Parallel computing for static response analysis of structures with uncertain-but-bounded parameters
Source abstract
Abstract
The vertex solution for estimation on the static displacement bounds of structures with uncertain-but-bounded parameters is studied in this paper. For the linear static problem, when there are uncertain interval parameters in the stiffness matrix and the vector of applied forces, the static response may be an interval. Based on the interval operations, the interval solution obtained by the vertex solution is more accurate and more credible than other methods (such as the perturbation method). However, the vertex solution method by traditional serial computing usually needs large computational efforts, especially for large structures. In order to avoid its disadvantages of large calculation and much runtime, its parallel computing which can be used in large-scale computing is presented in this paper. Two kinds of parallel computing algorithms are proposed based on the vertex solution. The parallel computing will solve many interval problems which cannot be resolved by traditional interval analysis methods.
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Research context
OpenAlex topics: Probabilistic and Robust Engineering Design · Structural Health Monitoring Techniques · Numerical Methods and Algorithms
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References (14)
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1. Oettli, W., On the solution set of a linear system with inaccurate coefficients. SIAM Journal on Numerical Analysis, 1965, Series 8, 2(1): 115–118.
2. Aberth, O., The solution of linear interval equations by a linear programming method. Linear Algebra and its Applications, 1997, 259: 271–279.10.1016/S0024-3795(96)00291-1 ↗
3. Qiu, Z.P., Chen, S.H. and Song, D.T., Displacement bound estimation for structures with an interval description of uncertain parameters. Communications in Numerical Methods in Engineering, 1996, 12(1): 1–12.10.1002/(SICI)1099-0887(199601)12:1<1::AID-CNM884>3.0.CO;2-N ↗
4. Qiu, Z.P. and Elishakoff, I., Anti-optimization of structures with large uncertain-but-non-random parameters via interval analysis. Computer Methods in Applied Mechanics and Engineering, 1998, 152(3–4): 361–372.10.1016/S0045-7825(96)01211-X ↗
5. McWilliams, S., Anti-optimization of uncertain structures using interval analysis. Computers & Structures, 2001, 79(4): 421–430.10.1016/S0045-7949(00)00143-7 ↗
6. Oettli, W. and Prager, W., Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides. Numerische Mathematik, 1964, 6: 405–409.10.1007/BF01386090 ↗
7. Neumaier, A., Interval Methods for Systems of Equations. Cambridge: Cambridge University Press, 1990.
8. Rump, S.M., On the solution of interval linear systems. Computing, 1992, 47(3-4): 337–353.10.1007/BF02320201 ↗
9. Hansen, E.R., Global Optimization Using Interval Analysis. New York: Marcel Dekker, Inc., 1992.
10. Qiu,Z.P., Wang,X.J. and Chen,J.Y., Exact bounds for the static response set of structures with uncertain-but-bounded parameters. International Journal of Solids and Structures, 43: 6574–6593.10.1016/j.ijsolstr.2006.01.012 ↗
11. Qiu, Z.P., Xia, Y.Y. and Yang, J.L., The static displacement and the stress analysis of structures with bounded uncertainties using the vertex solution theorem. Computer Methods in Applied Mechanics and Engineering, 2007, 196(49–52): 4965–4984.
12. Chen, G.L., Parallel Program Practice. Beijing: Higher Education Press, 2004.
13. Wang, D.R., Interval Arithemtic of Nonlinear Equation. Shanghai: Shanghai Scientific & Techincal Publishers, 1987.
14. Qiu, Z.P., Convex Method Based on Non-probabilistic Set-theory and Its Application. Beijing: National Defence Industry Press, 2005.