Abstract
When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method (FEM). The two parameters, median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. The solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
Similar content being viewed by others
References
GUO Shu-xiang, FENG Yuan-sheng, LÜ Zhen-zhou. Stochastic finite element method and structural reliability [J].Advances in Mechanics, 2000,30, (3): 343–350. (in Chinese)
Ben-Haim Y. A non-probabilistic concept of reliability [J].Structural Safety, 1994,14 (4): 227–245.
Elishakoff I. Essay on uncertainties in elastic and viscoelastic structures: from A M Freudenthal's criticisms to modern convex modeling[J].Computers & Structures, 1995,56 (6): 871–895.
Ben-Haim Y, Elishakoff I.Convex Models of Uncertainty in Applied Mechanics [M]. Amsterdam: Elsevier Science, 1990.
Ben-Haim Y. Convex models of uncertainty in radial pulse buckling of shells [J].Journal of Applied Mechanics, 1993,60 (3): 683–688.
Elishakoff I, Elisseeff P, Glegg S A L. Non-probabilistic, convex-theoretic modeling of scatter in material properties [J].AIAA Journal, 1994,32 (4): 843–849.
Qiu Z, Elishakoff I. Anti-optimization of structures with large uncertain-but-non-random parameters via interval analysis [J].Computer Methods in Applied Mechanics and Engineering, 1998,152, (3–4): 361–372.
Koylouglu H U, Cakmak A S, Nielsen S R K. Interval algebra to deal with pattern loading and structural uncertainties [J].Journal of Engineering Mechanics 1995,121 (11): 1149–1157.
Rao S S, Berke L. Analysis of uncertain structural system using interval analysis [J].AIAA Journal, 1997,35 (4): 727–735.
Alefeld G, Claudio D. The basic properties of interval arithmetric, its software realizations and some applications [J].Computers & Structures, 1998,67 (1/3): 3–8.
Author information
Authors and Affiliations
Additional information
Communicated by Zhang Ru-qing
Foundation item: the National Natural Science Foundation of China (59575040, 59775032)
Biography: Guo Shu-xiang (1964−), Doctor
Rights and permissions
About this article
Cite this article
Shu-xiang, G., Zhen-zhou, L. Interval arithmetic and static interval finite element method. Appl Math Mech 22, 1390–1396 (2001). https://doi.org/10.1007/BF02435542
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02435542