Dynamics & Vibration Research Group

In structural and mechanical design it is important to allow for the fact that uncertainties can exist in the properties of the designed system and in the applied loading. Traditionally this has been catered for through the use of factors of safety, which are developed and refined on the basis of experience and historical evidence. For systems where efficient design is of the utmost importance (for example the minimum weight design of an aircraft structure) it is possible that the traditional factors of safety may be overly conservative, so that optimal efficiency cannot be achieved. Furthermore, historical factors of safety are unlikely to be appropriate for new design concepts or new materials. It follows that there is a need for a method (or methods) that can be applied objectively to a new design to yield information on the safety and reliability of the system without reliance on established factors of safety. This project is concerned with the development of both probabilistic and deterministic (or "possibilistic") methods of safety assessment.

Project Details

The most direct approach to a theoretical reliability assessment is to attempt to derive the statistics of the system response (and therefore the failure probability) from a knowledge of the statistical properties of the system and the applied loads. However, this approach faces two major obstacles for a complex system: firstly, the evaluation of the response statistics can present severe mathematical and numerical difficulties, and secondly the statistical properties of the system and the loading may not be know in any detail. The first difficulty has led to the development of a number of approximate analytical methods, most notably Asymptotic Reliability Analysis, FORM (First Order Reliability Method) and SORM (Second Order Reliability Method). The second difficulty is perhaps more fundamental, in the sense that a complex statistical analysis cannot be justified in the absence of detailed statistical input data. This issue has been the subject of considerable debate in recent years, and a new family of non-probabilistic, or "possibilistic", assessment methods has been derived, including (i) interval analysis, (ii) convex modelling, and (iii) fuzzy set theory.

The developments in probabilistic and possibilistic analysis have tended to take place independently, and there has been little work on the relationship between them. By introducing the concept of a safety margin to possibilistic methods, the present work seeks a unified approach to the assessment of structural integrity that encompasses both probabilistic and possibilistic methods. It has been found that FORM, SORM and all three possibilistic methods can be cast in terms of a constrained minimisation problem involving the safety margin and a suitable objective function. The resulting analysis can be used to assess the system reliability under a specified level of system uncertainty, or to derive the maximum allowable uncertainties (or tolerances) for a specified level of reliability. Particular attention is now being focused on problems associated with structural dynamic systems, and an experiment involving a beam with adjustable mass attachments is being employed as part of the study.

Relevant/Recent Publications

• R. S. Langley, D. F. Johnson. 'Models of uncertainty in structural dynamics'. 138th Meeting of the Acoustical Society of America, Columbus, Ohio, November 1999.

Principal Investigator & Researchers

• Professor R. S. Langley
• Dexter Johnson

Funding Body

• Vibro-Acoustic Sciences Inc, San Diego, USA
• ORS award, September 1997 - September 2000