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

This article reviews the theory of finite element reliability analysis of geometrically nonlinear elastic structures (GNS) based on the total lagrangian formulation. It also provides computer implementation developments and establishes the basis of understanding of the applications presented in the second part of this investigation. Because of the slenderness of GNS, the structural responses are nonlinear even if the strains are within the elastic range. For this reason, the nonlinear relationships between strains and displacements 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 structural reliability, the linkage of system reliability analysis program RELSYS with the finite element analysis program (FEAP) is presented. The computer code RELSYS–FEAP is readily applicable to the evaluation of system reliability of GNS.