PROBABILISTIC NUMERICAL ANALYSIS OF LARGE, COMPLEX, STRUCTURAL DYNAMIC SYSTEM MODELS

摘要

In recent years, great progress has been made in the construction and solution of large finite element models of complex structural dynamic systems. For example, structural models with millions of degrees of freedom are being built and used to approximate responses of structural systems. Further, great progress is being made in stochastic system analysis. Techniques for the construction of stochastic system models have been developed and solution techniques proposed. However, the two areas have not been combined, on a large scale, because stochastic finite element approaches appear very intrusive in their pure form. That is, substantial modifications of deterministic finite element codes are required to accommodate stochastic analysis. In view of this, a technique that uses the techniques of stochastic finite elements in a non-intrusive manner is required. This research provides one such approach. Specifically, the problem is divided into three parts: (1) Model structural dynamic excitations using traditional approaches, and model physical system randomness using techniques of stochastic finite elements, namely, the Karhunen-Loeve expansion and polynomial chaos. (2) Generate stochastic structural realizations and realizations of the random excitation using a Monte Carlo approach, and analyze structural responses with parallel computation in a suitable, large-scale finite element code. (3) Analyze structural dynamic responses using the techniques of stochastic finite elements, namely, the Karhunen-Loeve expansion and polynomial chaos. This paper supplies the details of the analytical approach. A numerical example is presented.