Garbowski Tomasz, Gajewski Tomasz, Grabski Jakub Krzysztof
Institute of Structural Analysis, Poznan University of Technology, Piotrowo Street 5, 60-965 Poznań, Poland.
Institute of Applied Mechanics, Poznan University of Technology, Jana Pawła II Street 24, 60-965 Poznań, Poland.
Materials (Basel). 2020 Nov 6;13(21):5016. doi: 10.3390/ma13215016.
In the present work, an analytical equation describing the plate torsion test taking into account the transverse shear stiffness in sandwich plates is derived and numerically validated. Transverse shear becomes an important component if the analyzed plate or shell is thick with respect to the in-plane dimensions and/or its core has significantly lower stiffness than the outer faces. The popular example of such a sandwich plate is a corrugated cardboard, widely used in the packaging industry. The flat layers of a corrugated board are usually made of thicker (stronger) material than that used for the corrugated layer, the role of which is rather to keep the outer layers at a certain distance, to ensure high bending stiffness of the plate. However, the soft core of such a plate usually has a low transverse shear stiffness, which is often not considered in the plate analysis. Such simplification may lead to significant calculation errors. The paper presents the generalization of the Reissner's analytical formula, which describes the torsional stiffness of the plate sample including two transverse shear stiffnesses. The paper also presents the implementation of the numerical model of the plate torsion test including the transverse shear stiffnesses. Both approaches are compared with each other on a wide range of material parameters and different aspect ratios of the specimen. It has been proved that both analytical and numerical formulations lead to an identical result. Finally, the performance of presented formulations is compared with other numerical models using commercial implementation of various Reissner-Mindlin shell elements and other analytical formulas from the literature. The comparison shows good agreement of presented theory and numerical implementation with other existing approaches.
在本研究中，推导了一个考虑夹层板横向剪切刚度的平板扭转试验分析方程，并进行了数值验证。如果所分析的板或壳相对于平面尺寸较厚，和/或其芯层的刚度明显低于外层，则横向剪切成为一个重要因素。这种夹层板的一个常见例子是瓦楞纸板，广泛应用于包装行业。瓦楞纸板的平层通常由比瓦楞层更厚（更强）的材料制成，瓦楞层的作用主要是使外层保持一定距离，以确保板具有较高的弯曲刚度。然而，这种板的软芯层通常横向剪切刚度较低，在板的分析中常常未被考虑。这种简化可能导致显著的计算误差。本文给出了瑞利纳分析公式的推广，该公式描述了包含两个横向剪切刚度的板试样的扭转刚度。本文还给出了包含横向剪切刚度的平板扭转试验数值模型的实现。在广泛的材料参数和不同的试样长宽比下，对这两种方法进行了相互比较。结果表明，解析公式和数值公式都得到了相同的结果。最后，将所提出公式的性能与使用各种瑞利-明德林壳单元的商业实现以及文献中的其他解析公式的其他数值模型进行了比较。比较结果表明，本文提出的理论和数值实现与其他现有方法具有良好的一致性。
