Research project PA/31 (Research action PA)
Background and problem statement
Design procedures of civil and mechanical load carrying structures traditionally involve the application of safety factors. These safety factors are prescribed to guarantee that uncertainties on all kinds of parameters (loads, materials, geometry, boundary conditions, ...) can not cause failure by exceedance of structural limits. This approach goes back to the early days of structural design, when only manual and approximative methods were available for design analysis. In modern procedures, the finite element method (FEM) is a well-established and powerful tool to predict structural response to a desired level of accuracy. But the technique is purely deterministic. The effect of parameter uncertainties is not taken into account. The nominal design case that is considered in the FE analysis is transformed into a hypothetical worst case by application of safety factors. Aspects of uncertainty are relevant in all kinds of structural design (static, dynamic, ...) and in any type of application. Safety factors are prescribed by standards, and they are mostly used in static analysis. Dynamic analysis is very often done in spacecraft and space equipment design. The project addresses the space technology and normalisation chapters of the call for proposals.
Objectives of the project
The objective of this project is to develop a consistent and workable methodology to take into account the effect of parameter uncertainties, by using only real physical and geometrical properties of the structure. The approach should be consistent: it should be developed in an analytical framework that is as close as possible to the existing FE methods. The approach should be also workable: the user should be able to apply it without much further knowledge of non-FE techniques, and the analysis should not require excessive calculation times. The project focusses on both static and dynamic design procedures. The methods that are developed are afterwards applied to build up fundamental knowledge of realistic design criteria, both for static and dynamic analysis, and to finally compare them to existing criteria. The project is considered successful if problems with more than 5 uncertain parameters can be analysed, with ranges on the order of 10% of their nominal values, for FE models of at least 1000 nodes, in an analysis time that is not more than 100 times the time for 1 deterministic analysis.
The proposed methodology
Monte Carlo Simulation (MCS) is the most common technique for non-deterministic analysis. It is however applicable only when complete statistical information about the distribution of parameters is available. In many design cases this is not true, e.g. when the actual distribution of a parameter is unknown, or when a parameter is not yet fixed at the time when the analysis is done. With a fuzzy description of parameters, the probabilistic approach is replaced by a possibilistic one, and the requirement for availability of parameter data are relaxed to only extreme values which have to be known. The worst case condition is however always predicted. The core of the methodology development in this project is a fuzzy FE method.
The project work plan
The project structure consists of 5 major tasks:
1. identification and quantification of actual uncertainties in typical structures
2. development of a fuzzy finite element framework
3. development of a consistent methodology to determine safety factors in static structural analysis
4. development of a consistent methodology to model structural dynamics with uncertain parameters
5. derivation of guidelines on modelling structural behaviour with uncertain parameters
Valorisation of results
The possibility to take into account uncertainties on parameter data opens several new perspectives for improved design standards and design procedures:
• a fundamental knowledge of safety factors permits smaller margins of safety, which translates directly into less oversized design, and more economical products
• a designer will have the opportunity to analyse a range of design conditions, without the need for multiply repeating minor modifications to variants of a structure
• virtual design procedures in companies will be enhanced, with particular benefits for designs in a context of uncertainties, and yet with a target of robust product design
The partner group and users committee
The project team consists of 5 research partners: the Scientific and Technical Centre of the Metalworking Industry (CRIF-WTCM), the Belgian Building Research Institute (WTCB/CSTC/BBRI), the division Building Mechanics of the K.U.Leuven (KUL-BWM), the division Production Engineering, Machine Design & Automation of the K.U.Leuven (KUL-PMA), and the Space Centre of Liège (CSL). The users committee is very wide, with representatives having different backgrounds (civil, mechanical and spacecraft engineering), and in different types of activities (research, consulting, software, component suppliers and end OEM's). They have routine experience with parameter uncertainties and design criteria. They provide practical data to the active project partners.
Static and dynamic design analysis procedures for structures with uncertain parameters : final report
Brussels : Federal Science Policy, 2007 (SP1833)
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