以下为句子列表：
英文: Based on the classical nonlinear plate theory, axisymmetric post-buckling behavior of a functionally graded circular plate under radial compression was investigated.
中文: 摘要基于经典非线性板理论，研究了功能梯度圆板在均匀的径向压力作用下的轴对称过屈曲问题。
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英文: Furthermore, the effects of gradients of material properties and boundary conditions on the critical buckling load and post-buckling behavior of the functionally graded plates were discussed.
中文: 利用数值结果考察了梯度材料性质以及边界条件对板过屈曲行为的影响。
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英文: In accordance with the occurrence behavior of roof strata and the fracture characteristics of key stratum in shallow seam longwall mining, studied post-buckling behavior of roof key stratum in the process of mining by using initial post-buckling theory, w
中文: 摘要根据浅埋煤层顶板岩层的赋存特点和长壁开采时关键层的变形破断特征，应用初始后屈曲理论探讨了开采过程中顶板关键层的后屈曲性态，得出了老顶初次来压时顶板的临界载荷和破断步距，确定了顶板破断后的极限下沉量和回转角，并以神东矿区大柳塔1203工作面为例给出了工程实例。
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英文: Numerical results showed that the post-buckling behavior of a functionally graded plate was different from that of homogenous plate, the gradients of material properties and the boundary conditions played an important role in analyzing post-buckling behav
中文: 结果表明，功能梯度板的过屈曲行为与各向同性均匀板有很大区别，材料的梯度性质和边界条件都对其有重要影响。
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