T-Splines for Isogeometric Analysis of the Large Deformation of Elastoplastic Kirchhoff–Love Shells
Abstract
:1. Introduction
2. T-Splines
2.1. T-Mesh and the T-Spline Basis
2.2. BéZier Extraction
3. Formulations for the Large Deformation of Elastoplastic Kirchhoff–Love Shells
3.1. Finite Strain Plasticity
Algorithm 1 Return mapping algorithm. |
State: is computed in the time step , and are saved from the last time step |
Input:, , |
Output:, , |
|
Algorithm 2 Consistent elastoplastic tangent moduli. |
Input: Same as Algorithm 1 |
Output: |
|
3.2. Geometry Definition
3.3. Kinematics
Algorithm 3 Iterative update for . |
Input:, |
Output: |
|
3.4. Variational Formulation
3.5. Arc-Length Method
Algorithm 4 The algorithm of arc-length method. |
Input: The variables from the latest convergence point: |
Output: The next convergence point, updated increments: |
|
4. Adaptive Refinement
5. Numerical Tests
5.1. Pinched Elastoplastic Hemisphere
5.2. Pinched Elastoplastic Cylinder
5.3. Plastic Collapse of the Scordelis–Lo Roof
5.4. Plastic Cylinder with Holes Under Compression
5.5. Torsion of a Plastic Rectangular Sheet with a Hole
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
References
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Guo, M.; Wang, W.; Zhao, G.; Du, X.; Zhang, R.; Yang, J. T-Splines for Isogeometric Analysis of the Large Deformation of Elastoplastic Kirchhoff–Love Shells. Appl. Sci. 2023, 13, 1709. https://doi.org/10.3390/app13031709
Guo M, Wang W, Zhao G, Du X, Zhang R, Yang J. T-Splines for Isogeometric Analysis of the Large Deformation of Elastoplastic Kirchhoff–Love Shells. Applied Sciences. 2023; 13(3):1709. https://doi.org/10.3390/app13031709
Chicago/Turabian StyleGuo, Mayi, Wei Wang, Gang Zhao, Xiaoxiao Du, Ran Zhang, and Jiaming Yang. 2023. "T-Splines for Isogeometric Analysis of the Large Deformation of Elastoplastic Kirchhoff–Love Shells" Applied Sciences 13, no. 3: 1709. https://doi.org/10.3390/app13031709
APA StyleGuo, M., Wang, W., Zhao, G., Du, X., Zhang, R., & Yang, J. (2023). T-Splines for Isogeometric Analysis of the Large Deformation of Elastoplastic Kirchhoff–Love Shells. Applied Sciences, 13(3), 1709. https://doi.org/10.3390/app13031709