Simulation Strategies for FE Systems Under Uncertainties

The study of the performance of structural systems using digital computer simulations is nowadays a well established procedure in engineering practice. Structural behavior is thereby represented by Finite Element models which are further analyzed by Finite Element procedures. In civil and mechanical engineering, structures such as bridges, high-rise buildings, aircrafts, cars etc are digitally represented by Finite Element models. Well developed numerical tools and their software implementation allow the simulation and study of their response under various loads and environmental effects. Finite Element models contain in general a large number of parameters describing the geometry and mechanical properties of the structure. These parameters are specified deterministically, i.e. they are given specific values. However, this is almost never the case in reality. Most of these parameters cannot be assigned a fixed value with certainty. Instead they exhibit random fluctuations which can only be described in statistical terms. These uncertainties naturally affect the structural response which is subsequently uncertain as well. The proposed research aims at a quantitative mathematical investigation of the uncertain parameters using statistical models and of their effect on the structural response in conjunction with deterministic Finite Element procedures. Monte Carlo simulation is suggested as the general solution procedure, because it allows the combination of the well-established tools of deterministic analysis with stochastic procedures for the analysis of uncertainty. Special attention will be given to realistic models of structures, i.e. models with a large number of degrees of freedom (>>1000), non-linearities and a large number of uncertain parameters (>>100). Monte Carlo simulation requires a stochastic description of the uncertain parameters by random variables. Therefore, an important task is the specification of the probability distributions and correlations of the uncertain parameters in agreement with available statistical information. Following the necessary mathematical description of the uncertain parameters, their effect on the structural response will be investigated quantitatively. Hence, the reliability of actual structures will be expressed in probabilistic terms (e.g. finding the probability that a building will collapse under earthquake). Since such reliability investigations require a large number of simulations, the feasibility and efficiency of the proposed computational procedures will also be thoroughly investigated.

The ever-growing performance of computers has revolutionized all branches of engineering, since planned products, buildings, infrastructures can be virtually designed, analyzed and their behavior predicted beforehand. Computer simulation is now an integral part of the engineering design process. In structural mechanics computer simulation is based by and large on the finite element method, which has evolved and matured over several decades. One of the reasons for which the predictions of computer simulations deviate - sometimes massively - from the behavior of the actual physical system, is the unavoidable uncertainty related to some of its features. For instance, the material properties exhibit a random scatter, the geometry of every real object is subject to tolerances, the nature of the external disturbances of the system, too, is uncertain. In order to manage the risk associated with these uncertainties the concepts of probability and statistics are extremely useful: they provide quantitative tools for decision-making, allowing for instance the cost minimization for a specified level of risk. In the field of probabilistic methods, the so-called simulation methods are particularly robust, because they can be applied to virtually all types of problems encountered in engineering. The main challenge associated with simulation methods is the computational cost, since typically many repetitions of a given analysis task - each with modifications of the input - are required. Massive research efforts have been allocated to their improvement and advancement, by reducing the number of repetitions needed. The present project has pursued further development of simulation methods, with special emphasis on the improvement of the computational efficiency, in the context of large-scale problems, i.e. of the computer simulation of complex structural systems. A novel methodology, denoted as Line Sampling, has been introduced and extensive comparisons with alternative methods have been conducted. These activities have culminated in a Benchmark study, in which various research groups applied their respective approaches to a common set of structural analysis problems, under consideration of uncertainties.