Optimization problems (to which is dedicated this dissertation) of structural mechanics are introductory stage of structure optimum design based on principles of solid deformable body mechanics, mathematical programming theory, its methods and their mechanical interpretation. In order to base calculation on real operating conditions of structure, it is necessary evaluate as exact as possible structure material properties, external effects and other factors in mathematical models of optimization problems. Partially it is achieved by including plastic properties of material. Calculation and design of the structures, taking in to account plastic strains, allows to use their bearing capacity more efficiently and make more economic project (in this dissertation research is developed on the basis of perfect plasticity theory). From the other side, real effect for structure are often cyclic (variable repeated load character is also evaluated in this work). In the dissertation it is assumed that load is quasi–static and is characterised by load variation bounds (deterministic formulation of problems is considered). Under repeated loading a structure can lose its serviceability because of its progressive plastic failure or because of alternating strain. But, if residual forces together with variable part that do not violate the admissible bounds appear in the initial stage of loading, the structure adapts to existing load and further behaves elastically. This phenomenon is... [to full text]

Disertaciniame darbe išplėtota vieninga tamprių-plastinių prisitaikančių sistemų optimizavimo su stiprumo, standumo ir klumpamosios galios sąlygomis, taikant ekstreminius energinius principus, matematinio programavimo teoriją, šiuolaikines kompiuterines technologijas ir sąsajas su projektavimo standartais, metodika. Darbe parodyta, kad prisitaikomumo teorija yra bendriausias metodinis įrankis skirtas statybinių konstrukcijų skaičiavimui nuo įvairių apkrovų, įgalinantis išvengti detalios apkrovimo istorijos nagrinėjimo. Disertaciją sudaro įvadas, penkeri skyriai, rezultatų apibendrinimas, naudotos literatūros ir autoriaus publikacijų disertacijos tema sąrašai ir keturi priedai. Įvadiniame skyriuje aptariama tiriamoji problema, darbo aktualumas, aprašomas tyrimų objektas, formuluojamas darbo tikslas bei uždaviniai, aprašoma tyrimų metodika, darbo mokslinis naujumas, darbo rezultatų praktinė reikšmė, ginamieji teiginiai. Įvado pabaigoje pristatomos disertacijos tema autoriaus paskelbtos publikacijos ir pranešimų konferencijose sąrašas bei disertacijos struktūra. Pirmasis skyrius skirtas literatūros apžvalgai. Jame atlikta prisitaikančių konstrukcijų optimizavimo metodų apžvalga, išryškinta būtinybė pasitelkti sąsajas tarp teorinių optimizavimo metodų ir projektavimo standartų. Antrajame skyriuje aptariama konstrukcijų diskretizacija, sudaryti patobulinti projektinio ir patikrinamojo uždavinių matematiniai modeliai. Trečiajame skyriuje parodyta sąsaja tarp statybos inžinerijoje... [toliau žr. visą tekstą] / The optimization methodology of shakedow structures evaluating strength, stiffness and stability constraints and unifying extremum energy principles, mathematical programming theory, stat-of-the-art computer technologies and design standards was developed in the dissertation. There are shown in the work that shakedown theory is a generalized tool for calculation of civil engineering structures under different loading conditions that avoid detailed investigation of loading history. The dissertation consists of six parts including Introduction, 5 chapters, Conclusions, References and 4 Annexes. The introduction reveals the investigated problem, importance of the thesis and the object of research and describes the purpose and tasks of the paper, research methodology, scientific novelty, the practical significance of results examined in the paper and defended statements. 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. Chapter 1 revises used literature. The optimization methods of shakedown structures are reviewed and a demand of linkage between theoretical optimization methods and standards is highlighted. Chapter 2 describes the discretization of structures, the mathematical models for improved design and check problems was created. In the Chapter 3 the equivalence between load combinations of civil engineering... [to full text]

Šio darbo pagrindinis tikslas yra suprojektuoti ir sukurti internetinę matematinio programavimo ir modeliavimo sistemą. Šiam tikslui pasiekti buvo nagrinėjama matematinio programavimo samprata. Atlikta panašių matematinių programavimo sistemų bei matematinių funkcijų bibliotekų, skirtų įvairioms programavimo kalboms, analizė. Identifikuojamos ir nagrinėjamos problemos, kurios iškilo kuriant internetinę matematinio programavimo ir modeliavimo sistemą. Taip pat šiai sistemai parašytos testinės programos su C++, Java, Fortran programavimo kalbomis bei Netlib Repository LAPACK ir QT bibliotekomis. Sukurta sistema palyginta su Mathematica ir Scilab matematinio programavimo sistemomis. / The aim of this work is to design and develop web-based mathematical programming and simulation system. For this purpose were analyzed the concept of mathematical programming and performed analysis of similar mathematical programming systems and libraries of mathematical functions for various programming languages. Identified and analyzed the problems that arose in the development of an online mathematical programming and simulation system. Also, written test programs for created system in C++, Java, Fortran programming languages and Netlib Repository LAPACK, QT libraries. The developed system was compared with Mathematica and Scilab mathematical programming systems.