Abstract For most of the studies concerning about the transverse deflection of plates subjected to the loading of a rigid punch, the sections of the punch and the plate are usually circular and concentric. However, eccentric loading conditions in which the punch and the plate may not be circular and concentric have seldom been discussed. This paper firstly studied the solution behavior for a rigid-plastic clamped plate under quasi-static eccentric loading conditions based on the theory of rotation-rate continuity and the method of fundamental solutions (MFS). For eccentric loading, four types of loading conditions have been applied: circular punch vs circular plate (C C), circular punch vs elliptical plate (C-E), elliptical punch vs circular plate (E-C) and elliptical punch vs elliptical plate (E-E). The load position of the punch is also arbitrary with respect to the plate. Contour lines of transverse deflection, principal stress and strain and punching force-punch displacement curves have been obtained for different loading conditions. It has been proved that the circuit integral of the product of transverse deflection gradient and contour line's outer normal is constant for any contour line, leading to a linear relationship between the punching force and deflection of the punch. It turns out that the ratio of punch section area to plate section area and the deviation distance of the punch center from the plate center will both influence the value of the circuit integral term, which is correlated with the punching force, as they increase the punching force will also increase if the punch displacement is fixed, and vice versa. Finally, accounting for the merits of MFS in solving the Laplace equation, the solution procedure can be extended to multiple punches loading conditions. Results have revealed that rotation-rate continuity still prevails in rigid-plastic solids in this case. Finite element analysis has been conducted to show that its results agree with the analytical results at a satisfactory level.

中文翻译：

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刚性塑料夹板横向偏转的广义求解行为研究：偏心和多冲加载

摘要 在大多数关于刚性冲头加载下板的横向挠度的研究中，冲头和板的截面通常是圆形和同心的。然而，很少讨论冲头和板可能不是圆形和同心的偏心载荷条件。本文首先基于转速连续性理论和基本解法(MFS)研究了刚塑夹板在准静态偏心载荷条件下的求解行为。对于偏心加载，应用了四种类型的加载条件：圆形冲头对圆形板 (CC)、圆形冲头对椭圆板 (CE)、椭圆冲头对圆形板 (EC) 和椭圆冲头对椭圆板 (EE)。冲头的负载位置相对于板也是任意的。得到了不同加载条件下的横向挠度、主应力应变等高线以及冲切力-冲切位移曲线。已经证明，横向偏转梯度与轮廓线外法线的乘积的电路积分对于任何轮廓线都是恒定的，从而导致冲压力与冲头偏转之间的线性关系。结果表明，冲头截面积与板截面积的比值和冲头中心与板中心的偏差距离都会影响与冲压力相关的电路积分项的值，因为它们增加了冲压量。如果冲头位移固定，力也会增加，反之亦然。最后，考虑到 MFS 在求解拉普拉斯方程方面的优点，求解过程可以扩展到多冲加载条件。结果表明，在这种情况下，旋转速率连续性在刚塑性固体中仍然占优势。已经进行了有限元分析，表明其结果与分析结果在令人满意的水平上吻合。