The cell-based smoothed radial point interpolation method in conjunction with a second order cone programming is proposed for kinematic limit analysis of rigid-perfectly plastic thin plates in this paper. The transverse displacement field is interpolated by the radial point interpolation method (RPIM) and no rotational degrees of freedom are involved. The gradient smoothing technique is utilized to construct smoothed curvature field in every smoothing domain and there is no need to compute the second derivatives of shape functions. The rotational boundary conditions are satisfied in the process of curvature smoothing and the translational boundary conditions can be directly enforced without any special treatment. The limit analysis problem of thin plates is formulated by minimizing the dissipation power subject to a set of equality constraints and this minimization problem can be expressed easily as a standard second order cone programming. It is testified from the computational results that the proposed procedure can provide reasonable and satisfactory upper bound limit load multipliers for thin plates.

本文提出了基于单元的平滑径向点插值方法结合二阶锥规划用于刚完美塑性薄板的运动学极限分析。横向位移场采用径向点插值法（RPIM）插值，不涉及旋转自由度。利用梯度平滑技术在每个平滑域中构建平滑曲率场，无需计算形状函数的二阶导数。在曲率平滑过程中满足旋转边界条件，平移边界条件可以直接强制执行，无需特殊处理。薄板的极限分析问题是通过在一组等式约束下最小化耗散功率来制定的，这个最小化问题可以很容易地表示为标准的二阶锥规划。计算结果证明，所提出的程序可以为薄板提供合理和满意的上限极限载荷乘数。