Summary
The application of stochastic boundary elements to examining displacements, strains, stresses, natural frequencies and in the general case — an arbitrary functional with respect to stochastic shape of the boundary is presented. In order to solve this problem the idea of stochastic shape sensitivity analysis is used. It is assumed that the boundary undergoes small random variations which create the stochastic tolerance range. Analytical boundary integral expressions for random variations of displacements, stresses and natural frequencies are derived and boundary elements are used in computational procedures.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Burczyniski T.: Stochastic boundary value problems of elastostatics in terms of the boundary integral equation method. Papers of Inst Civil Engn., Wroclaw Technical University, Vol. 1, No. 28, pp. 61–68, Wroclaw 1981 (in Polish).
Burczyfiski T.: The boundary element method for stochastic potential problems. Applied Mathematical Modelling, Vol. 9, No. 3, pp. 189–194, 1985.
Burczynski T.: Stochastic formulation of wheelset dynamics by means of the boundary element method. Proc. 8th International Wheelset Congress, Vol.1, pp.1.3/1–3/15, Madrid 1985.
Burczynski T.: Stochastic boundary element method for wave propagation through continuous random media. In: BETECH’86 MIT (Eds. J.J.Connor and C.A.Brebbia ), CMP 1986.
Burczynski T.: The boundary element procedure for dependence of eigenvalues with respect to stochastic shape of elastic systems. Proc. 25th Symp. on Modelling in Mechanics, PTMTS, Vol.2, pp.235–238, Gliwice-Kudowa 1986.
Burczynski T.: The boundary element method in stochastic problems of elasticity. Mechanics and Computer, Vol.7, pp.125–147, PWN Warsaw 1988 (in Polish).
Burczynski.T.: Boundary element method for deterministic and stochastic shape design sensitivity analysis. In: Advanced Boundary Element Methods (Ed. C.T.Cruse ), pp. 73–80, Springer-Verlag 1988.
Burczynski T.: The Boundary Element Method for Selected Analysis and Optimization Problems of Deformable Bodies. Silesian Tech. Univ. Publications, Gliwice 1989 (in Polish).
Burczynski T.: Stochastic boundary element methods. In: Advances in Boundary Element Techniques (Eds.J.H.Kane, G.Maier, N.Tosaka and S.N.Atluri), Springer-Verlag (in press).
Burczynski T. and Fedelinski P.: Shape sensitivity analysis of natural frequencies of structures using boundary elements. Structural Optimization, 2, pp. 47–54, 1990.
Burczynski T. and John A.: Stochastic dynamic analysis of elastic and viscoelastic systems by means of the boundary element method. In: Boundary Elements VII (Eds. C.A.Brebbia and G.Maier), Vol.I, pp.6/536/61, Springer-Verlag 1985.
Burczynski T. and John A.: The stochastic boundary integral equation method for random vibrations of continuous media. Opole Technical University Publications, No.109, pp.61–74, Opole 1985.
Burczynski T. and John A.: Application of the stochastic boundary element method to analysis of elastic and viscoelastic structures. Proc. X Polish Conf. Computer Methods in Mechanics, pp.47–54, Swinoujscie 1991.
Cheng A.H-D. and Lafe O.E.: Boundary element solution for stochastic groundwater flow: random boundary condition and recharge. Water Resources, Vol. 27, No. 2, pp. 231–242, 1991.
Drewniak J.: Boundary elements for random heat conduction problems. Engineering Analysis, Vol. 2, No. 3, 1985
Ettouney M., Benaroya H. and Wright J.: Probabilistic boundary element methods. Chapter 5 in: Computational Mechanics of Probabilistic and Reliability Analysis (Eds. W.K.Liu and T.Belytschko ), Elmepress International 1989.
Mrbz Z.: Variational approach to shape sensitivity analysis and optimal design. in: The Optimum Shape (Eds. J.A.Bennet and M.E.Botkin ), Plenum Press, New York 1986, pp. 79–110.
Nakagiri S., Suzuki K. and Hisada T.: Stochastic boundary element method applied to stress analysis. In: Boundary Elements V (Eds. C.A.Brebbia, T.Futugami and M.Tanaka ), pp. 439–448, Springer-Verlag 1983.
Nakagiri S. and Suzuki K.: Indeterminate shape modification for stress reduction based on boundary element sensitivity analysis. In: Computer Aided Optimum Design of Structures: Recent Advances (Eds. C.A.Brebbia and S.Hemandez ), pp. 85–94, CMP, Springer-Verlag 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burczynski, T. (1992). Shape Sensitivity Analysis of Uncertain Static and Vibrating Systems Using Stochastic Boundary Elements. In: Kobayashi, S., Nishimura, N. (eds) Boundary Element Methods. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06153-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-06153-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-06155-8
Online ISBN: 978-3-662-06153-4
eBook Packages: Springer Book Archive