Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 186
A Suitable Representation of the Stiffness for the Analysis of Linear Uncertain Structures G. Falsone^{1} and N. Impollonia^{2}
^{1}Department of Civil Engineering, University of Messina, Italy
G. Falsone, N. Impollonia, "A Suitable Representation of the Stiffness for the Analysis of Linear Uncertain Structures", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 186, 2006. doi:10.4203/ccp.83.186
Keywords: uncertain parameters, parametric stiffness matrix, perturbation methods.
Summary
Uncertain structures are characterized by the fact that some of their mechanical and
geometrical properties are defined from a probabilistic point of view [1]. The
fundamental problem related to the analysis of these structures consists in finding
explicit relationships, almost always approximate, between the structural response
and the physical uncertainties. The principal difficulty is due to the nonlinear nature
of this problem always arising, even for linear structures [2]. All the analysis
approaches for uncertain structures are based on some approximating hypotheses
regarding the stiffness of the material or the stiffness of the discretized structure and,
in some cases, on some corresponding assumptions concerning the response. For example,
one of the most used methods, the first order perturbation approach, assumes a linear
dependence of the structural stiffness on the quantities describing the uncertainties
and, at the same time, furnishes a linear dependence between the corresponding
response and the uncertain parameters [3,4]. However, in any approach the hypothesis of
linear dependence of the stiffness on the uncertainty quantities could be very
appropriate, independent of the response assumptions.
In this work it is shown that, in the case of linear structures, it is always possible to express the structural stiffness as a linear combination of random quantities (fields or variables) representing the physical uncertainties. It will be shown that in some cases, as for the uncertain nonsymmetric continuum, this representation is straightforward. In other cases, where this relationship is nonlinear, and this surely happens when both geometrical and mechanical uncertainties are present, it is always possible to introduce a transformation of the random quantities in such a way that the stiffness depends linearly on the new random quantities. The threedimensional, twodimensional and onedimensional continua cases are treated together with the corresponding finite element discretized structures. The linear representation of the structural stiffness may be very useful for obtaining the response statistics, using both exact and approximate analyses. The use of the perturbation approach could be an example: if the structural stiffness is linear with respect to the uncertain parameters, the application of high order perturbation techniques becomes straightforward and greater accuracy is encountered as shown in the numerical application. References
purchase the fulltext of this paper (price £20)
go to the previous paper 
