Optimization of geometrically nonlinear elastic plastic framework structures under displacement constraints

Michail Popov

Doctoral dissertation

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The optimization mathematical models of geometrically nonlinear elastic plastic frameworks structures optimization under displacement constraints are created in the thesis. Original solution algorithm was created for the optimization of geometrically nonlinear elastic-plastic frameworks structures under displacement constraints. The dissertation consists of introduction, 3 chapters, conclusions, references and 8 annexes.

The introduction reveals the investigated problem, the object of research and describes the purpose and tasks of the thesis, research methodology, scientific novelty, the practical significance of results examined in the thesis. The introduction ends in presenting the author’s publications on the subject of the defended dissertation, offering the material of made presentations in conferences and defining the structure of the dissertation.

Construction design and structures optimization problems correlation is describing in chapter 1. Short historical review of optimization methods and structures optimization analytical analysis are presented. Reviewing problematic of non-elastic geometrically nonlinear steel frame structures optimization under displacements constraints. Describing basic accepted assumptions and physical dependences and values describing structures real stress-strain state (SSS). Structure optimization problem mathematical model is presented. Algorithm for such optimization problem solution is suggested. Optimization problem numerical realization possibilities are presented.

Elastic calculation nonlinear analysis and elastic plastic structure’s analysis – methods for real structure’s stress-strain state determination are presented in chapter 2. Methods formulation, necessary values determination and possibility of numerical realization are presented. Usage of extreme energy principle for optimization problems substantiated. Numerical experiment results are presented.

Structure optimization under displacements constraints problem mathematical model is presented in chapter 3. Strategy of optimization problem calculation is detailed: displacements variation methodic, and extended algorithm convergence quality for geometrical nonlinearity occurring. Results of numerical experiment by suggesting algorithm are presented.

7 articles focusing on the subject of the discussed dissertation are published: one into Thomson ISI database; three in other databases; two in international conferences proceedings; one in Lithuanian conference proceeding. 6 presentations on the subject have been given in conferences at national and international level.

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DOI: https://doi.org/10.20334/2251-M

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Imprint No:
145×205 mm
134 p.
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