A counterexample to FORM and SORM. Issue 6 (10th February 2020) - Ávila da Silva Júnior, Claudio Roberto; Damazio, Pedro Danizete; Matioli, Luiz Carlos; Cavichiolo, João Lucas
Abstract : Purpose: This paper aims to presents a counterexample that points to an inconsistency generated by the first- and second-order approximation methods, FORM and SORM, respectively, procedures for elliptical problems. Design/methodology/approach: The classical results of theory measure and functional analysis were used. Findings: The FORM and SORM are known to find solutions in a Gaussian space. This procedure does not satisfy the conditions of the Lax–Milgram theorem and does not assure the existence and uniqueness of the solution. Research limitations/implications: This paper alerts the engineering research community that uses these methods, initiating discussion and improvement of FORM and SORM procedures. Practical implications: This paper puts in check the feasibility of using FORM and SORM in engineering problems. Originality/value: From the moment they were introduced to the engineering and scientific communities, the FORM and SORM were taken as the bases for solving various problems found in the literature and indifferent documents scattered throughout the world over the past 50 years, for FORM, and 40 years, for SORM. Even though it was a very serious fault, at least for elliptical problems, pointed out in this work, it went unnoticed all those years by the research community. Therefore, the contribution of this paper is to present the engineering community that uses FORM and SORM in elliptical problems an unnoticed failure since the introduction of these methods.