Extended shakedown theory on optimization of steel structures

Gediminas Blaževičius

Doctoral dissertation

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This doctoral thesis was inspired by the acceleration of the designing process of civil structures, which calls for new and effective computer-based designing methods. Modern design practice often features lightweight steel structures with complex architectural expression, which has to be designed integrally, without elemental decomposition. Integrated structural design uses optimization algorithms, which allows for finding the best structural solution for a sustainable, reliable and material-wise economical project. This PhD thesis demonstrates that optimization can present a substantial advantage for designing steel structures more efficiently both in terms of time and material resources.

An important shift in structural steel design over the recent decades has been the standard-based legitimisation of design in the elastic-plastic material state – when particular places in the structure are allowed to reach the yield stress point. Combining the principles of the plasticity theory and the optimal solution search algorithms allows for a considerable reduction of the volume (or mass) of structures and therefore means lower cost. However, the transition to the elastic-plastic structural design raises a fundamental problem – the exact loading history of a structure has to be known in advance. Having in mind real-life structures subjected to unpredictable atmospheric impacts and moving human-caused live loads, only an approximate estimation of load variation limits, rather than exact loading history, may be defined. A solution to this problem was provided by the shakedown theory half a century ago. The theory allows determining whether or not the limit state of a structure subjected to cyclic loading will be reached.

A lack of effective optimisation algorithms (as well as the need of high computer resources), which are needed to find solutions of the shakedown theory, was a holdback for a successful implementation of the theory in practice. Modern technology allows conjoining shakedown theory, optimization and ever stricter standardised design requirements in a single problem formulation. This poses a complex problem as contemporary European standards define very specific requirements of strength, stability, deformability and overal reliability of structural elements. A development of research on optimisation issues, which includes standard requirements with a combination of an adequate definition of plastic structural behaviour of steel structures, is the objective of this thesis. This work contains theoretical as well as practical formulations of optimal shakedown design problems for particular building structures – trusses, frames and circular plates. Mathematical formulations are based on energy principles, finite element method and mathematical programing. The thesis includes multiple numerical results as well as conclusions and suggestions.

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DOI: https://doi.org/10.20334/2349-M

Book details

Data sheet

Year:
2015
ISBN:
978-609-457-860-1
Imprint No:
2349-M
Dimensions:
145×205 mm
Pages:
156 p.
Cover:
Softcover
Language:
Lithuanian
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