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A constraint-based approach for qualitative matrix structural analysis

Published online by Cambridge University Press:  27 February 2009

David I. Schwartz  and
Stuart S. Chen
David I. Schwartz
Affiliation:
Applied Artificial Intelligence Laboratory, State University of New York at Buffalo, Department of Civil Engineering, 202 Ketter Hall, Buffalo, New York 14260, USA
Stuart S. Chen
Affiliation:
Applied Artificial Intelligence Laboratory, State University of New York at Buffalo, Department of Civil Engineering, 202 Ketter Hall, Buffalo, New York 14260, USA
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Abstract

Qualitative physics, a subfield of artificial intelligence, adapts intuitive and non-numerical reasoning for descriptive analysis of physical systems. The application of a set-based qualitative algebra to matrix analysis (QMA) allows for the development of a qualitative matrix stiffness methodology for linear elastic structural analysis. The unavoidable introduction of arithmetic ambiguity requires the reinforcement of physical constraints complementary to standard matrix operations. The overall analysis technique incorporates such constraints within the set-based framework with logic programming. Truss, beam, and frame structures demonstrate constraint relationships, which prune spurious solutions resulting from qualitative arithmetic relations. Though QMA is not a panacea for all structural applications, it provides greater insight into new notions of physical analysis.

Keywords

Qualitative ReasoningStructural EngineeringArtificial IntelligenceConstraint SatisfactionLogic Programming
Type
Articles
Information
AI EDAM , Volume 9 , Issue 1 , January 1995 , pp. 23 - 36
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Bozzo, L.M., & Fenves, G.L. (1992). Qualitative reasoning about structural behavior for conceptual design. Report No. UCB/SEMM-92/96, Department of Civil Engineering, University of California, Berkeley, California.Google Scholar
Bozzo, L.M., & Fenves, G.L. (1993). Reducing ambiguity in qualitative reasoning. Cohn, L. (Ed.), In Computing in Civil and Building Engineering: Proceedings of the Fifth International Conference (Cohn, L., Ed.), pp. 1259–1266. ASCE, New York.Google Scholar
Bratko, I. (1990). Prolog Programming for Artificial Intelligence, 2nd ed. New York: Addision-Wesley Publishing Company.Google Scholar
Colmerauer, A. (1985). Prolog in 10 figures. Commun. ACM 12(28), 1296–1310.Google Scholar
de Kleer, J., & Brown, J.S. (1990). A qualitative physics based on confluences. In Readings In Qualitative Reasoning About Physical Systems, (Weld, D.S., and de Kleer, J., Eds.), pp. 83–87. Morgan Kaufmann Publishers, San Mateo, California.Google Scholar
Del Grosso, A., & Zucchini, A. (1992). Qualitative physics and its applications to structural engineering systems. In Intelligent Structures 2 (Wen, Y.K., Ed.), pp. 107–127. Elsevier, New York.Google Scholar
Dormoy, J., & Raiman, O. (1990). Assembling a device. (Weld, D.S. and de Kleer, J., Eds.), pp. 306–311. In Readings In Qualitative Reasoning About Physical Systems Morgan Kaufmann Publishers, San Mateo, California.Google Scholar
Fruchter, R. (1993). Deriving alternate structural modifications based on qualitative interpretation at the conceptual design stage. In Computing in Civil and Building Engineering: Proceedings of the Fifth International Conference (Cohn, L., Ed.), pp. 1243–1250. ASCE, New York.Google Scholar
Fruchter, R., Iwasaki, Y., & Law, K.H. (1991). Generating qualitative models for structural engineering analysis and design. In Proceedings of the Seventh Conference on Computing in Civil Engineering (Cohn, L., Ed.), pp. 268–277. ASCE, New York.Google Scholar
