Comparison between non-probabilistic interval analysis method and probabilistic approach in static response problem of structures with uncertain-but-bounded parameters

Communications in Numerical Methods in Engineering

Volumn 20, Issue 4, 2004, Pages 279-290

  Qiu, Zhiping ^a   Ma, Yi ^a   Wang, Xiaojun ^a  

^a BEIHANG UNIVERSITY   (China)

Author keywords

Non probabilistic interval analysis method; Probabilistic approach; Static response; Uncertain but bounded parameters

Indexed keywords

INFORMATION ANALYSIS; OPTIMIZATION; PARAMETER ESTIMATION; PROBLEM SOLVING; STATISTICAL METHODS; UNCERTAIN SYSTEMS;

INTERVAL ANALYSIS; PROBABILISTIC MODELS; STATIC RESPONSE; UNCERTAINTY MODEL;

PROBABILISTIC LOGICS;

MATHEMATICAL METHOD;

EID: 1942466604     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.668     Document Type: Article

References (21)

1. Ben-Haim Y, Elishakoff I. Convex Models of Uncertainty in Applied Mechanics. Elsevier Science: Amsterdam, 1990.
2. Ben-Haim Y, Chen G, Soong TT. Maximum structural response using convex models. ASCE Journal of Engineering Mechanics 1996; 122(4):325-333.
3. Elishakoff I. Probabilistic Methods in the Theory of Structures. Wiley: New York, Inc., 1983.
4. Qiu ZP, Elishakoff I. Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis. Computer Methods in Applied Mechanics and Engineering 1998; 152:361-372.
5. Rao SS, Cao L. Fuzzy boundary element method for the analysis of imprecisely defined systems. AIAA Journal 2001; 39(9):1788-1797.
6. Schweppe FC. Uncertain Dynamical Systems. Prentice-Hall: Englewood Cliffs, NJ, 1973.
7. Drenick RF. Functional analysis of effects of earthquakes. 2nd Joint United States-Japan Seminar on Applied Stochastic, Washington, DC, 19-24 September 1968.
8. Bialas S. A necessary and sufficient condition for stability of interval matrices. International Journal of Control 1983; 37(4):717-722.
9. Qiu ZP, Chen SH, Elishakoff I. Natural frequencies of structures with uncertain but non-random parameters. Journal of Optimization Theory and Applications 1995; 86:669-683.
10. Pantclides CP, Ganerli S. Comparison of fuzzy set and convex model theories in structural design. Mechanical Systems and Processing 2001; 15(3):499-511.
11. Ganzerli S, Pantelides CP. Optimum structural design via convex model superposition. Computer and Structures 2000; 74(6):639-647.
12. Pantelides CP, Ganerli S. Design of trusses under uncertain loads using convex models. Journal of Structural Engineering (ASCE) 1998; 124(3):318-329.
13. Ganzerli S, Pantelides CP. Load and resistance convex models for optimum design. Journal of Structural Optimization 1999; 17:259-268.
14. Tzou S-R, Pantelides CP. Convex models for impulsive response of structures. Journal of Engineering Mechanics (ASCE) 1996; 122(6):521-529.
15. Alefeid G, Herzberger J. Introduction to Interval Computations. Academic Press: New York, 1983.
16. Moore RE. Methods and Applications of Interval Analysis. Prentice-Hall: London, 1979.
17. Schweppe FC. Recursive state estimation: unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control 1968; AC-13:22-28.
18. Ben-Haim Y, Elishakoff I. Convex models of vehicle response to unknown but bounded terrain. Journal of Applied Mechanics 1991; 58:355-361.
19. Qiu ZP, Elishakoff I, Strarnes Jr JH. The bound set of possible eigenvalues of structures with uncertain but non-random parameters. Chaos, Solitons and Fractals 1996; 7:1845-1857.
20. Qiu ZP, Wong XJ. Comparison of dynamics response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach. International Journal of Solids and Structures 2003a; 40(20):5423-5439.
21. Qiu ZP. Comparison of static response of structures using convex models and interval analysis method. International Journal for Numerical Methods in Engineering 2003b; 56:1735-1753.