Geometrically nonlinear finite element reliability analysis of structural systems. I: theory

This article reviews the theory of finite element reliability analysis of g eometrically nonlinear elastic structures (GNS) based on the total lagrangi an formulation. It also provides computer implementation developments and e stablishes the basis of understanding of the applications presented in the second part of this investigation. Because of the slenderness of GNS, the s tructural responses are nonlinear even if the strains are within the elasti c range. For this reason, the nonlinear relationships between strains and d isplacements should be considered. Since the failure surface is nonlinear, this study reviews the evaluation of structural reliability of GNS by using both first-order and second-order reliability methods. To evaluate the str uctural reliability, the linkage of system reliability analysis program REL SYS with the finite element analysis program (FEAP) is presented. The compu ter code RELSYS-FEAP is readily applicable to the evaluation of system reli ability of GNS. (C) 2000 Elsevier Science Ltd. All rights reserved.