In the present paper, a previously introduced numerical method, GDDR (Generalized Differential Dynamic Relaxation), is developed to analyze ratcheting behavior of moderately thick rectangular plates. The validity of the method is verified by comparison with literature data and finite element method results. Classical Plate Theory (CPT) and First-order Shear Deformation Theory (FSDT) are utilized to define the displacement field of plates. Incremental strain equations are derived according to von Karman relations. Prandtl-Reuss flow rule and von Mises yield criterion and are used to express the behavior of the plates in the plastic region. The Armstrong-Frederick nonlinear kinematic hardening model is incorporated for elastic-plastic analyses. Finally the results of ratcheting analysis obtained by GDDR method based on two mentioned theories are compared. Results showed that higher amounts of strains are predicted when FSDT theory is employed. Moreover, the area of hysteresis loops obtained by FSDT analysis are larger than those of CPT analysis, meaning that FSDT approach predicts more energy dissipation during each cycle of loading compared with CPT approach. Finally, comparing the results for different ratios of thickness to width shows that GDDR method can predict more accurate results, especially for higher ratios, when it utilizes FSDT theory.

中文翻译：

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中厚板棘轮分析GDDR方法的发展

在本文中，开发了一种先前介绍的数值方法 GDDR（广义微分动态松弛）来分析中等厚度矩形板的棘轮行为。通过与文献数据和有限元方法结果的比较，验证了该方法的有效性。利用经典板理论（CPT）和一阶剪切变形理论（FSDT）来定义板的位移场。根据冯卡门关系推导出增量应变方程。 Prandtl-Reuss 流动法则和 von Mises 屈服准则用于表达板在塑性区域中的行为。 Armstrong-Frederick 非线性运动硬化模型被纳入弹塑性分析中。最后对基于两种理论的GDDR方法得到的棘轮分析结果进行了比较。结果表明，当采用 FSDT 理论时，可以预测出更高数量的菌株。此外，FSDT 分析获得的磁滞回线面积大于 CPT 分析的面积，这意味着与 CPT 方法相比，FSDT 方法预测每个加载循环期间的能量耗散更多。最后，比较不同厚宽比的结果表明，当利用 FSDT 理论时，GDDR 方法可以预测更准确的结果，尤其是对于更高的厚宽比。