Sensitivity and Reliability Analysis of Engineering Structures: Sampling Based Methods

Abstract

This chapter intends to present an overview of Monte Carlo-type methods currently in use in the probabilistic analysis of large engineering structures. It starts with an introduction to the generation of multi-dimensional random quantities. Next, spatially distributed random properties, e.g., material or geometrical properties in continuum mechanics, are modeled as random fields. Approximations to random fields by means of Karhunen–Loeve expansion and polynomial chaos expansion are introduced. These tools are employed to study the response of continuous structures with loads, material or geometrical properties given by random fields. The main focus is on sensitivity analysis of large engineering structures, where small Monte Carlo sample sizes are mandatory. The transition to reliability is undertaken by means of the concept of tolerance intervals. Further, current sampling methods for accurate reliability estimates are discussed, and practical applications are presented.