Optimal shakedown design of spherical shell

Tomas Ulitinas

Doctoral dissertation

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Optimization problem elastic-plastic spherical shell at shakedown using energy principles, the nonlinear mathematical programming, numerical methods of mechanics are analyzed affected by repeated-variable load (RVL) in the dissertation. Equilibrium finite element method applied to discretization of spherical shell under the assumption of small displacements. Complete equations system of internal forces and deformation analysis problem of elastic-plastic spherical shells at shakedown state is basis of mathematical models of optimization problems. The limits of displacement (serviceability limit state) at shakedown input near the yield conditions (ultimate limit state) in the optimization problems.

The dissertation consists of an introduction, three chapters, conclusions and suggestions, references, author of publications on the dissertation topic and annexes.

Research problem, topicality of the work, research methodology, goal of the task are discussed in the introductory chapter. Doctoral student publications, conferences and dissertation structure and chapters volumes are presented in the end of chapter.

An analytical review of the science literature dissertation topic was performed in the first chapter. The optimization of spherical shells are analyzed at shakedown state: discretization problem, principles of mechanic’s energy principles,  application of the mathematical programming. Conclusions about the dissertation objectives actuality are made in the end of chapter.

In the second chapter discretization of spherical shell is developed equilibrium finite element: the basic equations and matrix expression dependency methodologies, performed a comparative analysis. Also the calculation of elastic shells are detailed. After that the mathematical models of the stress and strain state are formulated acting single load. Conclusions about equilibrium finite elements usefulness by calculating shells are made in the end of chapter.

In the third chapter the minimum limit internal force problem and its distribution of spherical shell, at shakedown are realized, when displacements are restricted. Stress and strain analysis are performed, possible displacements limits are set, when the material is elastic-plastic. Conclusions are made about dissertation author created methodology for spherical shell optimization at shakedown state in the end of chapter.

7 articles have been published on themes of the dissertation: 3 in ISI Web of Science database, 1 in ISI proceeding conference materials, 2 in other database, 1 in international conference database. Dissertation approved in the 4 scientific conferences, including two international.

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DOI: https://doi.org/10.20334/2306-M

Book details

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Imprint No:
145×205 mm
128 p.
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