A Mindlin shell model based on the corrective smoothed particle method and accuracy implementation of the free boundary

Abstract

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.