The reciprocal approximation in stochastic analysis of structures

A stochastic analysis of structures usually requires multiple reanalysis of the structures to compute the statistics of the structural response. A sim ilar problem exists in the design of optimal structures where many analysis are needed before reaching the extremal solution. In both fields the reana lysis requirements are considered as an unacceptable numerical burden. To c ircumvent the reanalysis obstacle investigators have been using approximate analysis. Common methods are first and second-order series expansions of t he nodal displacements, and related perturbation methods. Interestingly, a popular approximation method in structural design, the reciprocal approxima tion technique, has not been used in stochastic analysis. This paper shows that this method can easily be used to compute the statistics of the struct ural response. When expanding the displacements linearly in terms of the re ciprocals of the element stiffnesses, one obtains, as a rule, better result s than with a linear Taylor expansion. It is shown that for low values of t he relative redundancy the method yields second order quality approximation s. Unlike many other techniques, the reciprocal approximation also produces the statistics of the internal forces. The theory is illustrated with typi cal beam and arch trusses and is compared with existing stochastic methods. (C) 2000 Elsevier Science Ltd. All rights reserved.