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Modelling of heat transfer in biological tissue by interval FEM

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Konferencja
Polish Conference on Computer methods in mechanics ; (14 ; 26-28.05.1999 ; Rzeszów, Poland
Języki publikacji
EN
Abstrakty
EN
In this paper, an algorithm of calculation of extreme values of temperature based on interval arithmetic is presented. Many mechanical systems with uncertain parameters lambda in Lambda can be described by a parameter dependent system of linear equations K(lambda)T=B(lambda). Using natural interval extension of a real function, one can transform the system of linear equations into the system of linear interval equationsK(lambda)T=B(lambda). Solution of the system of linear interval equations always contains the exact solution of the parameter dependent system of equations. A new method of computation of extreme values of mechanical quantities based on the monotonicity test is introduced. This method can give exact solution of a parameter dependent system of equations.
Rocznik
Strony
551--558
Opis fizyczny
Bibliogr. 37 poz., rys., tab.
Twórcy
autor
  • Silesian University of Technology [Politechnika Śląska], ul. Konarskiego 18a, 44-100 Gliwice, Poland
autor
  • Silesian University of Technology [Politechnika Śląska], ul. Konarskiego 18a, 44-100 Gliwice, Poland
Bibliografia
  • [1] G. Alefeld, J. Herzberger. Introduction to Interval Computations. Academic Press, New York 1983.
  • [2] Y. Ben-Haim, I. Elishakoff. Convex Models of Uncertainty in Applied Mechanics. Elsevier Science Publishers, New York, 1990.
  • [3] I. Elishakoff. Essay on uncertainties in elastic and viscoelastic structures: from A.M. Freudenthal's criticisms to modern convex modelling. Computers and Structures, 56(6): 871-895, 1995.
  • [4] I. Elishakoff, R. T. Haftka, J. Fang. Structural design under bounded uncertainty - Optimization with antioptimization. Computers and Structures, 53(6): 1401-1405, 1994.
  • [5] I. Elishakoff, Y. W. Li, J. H. Starnes. 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, 111: 155-167, 1994.
  • [6] I. Elishakoff. Three versions of the finite element method based on concepts of either stochasticity, fuzziness or anti-optimization. Applied Mechanics Review, 51(3): 209-218, 1998.
  • [7] P. Elisseeff, A. L. Glegg, I. Elishakoff. Nonprobablistic, convex-theoretic modelling of scatter in material properties. AIAA Journal, 32(4): 843-849. 1994.
  • [8] K. G. Guderley, C. L. Keller. A basic theorem in the computation of ellipsoidal error bounds. Numerishe Mathematic, 19: 218-229, 1972.
  • [9] P. Gutman, C. Baril, L. Neumann. An algorithm for computing value sets of uncertain transfer functions in factored real form. IEEE Transactions on Automatic Control, 39(6): 1268-1273, 1994.
  • [10] H. W. Huang, C. L. Chan, R. B. Roemer. Analytical solution of Pennes bio-heat transfer equation with a blood vessel. Journal of Biomechanical Engineering, 116: 208-212, 1994.
  • [11] E. Hyv6nen. Constraint reasoning based on interval arithmetic: the tolerance propagation approach. Artificial Intelligence, 58: 71-112, 1992.
  • [12] C. Jansson. Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side. Computing, 46: 265-274, 1991.
  • [13] R. B. Kearfott, V. Kreinovich. Applications of Interval Computations. Kluwer Academic Publishers, London 1996.
  • [14] R. B. Kearfott, Z. Xing. An interval method step control for continuation methods. SIAM Journal on Numerical Analysis, 31(3): 892-914, 1994.
  • [15] H. U. K5yliioglu, A. Cęakmak, S. R. K. Nielsen. Interval mapping in structural mechanics. In: Spanos, ed., Computational Stochastic Mechanics, 125-133. Balkema, Rotterdam 1995.
  • [16] H. U. Kryliioglu, I. Elischakoff. A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties. Computers and Structures, 67(1-3): 91-98, 1998.
  • [17] V. Kreinovich, A. Lakeyev, J. Rohn, P. Kahl. Computational Complexity Feasibility of Data Processing and Interval Computations. Kluwer Academic Publishers, Dordrecht, 1998.
  • [18] Z. Kulpa, A. Pownuk, I. Skalna. Analysis of linear mechanical structures with uncertainties by means of interval methods. Computer Assisted Mechanics and Engineering Sciences, 5: 443-477, 1998.
  • [19] Z. S. Liu, S. H. Chen, W. Z. Han. Solving the extremum of static response for structural systems with unknown-but-bounded parameters. Computers and Structures, 50(4): 557-561, 1994.
  • [20] R. E. Moore. Interval Analysis. Prentice Hall, Englewood Cliffs, NJ, 1966.
  • [21] R. L. Mullen, L. Muhanna. Bounds of structural response for all possible loading combinations. Journal of Structural Engineering, 125(1): 98-106, 1999.
  • [22] S. Nakagiri, K. Suzuki. Finite element interval analysis of external loads identified by displacement input with uncertainty. Computer Methods in Applied Mechanics and Engineering, 168: 63-72, 1999.
  • [23] A. Neumaier. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge 1990.
  • [24] A. Neumaier. Rigorous sensitivity analysis for parameter-dependent systems of equations. Journal of Mathematical Analysis and Applications, 144: 26-25, 1989.
  • [25] A. Neumaier. The enclosure of solutions of parameter-dependent systems of equations. In: Reliability in Computing, 269-286, 1988.
  • [26] P. Pantelides, S. Gamerli. Design of trusses under uncertain loads using convex models. Journal of Structural Engineering, 124(3): 318-329, 1998.
  • [27] Z. Qiu, I. Elishakoff. Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis. Computer Methods in Applied Mechanics and Engineering, 152: 361-372, 1998.
  • [28] S. S. Rao, S. Berke. Analysis of uncertain structural systems using interval analysis. AIAA Journal, 35(4): 727-735, 1997.
  • [29] W. C. Rheinboldt. Numerical Analysis of Parametrized Nonlinear Equations. John Wiley and Sons, New York, 1986.
  • [30] J. Rohn. Systems of linear interval equations. Linear Algebra and Its Applications, 126: 39-78, 1989.
  • [31] P. Saint-Pierre. Newton and other continuation methods for multivalued inclusions. Set-Valued Analysis, 3: 143-156, 1995.
  • [32] J. Skrzypczyk, A. Pownuk. On a way of finding upper approximation to the mechanical values under conditions of interval uncertainty in parameters of their mathematical models. Publications Of The Silesian University Of Technology, 7: 323-328, Gliwice 1998.
  • [33] K. Sobczyk. Stochastic Differential Equations with Applications to Physics and Engineering. Kluwer Academic Publishers, B.V. 1991.
  • [34] F. Tonon, A. Bernardini. A random set approach to the optimization of uncertain structures. Computers and Structures, 68: 583-600, 1998.
  • [35] F. Z. Wilke, B. R. T. Franciosi, P. W. Oliveira, D. M. Claudio. Modelling the measurement uncertainty by intervals. Journal of Universal Computer Science, 4(1): 82-88, 1998.
  • [36] K. Wojciechowski. System with Limited Uncertainty (in Polish). Akademicka Oficyna Wydawnicza PLJ, Warszawa, 1998.
  • [37] N. Yoshikawa, I. Elischakoff, S. Nakagiri. Worst case estimation of homology design by convex analysis. Computers and Structures, 67(1-3): 191-196, 1998.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0005-0033
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