# The mathematical algorithm of multi-point constraints in the simulations of three-dimensional Numerical Manifold Method

Y. Q. Wu, Guangqi Chen, Z. S. Jiang, X. X. Liu, W. X. Wei, W. Y. Liu, W. S. Chen

Research output: Contribution to conferencePaper

1 Citation (Scopus)

### Abstract

In this paper, we introduce the parameter adjustment method with condition equations(one surveying adjustment method in geodetic data processing) to three-dimensional Manifold Method through formula derivation, and present the strict-constraint solution and least-squares solution strategies. In least-square solution, we develop the power conception of surveying adjustment and use power ratio to balance the physical and mathematical equations. Then, we use the uniaxial tensile model to verify the validity of above two solution strategies, and analyze their difference. Furthermore, the shearing failure simulation with mathematical constraint is presented. In conclusion, the essential difference of above two strategies is that the strict-constraint strategy can realize strong constraint on some unknowns and have minimum influence on others in the examples of this paper. On the other hand, the least-square strategy influences more than constrained unknowns, and perhaps affects the whole equations. Furthermore, we can control the constraint intensity by adjusting power ratio when using least-square strategy, because the constraint intensity is directly proportional to the power ratio.

Original language English 335-340 6 Published - Oct 1 2013 11th International Conference on Analysis of Discontinuous Deformation, ICADD 2013 - Fukuoka, JapanDuration: Aug 27 2013 → Aug 29 2013

### Other

Other 11th International Conference on Analysis of Discontinuous Deformation, ICADD 2013 Japan Fukuoka 8/27/13 → 8/29/13

### Fingerprint

Numerical Manifold Method
Three-dimensional
Surveying
Simulation
Least-squares Solution
Least Squares
Shearing
Unknown
Strategy
Directly proportional
Verify

### All Science Journal Classification (ASJC) codes

• Modelling and Simulation

### Cite this

Wu, Y. Q., Chen, G., Jiang, Z. S., Liu, X. X., Wei, W. X., Liu, W. Y., & Chen, W. S. (2013). The mathematical algorithm of multi-point constraints in the simulations of three-dimensional Numerical Manifold Method. 335-340. Paper presented at 11th International Conference on Analysis of Discontinuous Deformation, ICADD 2013, Fukuoka, Japan.

The mathematical algorithm of multi-point constraints in the simulations of three-dimensional Numerical Manifold Method. / Wu, Y. Q.; Chen, Guangqi; Jiang, Z. S.; Liu, X. X.; Wei, W. X.; Liu, W. Y.; Chen, W. S.

2013. 335-340 Paper presented at 11th International Conference on Analysis of Discontinuous Deformation, ICADD 2013, Fukuoka, Japan.

Research output: Contribution to conferencePaper

Wu, YQ, Chen, G, Jiang, ZS, Liu, XX, Wei, WX, Liu, WY & Chen, WS 2013, 'The mathematical algorithm of multi-point constraints in the simulations of three-dimensional Numerical Manifold Method', Paper presented at 11th International Conference on Analysis of Discontinuous Deformation, ICADD 2013, Fukuoka, Japan, 8/27/13 - 8/29/13 pp. 335-340.
Wu YQ, Chen G, Jiang ZS, Liu XX, Wei WX, Liu WY et al. The mathematical algorithm of multi-point constraints in the simulations of three-dimensional Numerical Manifold Method. 2013. Paper presented at 11th International Conference on Analysis of Discontinuous Deformation, ICADD 2013, Fukuoka, Japan.
Wu, Y. Q. ; Chen, Guangqi ; Jiang, Z. S. ; Liu, X. X. ; Wei, W. X. ; Liu, W. Y. ; Chen, W. S. / The mathematical algorithm of multi-point constraints in the simulations of three-dimensional Numerical Manifold Method. Paper presented at 11th International Conference on Analysis of Discontinuous Deformation, ICADD 2013, Fukuoka, Japan.6 p.
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N2 - In this paper, we introduce the parameter adjustment method with condition equations(one surveying adjustment method in geodetic data processing) to three-dimensional Manifold Method through formula derivation, and present the strict-constraint solution and least-squares solution strategies. In least-square solution, we develop the power conception of surveying adjustment and use power ratio to balance the physical and mathematical equations. Then, we use the uniaxial tensile model to verify the validity of above two solution strategies, and analyze their difference. Furthermore, the shearing failure simulation with mathematical constraint is presented. In conclusion, the essential difference of above two strategies is that the strict-constraint strategy can realize strong constraint on some unknowns and have minimum influence on others in the examples of this paper. On the other hand, the least-square strategy influences more than constrained unknowns, and perhaps affects the whole equations. Furthermore, we can control the constraint intensity by adjusting power ratio when using least-square strategy, because the constraint intensity is directly proportional to the power ratio.

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