Comparison of static response of structures using convex models and interval analysis method

International Journal for Numerical Methods in Engineering

Volumn 56, Issue 12, 2003, Pages 1735-1753

  Qiu, Zhiping ^a  

^a BEIHANG UNIVERSITY   (China)

Author keywords

Convex models; Finite element analysis; Interval analysis method; Non probabilistic approach; Static response; Uncertain but bounded parameters

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PROBABILITY; VECTORS;

STATIC RESPONSE;

STRUCTURAL ANALYSIS;

STATIC RESPONSE;

EID: 0037471024     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.636     Document Type: Article

References (20)

1. Ben-Haim Y, Elishakoff I. Convex Models of Uncertainty in Applied Mechanics, Elsevier: Amsterdam, 1990.
2. Elishakoff I, Li YW, Starnes Jr. JH. A deterministic method to predict the effect of unknown-but-bounded elastic moduli on the buckling of composite structures. Computer Methods in Applied Mechanics and Engineering 1994; 111:155-167.
3. Elishakoff I, Eliseeff P, Glegg S. Convex modelling of material uncertainty in vibrations of a viscoelastic structure. AIAA Journal 1994; 32:843-849.
4. 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.
5. 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.
6. Qiu ZP, Mueller PC, Frommer A. Stability robustness bounds for linear state-space models with structured uncertainty based on ellipsoidal set-theoretic approach. Mathematics and Computers in Simulation 2001: 56: 35-53.
7. Qiu ZP, Mueller PC, Frommer A. An approximate method for the standard interval eigenvalue problem of real non-symmetric interval matrices. Communications in Numerical Methods in Engineering 2001; 17:239-251.
8. 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.
9. Chen SH, Yang XW. Interval finite element method for beem structures. Finite Element in Analysis and Design 2000; 34:75-88.
10. Mullen RL, Muhanna RL. Bounds of structural response for all possible loading combinations. Structural Engineering (ASCE) 1999; 125:98-106.
11. Pantelides CP, Ganerli S. Comparison of fuzzy set and convex model theories in structural design. Mechanical Systems and Processing 2001; 15(3):499-511.
12. Ganzerli S, Pantelides CP. Optimum structural design via convex model superposition. Computers and Structures 2000; 74(6):639-647.
13. Ganzerli S, Pantelides CP. Load and resistance convex models for optimum design. Structural Optimization 1999; 17(4):259-268.
14. Deif A. Advanced Matrix Theory for Scientists and Engineers. Abacus Press, 1991; 262-281.
15. Moore RE. Methods and Applications of Interval Analysis. SIAM: Philadelphia, 1979.
16. Schweppe FC. Recursive state estimation: unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control 1968; AC-13:22-28.
17. Drenick RF. Functional analysis of effects of earthquakes. 2nd Joint United States-Japan Seminar on Applied Stochastics, Washington, D.C., Sept. 19-24, 1968.
18. Goffman C. Calculus of Several Variables. Harper & Row: New York, 1965.
19. Haug EJ, Choi, KK, Komkov V. Design Sensitivity Analysis of Structural Systems. Academic Press, Inc.: New York, 1986.
20. Haftka RT, Guerdal Z, Kamat MP. Elements of Structural Optimization. Kluwer Academic Publishers, Dordrecht, 1990.