Abstract
The boundary element approach to shape sensitivity analysis of eigenvalues of free vibrating elastic structures is presented. The eigenvalue problem is described in terms of the boundary integral equation method. Using the variational approach for variable regions, first-order sensitivities of simple frequencies are derived. Dependence of eigenvalues with respect to the stochastic shape of the boundary is considered. The numerical procedure of discretization of the problem is characterized. Numerical examples for two-dimensional problems are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banjeree, P.K.; Butterfield, R. 1981:Boundary element methods in engineering sciences. London: McGraw-Hill
Brebbia, C.A.; Telles, J.C.F.; Wrobel, L.C. 1984:Boundary element techniques — theory and applications in engineering. Berlin, Heidelberg, New York: Springer
Burczynski, T. 1986: The boundary element procedure for dependence of eigenvalues with respect to stochastic shape of elastic systems.Proc. 25th Symp. on Modelling in Mechanics PTMTS, pp. 235–238. Gliwice: Kudowa
Burczynski, T. 1988a: Boundary element method for deterministic and stochastic shape design sensitivity analysis. In: Cruse, T.A. (ed.)Advanced boundary element methods, pp. 73–80. Berlin, Heidelberg, New York: Springer
Burczynski, T. 1988b: Shape sensitivity analysis and optimal design using boundary elements. In: Brebbia, C.A. (ed.)Topics in boundary element research. Vol. on advanced structural analysis. Berlin, Heidelberg, New York: Springer (in press)
Burczynski, T. 1989: The boundary element method for selected analysis and optimization problems of deformable systems.Mechanics Seriers 97. Gliwice: Silesian Technical University Publications (in Polish)
Burczynski, T.; Fedelinski, P. 1988: Boundary elements in shape design sensitivity analysis and optimal design of vibrating structures.Eng. Analysis (in press)
Choi, K.K.; Haug, E.J. 1983: Shape design sensitivity analysis of elastic structures.J. Struct. Mech. 11, 231–269
Dems, K.; Mróz, Z. 1984: Variation approach by means of adjoint systems to structural optimization and sensitivity analysis — II: structure shape variation.Int. J. Solids Struct. 20, 527–552
Fedelinski, P.; Burczynski, T. 1988a: Shape sensitivity analysis of eigenvalues using boundary elements.Proc. 13 Symp. on Vibrations and Waves in Physical Systems, pp. 77–78. Poznan: Blazejewko
Fedelinski, P.; Burczynski, T. 1989: Analysis of vibrating structural elements by the boundary element method.Scient. Pap. of Inst. Mach. Constr. and Expl., Tech. Univ. Wroclaw 56, pp. 129–133. Wroclaw
Fedelinski, P.; Burczynski, T. 1988b: The boundary element method for shape design sensitivity of natural frequencies.Scient. Pap. of Inst. Mach. Constr. and Expl., Tech. Univ. Wroclaw 55, pp. 138–141. Wroclaw
Nardini, D.; Brebbia, C.A. 1982: A new approach to free vibration analysis using boundary elements. In: Brebbia, C.A. (ed.)Boundary element methods in engineering, pp. 312–326. Berlin, Heidelberg, New York: Springer
Rousselet, B.; Haug, E.J. 1982–1983: Design sensitivity analysis in structural mechanics, III, effect of shape variation.J. Struct. Mech. 10, 273–310
Szefer, G. 1982: Analysis of sensitivity and optimization of dynamic systems with distributed parameters.Scient. Bul. Acad. Mining and Metallurgy, Mechanics 1, 5–36. Cracow
Author information
Authors and Affiliations
Additional information
Communicated by G. Maier
Rights and permissions
About this article
Cite this article
Burczynski, T., Fedelinski, P. Shape sensitivity analysis of natural frequencies of structures using boundary elements. Structural Optimization 2, 47–54 (1990). https://doi.org/10.1007/BF01743520
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01743520