Reliability of Complex Structures by Large Admissible Perturbations

Abstract

The perturbation approach to reliability (PAR) is a powerful methodology for reliability analysis and design of large structures. Its main features are: F1) PAR provides the exact global failure equation for any failure criterion for which the corresponding structural analysis can be performed by finite elements. F2) Geometry, material, and loads appear explicitly in the global failure equations and are treated as random variables. No need arises for load path selection or load pattern specification. F3) PAR introduces an invariant and consistent redundancy definition as an injective mapping restricted on the failure surface. Thus, the redundancy/reliability of the structure is expressed in terms of the redundancy/reliability of its structural components. F4) The norm of the Rosenblatt transformed reliability injection is the reliability index. F5) For each global failure equation or combination of failure equations, PAR computes the individual or joint design points without enumerating paths to failure, trial and error, or repeated finite element analyses. F6) Serviceability or ultimate global structural failure is defined by specifying a threshold value of any quantity that can be computed by finite elements: natural frequencies, dynamic normal modes, static deflections, static stresses, buckling loads, and buckling modes are implemented in PAR. Stress failure equations are used along with linearized plasticity surfaces to identify element failure. Several applications are presented to assess PAR.