Structural reliability estimation using finite elements

Probability-based safety analysis is a rational method for quantifying the safety of structures when compared with conventional factor of safety. However, most reliability analysis methods are based on simple structures in which the limit state functions can be expressed explicitly in terms of the basic random variables. In fact, the failure mode for many practical structures is described by structural responses. The relationship of the response and the basic random variables can only be solved by a numerical method, such as finite element analysis. The use of the finite element methods in non-deterministic way is called Probabilistic Finite Elements (PFE). The early work in PFE analysis calculated response statistics, such as the mean and standard deviation. When structural reliability analysis is combined with PFE analysis, the computing time becomes very high when accurate results for complex structures are required. This study aims to develop a finite element reliability method which can be used to calculate the structural failure probability more efficiently and accurately. In the study, three methods have been developed. These are (1) the Load Space Formulation (LSF) in conjunction with PFE analysis; (2) the Exterior (or Tangent) Multi-Plane Surface (EMPS or TMPS) method; and (3) the Interior Multi-Plane Surface (IMPS) method. In particular, the attention has been focused on two-dimensional plane stress/strain problems. Also, only component structural reliability (where only one limit state function is assumed for the structure) is analysed.