Journal of Changjiang River Scientific Research Institute ›› 2025, Vol. 42 ›› Issue (4): 211-218.DOI: 10.11988/ckyyb.202401142
• Numerical Manifold Method Based on Independent Covers • Previous Articles
SU Hai-dong1,2(), SONG Wen-shuo1, GONG Ya-qi1,2, HAN Lu-chao1, WEI Yu-xia1
Received:
2024-02-02
Revised:
2024-05-07
Published:
2025-04-01
Online:
2025-04-01
CLC Number:
SU Hai-dong, SONG Wen-shuo, GONG Ya-qi, HAN Lu-chao, WEI Yu-xia. General Formulas and Program Design for Manifold Method Based on Independent Covers Ⅲ: Example Verification[J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(4): 211-218.
Fig.1 Comparison between numerical solutions and theoretical solutions of one-dimensional steady state analysis examples (10 covers and 10-order polynomials)[1]
Fig.2 Comparison between numerical solutions and theoretical solutions of one-dimensional steady state analysis examples (60 covers and 3-order polynomials)[1]
t/s | u值 | |
---|---|---|
数值解 | 理论解 | |
0.1 | 0.151 059×100 | 0.151 059×100 |
0.2 | 0.562 983×10-1 | 0.562 986×10-1 |
0.3 | 0.209 827×10-1 | 0.209 829×10-1 |
0.4 | 0.782 035×10-2 | 0.782 049×10-2 |
0.5 | 0.291 469×10-2 | 0.291 475×10-2 |
0.6 | 0.108 632×10-2 | 0.108 635×10-2 |
0.7 | 0.404 883×10-3 | 0.404 892×10-3 |
0.8 | 0.150 906×10-3 | 0.150 906×10-3 |
0.9 | 0.562 467×10-4 | 0.562 440×10-4 |
1.0 | 0.209 655×10-4 | 0.209 625×10-4 |
Table 1 Comparison of u values at different instances when x=0.5
t/s | u值 | |
---|---|---|
数值解 | 理论解 | |
0.1 | 0.151 059×100 | 0.151 059×100 |
0.2 | 0.562 983×10-1 | 0.562 986×10-1 |
0.3 | 0.209 827×10-1 | 0.209 829×10-1 |
0.4 | 0.782 035×10-2 | 0.782 049×10-2 |
0.5 | 0.291 469×10-2 | 0.291 475×10-2 |
0.6 | 0.108 632×10-2 | 0.108 635×10-2 |
0.7 | 0.404 883×10-3 | 0.404 892×10-3 |
0.8 | 0.150 906×10-3 | 0.150 906×10-3 |
0.9 | 0.562 467×10-4 | 0.562 440×10-4 |
1.0 | 0.209 655×10-4 | 0.209 625×10-4 |
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[2] | SU Hai-dong, YANG Zhen, XIE Zhi-qiang, QI Yong-feng, GONG Ya-qi. General Formulas and Program Design for Manifold Method Based on Independent Covers Ⅱ: General Program Design [J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(4): 202-210. |
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[4] | WANG Fang-yi, ZHENG Hong. Numerical Manifold Method for Unbounded Domain Problems [J]. Journal of Changjiang River Scientific Research Institute, 2023, 40(7): 110-117. |
[5] | SU Hai-dong, HAN Lu-chao, XIE Zhi-qiang. Analysis of Thin Curved Beam and Curved Shell with Exact Geometry Using Piecewise-defined Series Solutions [J]. Journal of Changjiang River Scientific Research Institute, 2022, 39(9): 144-151. |
[6] | SU Hai-dong, WEI Yu-xia, HAN Lu-chao, XIE Zhi-qiang. Rigid Connection Between Plate Shell Elements and Solid Elements in the Manifold Method Based on Independent Covers [J]. Journal of Changjiang River Scientific Research Institute, 2022, 39(9): 152-158. |
[7] | SU Hai-dong, DONG Peng, XIE Zhi-qiang. Solving Geometric Nonlinear Problems in Fixed Meshes of Independent Covers [J]. Journal of Changjiang River Scientific Research Institute, 2022, 39(9): 159-166. |
[8] | YANG Shi-kou, AI Hua-dong. Essential Boundary Treatment of Three-dimensional Numerical Manifold Method [J]. Journal of Changjiang River Scientific Research Institute, 2022, 39(3): 137-142. |
[9] | SU Hai-dong, FU Zhi, XIE Zhi-qiang. Automatic Two-dimensional Computation Based on Arbitrary Mesh Division [J]. Journal of Changjiang River Scientific Research Institute, 2020, 37(7): 160-166. |
[10] | SU Hai-dong, FU Zhi, XIE Zhi-qiang. Numerical Computations Based on Cover Meshes with Arbitrary Shapes and on Exact Geometric Boundaries [J]. Journal of Changjiang River Scientific Research Institute, 2020, 37(7): 167-174. |
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[12] | ZHANG You-liang, MO Si-yang. Parallel Algorithm of Cover System Generation in Numerical Manifold Method [J]. Journal of Changjiang River Scientific Research Institute, 2020, 37(10): 1-8. |
[13] | SU Hai-dong. Application Prospect of Manifold Method Based on Independent Covers in Hydraulic Structure Analysis [J]. Journal of Changjiang River Scientific Research Institute, 2019, 36(6): 1-8. |
[14] | GAO Dai-heng, GUO Hong-wei, ZHENG Hong. A Rigorous Mass Lumping Scheme for Vibration of Beams [J]. Journal of Changjiang River Scientific Research Institute, 2019, 36(4): 118-122,139. |
[15] | SU Hai-dong, ZHOU Chao, XIE Zhi-qiang, CHEN Qin. Analysis of Curved Shells with Exact Geometric Description Using Numerical Manifold Method Based on Independent Covers [J]. Journal of Changjiang River Scientific Research Institute, 2018, 35(4): 158-166. |
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