Digital Representation of Structural Response for the Reliability Assessment of Complex Systems

Cuny City College, New York NY

Investigators

Abstract

DIGITAL REPRESENTATION OF STRUCTURAL RESPONSE FOR THE RELIABILITY ASSESSMENT OF COMPLEX SYSTEMS ABSTRACT Current research efforts in structural engineering are geared toward the development of performance based design and safety evaluation criteria that take into consideration the various uncertainties in estimating system behavior and future loading conditions. System reliability methods provide the means to address these important points. However, most existing analytical reliability techniques have one or more limitations in their ablity to: a) accurately model structural behavior at high loads, b) consider different performance criteria, c) identify multiple equally important failure modes, and d) account for load combinations. The application of simulation techniques in conjunction with general purpose finite element packages provides methods with a strong potential for resolving many of these outstanding issues. The purpose of this research is then to develop a simulation-based method for the reliability assessment of structural systems, which would realistically model their behavior at high loads, be implementable in practical situations, and provide accurate solutions for complex structures using efficient algorithms. The first tool required to perform a simulation-based reliability analysis of a structural system consists of an accurate and efficient nonlinear analysis program capable of modeling the behavior of the structure for a specific (deterministic) set of conditions. The second tool is a systematic search algorithm that can identify probabilistically dominant failure modes accounting for the randomness of loads and material properties. Closed-form solutions for the response of complex nonlinear structures are difficult to obtain and only a digital representation of their behavior is possible through the application of the finite element method. Point estimates of the response under different load intensities and material properties are usually obtained from variations on the Newton-Raphson algorithm. These point estimates may often misidentify the ultimate capacity and may not accurately model the softening part of the loading curve due to the accumulation of numerical errors and because of the properties of the stiffness matrix in these ranges. In this study, the Singular Value Decomposition, SVD, method in combination with the Lanczos algorithm will be used to accurately trace the response of a structure at high loads. The efficiency, robustness, and stability of the proposed method will be demonstrated. Due to the random nature of the problem, the safety assessment of a structure can only be established using reliability techniques. Since the behavior of a structure with several failure modes is best represented in digital form, modern heuristic techniques may provide the most appropriate tools to assess its reliability. In particular, Genetic Algorithms, GA, have been shown to provide robust techniques for the reliability analysis of structures with multiple failure modes but may be inefficient due to the shotgun search strategy that they are based upon. To improve the efficiency of GA, a filtration operator will be introduced based on the principle of genetic elitism. The modified GA will provide an efficient method to estimate the reliability of complex structures, as well as identify its dominant failure modes and controlling random variables. This project will introduce advanced tools of computational mathematics into the field of structural mechanics. The study will stress the application of the proposed methods for the simulation based design of civil engineering structures although they will be applicable to fields as varied as electronic circuit design and Micro-Electro-Mechanical-Systems. Training of students in the subjects of matrix computational methods, artificial intelligence, and statistical computing will be a primary goal. Such training will provide future generations of structural engineers with the well-rounded education needed to make decisions and provide solutions to real life complex problems under uncertainty.