A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme
Abstract
:1. Introduction
2. Finite Element Formulation Enriched by Cover Functions
3. Improving 3D Solid FE Solutions
3.1. Error Indicator and Cover Function Selection Scheme
3.2. Cover Function Selection Scheme
4. Numerical Examples
- HEX8: standard 8-node hexahedral element
- PRI6: standard 6-node prismatic element
- PYR5: standard 5-node pyramidal element
- TET4: standard 4-node tetrahedral element
4.1. Ad Hoc Problem
4.2. Gear Problem
4.3. Tool Jig Problem
4.4. Connecting Rod Problem
4.5. Proximal Femur Problem
5. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Element | NE | Energy | von Mises Stress | ||
---|---|---|---|---|---|
Standard Solution | Adaptive Solution | Standard Solution | Adaptive Solution | ||
HEX8 | 6 | 9.66% | 4.56% | 60.48% | 19.39% |
8 | 13.68% | 1.46% | 16.21% | 12.10% | |
10 | 11.48% | 0.75% | 8.03% | 5.57% | |
12 | 8.72% | 0.53% | 5.05% | 4.03% | |
TET4 | 6 | 58.36% | 6.51% | 46.86% | 13.98% |
8 | 42.94% | 1.96% | 39.86% | 9.72% | |
10 | 31.72% | 0.65% | 32.98% | 4.26% | |
12 | 23.98% | 0.25% | 26.96% | 1.86% | |
Reference solution |
Mesh | Strain Energy | von Mises Stress | ||
---|---|---|---|---|
Standard Solution | Adaptive Solution | Standard Solution | Adaptive Solution | |
Coarse mesh | 19.06% | 9.84% | 25.40% | 9.65% |
Fine mesh | 7.44% | 4.27% | 12.72% | 6.18% |
Reference solution |
Mesh | DOFs | Number of Nodes | ||||
---|---|---|---|---|---|---|
Standard Solution | Adaptive Solution | None | Linear Cover | Quadratic Cover | ||
Coarse mesh | 7308 | 17,469 | 0.22 | 2021 | 293 | 293 |
Fine mesh | 24,579 | 47,637 | 0.15 | 7396 | 646 | 646 |
Mesh | von Mises Stress | |
---|---|---|
Standard Solution | Adaptive Solution | |
Coarse mesh | 39.46% | 14.73% |
Fine mesh | 28.83% | 5.60% |
Reference solution |
Mesh | DOFs | Number of Nodes | ||||
---|---|---|---|---|---|---|
Standard Solution | Adaptive Solution | None | Linear Cover | Quadratic Cover | ||
Coarse mesh | 1944 | 5040 | 0.25 | 506 | 86 | 86 |
Fine mesh | 10,575 | 21,762 | 0.17 | 2999 | 310 | 311 |
Mesh | von Mises Stress | |
---|---|---|
Standard Solution | Adaptive Solution | |
Coarse mesh | 39.11% | 19.32% |
Fine mesh | 23.73% | 8.35% |
Reference solution |
Mesh | DOFs | Number of Nodes | ||||
---|---|---|---|---|---|---|
Standard Solution | Adaptive Solution | None | Linear Cover | Quadratic Cover | ||
Coarse mesh | 3435 | 7179 | 0.19 | 898 | 104 | 104 |
Fine mesh | 13,854 | 23,268 | 0.11 | 4178 | 262 | 262 |
DOFs | Number of Nodes | von Mises Stress | |||||
---|---|---|---|---|---|---|---|
Standard Solution | Adaptive Solution | None | Linear Cover | Quadratic Cover | Standard Solution | Adaptive Solution | |
9627 | 24,189 | 0.25 | 2429 | 415 | 415 | 33.3% | 8.9% |
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Choi, H.-G.; Byun, Y.I.; Song, C.K.; Jun, M.B.G.; Lee, C.; Kim, S. A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme. Appl. Sci. 2023, 13, 7114. https://doi.org/10.3390/app13127114
Choi H-G, Byun YI, Song CK, Jun MBG, Lee C, Kim S. A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme. Applied Sciences. 2023; 13(12):7114. https://doi.org/10.3390/app13127114
Chicago/Turabian StyleChoi, Hyung-Gyu, Young Il Byun, Chul Ki Song, Martin B.G. Jun, Chaemin Lee, and San Kim. 2023. "A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme" Applied Sciences 13, no. 12: 7114. https://doi.org/10.3390/app13127114
APA StyleChoi, H.-G., Byun, Y. I., Song, C. K., Jun, M. B. G., Lee, C., & Kim, S. (2023). A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme. Applied Sciences, 13(12), 7114. https://doi.org/10.3390/app13127114