First order stochasticity in boundary geometry: a computer algebra BE development

Evaluation of boundary element responses due to a small change in the syste m data always involves elaborate differentiation of complicated expressions associated with inverses of matrices containing elementary and special fun ctions of mathematical physics. Such calculations are essential in reliabil ity analysis of structural and mechanical systems, particularly in aerospac e engineering, and bioengineering modeling, for which high quality solution s are necessary. In a computer algebra environment, modification of multipl ication and power expansion rules is sufficient for automatic implementatio n of first order perturbation in an existing boundary element package writt en for deterministic variables. The closed form algebraic manipulations are independent of the problem size. (C) 2001 Elsevier Science Ltd. All rights reserved.