A meshless shell method for large deformation and a linear relation between the Cauchy stress tensor and the Almansi strain tensor based on the corrective smoothed particle method (CSPM) is presented in this paper. Due to the use of the shell theory, only one layer of particles in the reference plane is required to discretize the shell model. The CSPM combining the kernel estimate with the Taylor series expansion is adopted, which resolves the general problems of low precision and particle deficiency in standard smoothed particle hydrodynamics (SPH). The discrete governing equations of the shell in the strong form are derived using the conservation condition and the CSPM interpolation function. Aiming at the sore point of the free boundary in the meshless method, the developed model enables the modified governing equations to automatically satisfy the free boundary condition without additional treatment. Moreover, the total Lagrangian kernel function and stress points are employed to eliminate tensile instability and instability induced by the rank deficiency. Finally, several numerical examples are used to verify the validity and accuracy of the meshless shell model.

本文提出了一种基于修正平滑粒子法(CSPM)的大变形无网格壳法以及柯西应力张量和阿尔曼西应变张量之间的线性关系。由于使用壳理论，离散化壳模型只需要参考平面中的一层粒子。采用核估计与泰勒级数展开相结合的CSPM ，解决了标准平滑粒子流体力学(SPH)中精度低和粒子缺乏的普遍问题。利用守恒条件和CSPM插值函数推导出强形式壳的离散控制方程。针对自由边界的痛点无网格方法，开发的模型使修改后的控制方程自动满足自由边界条件，无需额外处理。此外，采用总拉格朗日核函数和应力点来消除由秩不足引起的拉伸不稳定性和不稳定性。最后，通过几个数值算例验证了无网格壳模型的有效性和准确性。