Stochastic Computational Mechanics for Aerospace Structures

Abstract

F RACTURE and fatigue have become important factors in the structural design and safety considerations of aerospace structures. Due to uncertainty in the loads generated by wind gusts and jet engines, in the material properties of advanced materials (ceramics and composites), and in the shortcomings of the computational model, it is apparent that deterministic methods are not sufficient for the design of aerospace structures. Probabilistic approaches employing a theory of stochastic processes and statistics are needed to provide rational reliability analysis and to describe the behavior of a structure. Stochastic computational mechanics is the methodology which forms the basis of the reliability and risk analysis of structures, mechanical components, and systems. The fundamentals of probabilistic mechanics and its application to the analysis of uncertain structural systems are summarized in Ref. 51. Based on the nature of uncertainties in the external loads and the parameters of a structural system (such as material properties and structural geometry), problems can be classified into two categories: 1) problems for which the structure's parameters are deterministic, and the external loads are random with time-variant uncertainties; and 2) problems for which the external loading, material properties, and structural geometry involve time-invariant uncertainties. The term random vibration is often used to designate the first category of problems. The field of random vibrations is reviewed well in Ref. 5. The problem of a combination of both of the above categories has also been investigated.' It has been found that the