是弯曲为主、横向剪切为主或两者都不是（中间）。我们发现Reissner-Mindlin模型比Kirchhoff-Love模型具有更广泛的适用性，但它并不总是收敛于弹性理论。在弯曲控制的情况下，这两个模型都是准确的。在横向剪切支配的情况下，Reissner-Mindlin模型是准确的，而Kirchhoff-Love模型则完全失败。在中间情况下，在Kirchhoff-Love模型失效的同时，Reissner-Mindlin解与弹性解相比也存在相对误差，当板厚趋于零时，Reissner-Mindlin解不减小。我们还表明，在合成荷载函数的常规定义下，Reissner-Mindlin模型中众所周知的剪切修正系数5/6应被1取代。否则，Reissner-Mindlin模型的适用范围并不比Kirchhoff - Love模型更广。
For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the Reissner–Mindlin model is accurate but the Kirchhoff–Love model totally fails. In the intermediate case, while the Kirchhoff–Love model fails, the Reissner–Mindlin solution also has a relative error comparing to the elasticity solution, which does not decrease when the plate thickness tends to zero. We also show that under the conventional definition of the resultant loading functional, the well known shear correction factor 5/6 in the Reissner–Mindlin model should be replaced by 1. Otherwise, the range of applicability of the Reissner–Mindlin model is not wider than that of Kirchhoff– Love's.