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

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 plan...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2021-11, Vol.385, p.114028, Article 114028
Main Authors: Huang, Y.H., Niu, M.C., Duan, N.Y., Hua, H.X.
Format: Article
Language:English
Subjects:
Boundary conditions
CSPM
Finite element method
Free boundaries
Free boundary
Geometric nonlinearity
Interpolation
Kernel functions
Mathematical analysis
Mathematical models
Meshless method
Meshless methods
Mindlin plates
Mindlin shell
Series expansion
Shell theory
Smooth particle hydrodynamics
Taylor series
Tensors
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Summary: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.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.114028