The reproducing kernel (RK) approximation based direct collocation method (DCM) requires the complex and time-consuming derivatives calculation of the approximation function, and the DCM has the poor accuracy and stability, which hinder the extensive application of this method. Therefore, in this work, we propose a gradient reproducing kernel (GRK) based stabilized collocation method (SCM) which can manage the computational complexity of the RK derivatives calculation and significantly improve the efficiency by directly constructing the GRK approximations, and handle the accuracy and stability problems of the DCM by employing the SCM. Moreover, the computation cost of the SCM is about the same level of the DCM, which is much more efficient than the Galerkin meshfree methods. The proposed method is particularly suitable for solving the thin beam and plate problems which requests the fourth-order differentiation in the strong form. The implementations of this method for the static and dynamical problems are detailedly exhibited. Numerical examples confirm that the presented algorithm provides high efficiency and good performance for the beam and plate simulations.

基于再现核（RK）近似的直接搭配法（DCM）需要对近似函数进行复杂且耗时的导数计算，DCM精度和稳定性较差，阻碍了该方法的广泛应用。因此，在这项工作中，我们提出了一种基于梯度再现核（GRK）的稳定搭配方法（SCM），它可以管理 RK 导数计算的计算复杂度，并通过直接构造 GRK 近似来显着提高效率，并处理精度和通过使用 SCM 解决 DCM 的稳定性问题。此外，SCM 的计算成本与 DCM 大致相同，比 Galerkin 无网格方法效率更高。该方法特别适用于求解要求强形式四阶微分的薄梁和薄板问题。详细展示了该方法在静态和动态问题上的实现。数值例子证实了所提出的算法为梁和板模拟提供了高效率和良好的性能。