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INNOVATION IN COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero, R. Montenegro
Uncertainties in Structural Analysis
Institute of Engineering Mechanics, Leopold-Franzens University, Innsbruck, Austria
G.I. Schuëller, "Uncertainties in Structural Analysis", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Innovation in Computational Structures Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 4, pp 75-93, 2006. doi:10.4203/csets.14.4
Keywords: uncertainty, Monte Carlo simulation, structural reliability, advanced algorithms, computational efficiency.
Uncertainties affect all aspects of structural analysis and design, that is, loading, structural properties (such as strength and geometry) and modelling, to name but a few. While uncertainties in mechanical modelling can be reduced as additional knowledge becomes available, this is not the case for physical or intrinsic uncertainties, for example, for loading conditions due to the natural environment (such as wind, earthquakes, water and waves). Generally it can be said that the entire spectrum of uncertainties is also not known. Model validation procedures, for example, show clearly that neither the true structural model nor the model parameters are known with absolute certainty, that is, they are not deterministic. Assuming that by FE procedures structures and continua can be represented reasonably well, the question of the effect of the discretisation still remains. It is generally expected, that an increase in the size of the structural models, in terms of degrees of freedom, will increase the level of realism of the model. Comparisons with measurements, however, clearly show that these expectations are not met. An ever refined FE model just decreases the discretisation error, but all other aspects contributing to the discrepancy between prediction and measurement will not improve (see for example, ). Besides referring to loading conditions, uncertainties also refer to structural properties, such as imperfections of geometry, thickness, Young's modulus, material strength, fracture toughness and damping characteristics. Depending on the respective conditions and the respective problem to be solved, uncertainties may be qualified either in terms of random variables, random processes or random fields. While random variables describe the time invariant uncertainties or variabilities at a particular point, random fields or processes are used to describe random phenomena in space and/or time, respectively. The basic ingredients for characterising random variables are the particular type of probability law, the mean and the variance respectively. For random processes and fields, however, information on the correlation structure is required in addition. The parameters are statistically estimated from data and the selection of the suitable probability distributions is also based on these data. In other words, in probabilistic or rational uncertainty analysis the entire information on data is used, while in traditional, deterministic analysis representative values, such as 'maximum' or 'minimum' values are preselected on a more or less arbitrary basis. This also applies to the still frequently used global safety factors. The choice of the latter is indeed in contradiction to the accuracy demands on for example, finite element analyses. The recently introduced semi-probabilistic partial safety factor concept (LRFD) at least partially rectifies this situation.
The present paper focuses on a particular method to process uncertainties through structural systems, that is, the Monte Carlo method is discussed along with procedures to improve the computational efficiency, for example, by parallel processing. The main advantage of the simulation-based methods advocated in this paper is the suitability for problems involving large numbers of uncertain parameters . As this scenario is increasingly encountered in real-life applications this advantage is frequently of critical importance.
Due to space limitations only two selected areas of application in the engineering practice could be discussed, namely i) fatigue and fracture and ii) system identification and structural control.
With respect to the former area, this paper reviews concepts which have the potential to accommodate aspects of damage estimation such as maintenance, inspection, and repair. This way costs can be minimised while maintaining a particular level of target reliability (for example, by optimization of life cycle costs).
Concerning the second area of application mentioned above, it should be noted that actual structural systems, are in general, more complex than their mathematical or mechanical models. For example, nonlinearities are neglected when using a linear model, short or long-term time variance of the system characteristics are generally also neglected. A more realistic description of the structural system and its dynamic characteristics is preferably carried out by procedures of systems identification.
The related field of structural control aims at controlling and reducing the structural response under external dynamic excitation by active as well as passive devices. Both these types of control devices are addressed in this paper.
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