Fruchter, R., Law, K.H., & Iwasaki, Y. (1993). An approach for qualitative structural analysis. Art. Intell. Eng. Design, Analysis Manuf. 7(3), 189–209.CrossRefGoogle Scholar
Kawamura, H., Tani, A., Nakano, H., & Yamada, M. (1992). Critical analysis of structures by qualitative reasoning. Microcomputers Civ. Eng. 7, 131–142.CrossRefGoogle Scholar
Kuipers, B.J. (1989). Qualitative reasoning: Modeling and simulation with incomplete knowledge. Automatica 24, 571–586.CrossRefGoogle Scholar
Luzeaux, D. (1991). Formalizing symbolic reasoning. In Decision Support Systems and Qualitative Reasoning (Singh, M.G., and Travé-Massuyés, L., Eds.), pp. 315–320. Elsevier Science Publishers, Holland.Google Scholar
Martin, J.L., & Roddis, W.M.K. (1993). Integrating qualitative and quantitative reasoning in structural engineering. In Computing in Civil and Building Engineering: Proceedings of the Fifth International Conference (Cohn, L., Ed.), pp. 1235–1242. ASCE, New York.Google Scholar
Sack, R.L. (1984). Structural Analysis. McGraw-Hill, Boston.Google Scholar
Schwartz, D.I. (1994). Qualitative Reasoning for Matrix Structural Analysis. M.S. Thesis, Dept. of Civil Engineering, State University of New York at Buffalo.Google Scholar
Schwartz, D.I., & Chen, S.S. (1992). Spatial and temporal aspects of qualitative structural reasoning. In Proceedings of the Eighth Conference on Computing in Civil Engineering (Goodno, B.J., and Wright, J.R., Eds.), pp. 277–284. ASCE, New York.Google Scholar
Schwartz, D.I., & Chen, S.S. (1993). Order of magnitude reasoning for qualitative matrix structural analysis. In Computing in Civil and Building Engineering: Proceedings of the Fifth International Conference (Cohn, L., Ed.), pp. 1267–1274. ASCE, New York.Google Scholar
Schwartz, D.I., & Chen, S.S. (1994). Towards a unified framework for interval based qualitative computational matrix structural analysis. Comput. Syst. Eng. 5, 147–158.CrossRefGoogle Scholar
Shoham, Y. (1994). Artificial Intelligence Techniques in Prolog, Chap. 6. Morgan Kaufmann, San Francisco.Google Scholar
Smith, I.F.C., & Faltings, B. (1993). Implementing qualitative reasoning for structural design using constraint propagation. In Computing in Civil and Building Engineering: Proceedings of the Fifth International Conference (Cohn, L., Ed.), pp. 1251–1258. ASCE, New York.Google Scholar
Slater, J.H. (1986). Qualitative physics and the prediction of structural behavior. In Proceedings of ASCE Symposium on Expert Systems in Civil Engineering (Kostem, C.N., and Maher, M.L., Eds.), pp. 239–248. ASCE, New York.Google Scholar
Sterling, L., & Shapiro, E. (1986). The Art of Prolog. MIT Press, Cambridge, Massachusetts.Google Scholar
Struss, P. (1990). Problems of interval based qualitative reasoning. In Readings In Qualitative Reasoning About Physical Systems (Weld, D.S., and de Kleer, J., Eds.), pp. 288–305. Morgan Kaufmann Publishers, San Matea, California.CrossRefGoogle Scholar
Tsang, E. (1993). Foundations of Constraint Satisfaction. Academic Press, New York.Google Scholar
Weinberg, J.B., Uckun, S., Biswas, G., & Manganaris, S. (1992). Qualitative vector algebra. In Recent Advances in Qualitative Physics (Faltings, B., and Struss, P., Eds.), pp. 193–210. MIT Press, Cambridge, Massachusetts.Google Scholar
Williams, B.C. (1990). MINIMA: A symbolic approach to qualitative algebraic reasoning.” In Readings In Qualitative Reasoning About Physical Systems (Weld, D.S., and de Kleer, J., Eds.), pp. 312–317. Morgan Kaufmann Publishers, San Mateo, California.CrossRefGoogle Scholar
Williams, B.C. (1991). A theory of interactions: Unifying qualitative and quantitative algebraic reasoning. Artif. Intell. 51, 39–94.Google Scholar