Optymalizacja topologiczna konstrukcji budowlanych wykonanych z niejednorodnego materiału z założoną klasą anizotropii

Radosław Tomasz Czubacki

Abstract

The Thesis concerns the topology optimization methods for designing continuum and skeletal engineering structures. The first part of the paper deals with material design methods in which the optimal structure is made of an anisotropic non-homogeneous material. The material design methods are delivered for three cases of anisotropy: full anisotropy in which no constraints are imposed on the Hooke tensor, cubic symmetry and isotropy. These methods give information about topology of the structure and simultaneously they deliver values of the optimal elastic moduli along with the optimal orientation of the material. The isoperimetric condition which can be interpreted as a cost condition, is expressed as a linear combination of the elastic moduli. The work discusses the optimum solutions corresponding to the anisotropic material design, isotropic material design and cubic material design. Moreover, the dissertation discusses the problem of optimal orientation design for ortotropic materials. In the latter case, the elastic moduli of the ortotropic material are prescribed and the only unknowns are the vectors defining the orientation of the material.

The second part of the dissertation concerns the problem of minimal weight of arch structures subjected to transmissible vertical loads. In case of the pin supports lying at the same level this problem has been for the first time discussed by William Prager and George Rozvany in 1970's. The arches are bending-free; consequently they are not subject to transverse shear. The Prager structures are uniformly stressed and the lightest among all bending-free structures transmitting the given load to the given support. The optimum design problem has been set variationally and extended to the case of arches unevenly supported on the level determined by a specific ruled surface. The optimization problem of minimal weight results in two mutually dual auxiliary problems similarly as in case of free material design (FMD). New efficient numerical algorithms are put forward.

Diploma typeDoctor of Philosophy
Author Radosław Tomasz Czubacki (FCE / ICE)
Radosław Tomasz Czubacki,,
- The Institute of Civil Engineering
Title in PolishOptymalizacja topologiczna konstrukcji budowlanych wykonanych z niejednorodnego materiału z założoną klasą anizotropii
Languagepl polski
Certifying UnitFaculty of Civil Engineering (FCE)
Disciplineconstruction / (technology domain) / (technological sciences)
Scientific discipline (2.0)2.6 civil engineering and transport
Start date25-11-2015
Defense Date20-05-2020
Supervisor Tomasz Denis Lewiński (FCE / ICE)
Tomasz Denis Lewiński,,
- The Institute of Civil Engineering

External reviewers Dariusz Bojczuk - Silesian University of Technology (PolSL)
Dariusz Bojczuk,,
-

Łukasz Jankowski - [Instytut Podstawowych Problemów Techniki Polskiej Akademii Nauk (IPPT PAN)]
Łukasz Jankowski,,
-
- Instytut Podstawowych Problemów Techniki Polskiej Akademii Nauk
Pages180
Keywords in Englishtopology optimization, material design, archgrids (Prager structures)
Abstract in English

The Thesis concerns the topology optimization methods for designing continuum and skeletal engineering structures. The first part of the paper deals with material design methods in which the optimal structure is made of an anisotropic non-homogeneous material. The material design methods are delivered for three cases of anisotropy: full anisotropy in which no constraints are imposed on the Hooke tensor, cubic symmetry and isotropy. These methods give information about topology of the structure and simultaneously they deliver values of the optimal elastic moduli along with the optimal orientation of the material. The isoperimetric condition which can be interpreted as a cost condition, is expressed as a linear combination of the elastic moduli. The work discusses the optimum solutions corresponding to the anisotropic material design, isotropic material design and cubic material design. Moreover, the dissertation discusses the problem of optimal orientation design for ortotropic materials. In the latter case, the elastic moduli of the ortotropic material are prescribed and the only unknowns are the vectors defining the orientation of the material.

The second part of the dissertation concerns the problem of minimal weight of arch structures subjected to transmissible vertical loads. In case of the pin supports lying at the same level this problem has been for the first time discussed by William Prager and George Rozvany in 1970's. The arches are bending-free; consequently they are not subject to transverse shear. The Prager structures are uniformly stressed and the lightest among all bending-free structures transmitting the given load to the given support. The optimum design problem has been set variationally and extended to the case of arches unevenly supported on the level determined by a specific ruled surface. The optimization problem of minimal weight results in two mutually dual auxiliary problems similarly as in case of free material design (FMD). New efficient numerical algorithms are put forward.

Thesis file
Czubacki_Rozprawa_zab_kom.pdf 8.15 MB
Reviews
Recenzja rozprawy doktorskiej mgr inż. Radosława Czubackiego wykonana przez dr hab. inż. Dariusza Bojczuka prof. PŚ of 16-12-2019
6.47 MB
Recenzja rozprawy doktorskiej mgr inż. Radosława Czubackiego wykonana przez dr hab. inż. Łukasza Jankowskiego prof. IPPT PAN of 23-12-2019
5.67 MB

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