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 (usually both cases are called cyclic–plastic collapse). 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... [to full text]

Disertaciniame darbe, pasitelkus deformuojamo kūno mechanikos energinius principus ir matematinio programavimo teoriją, iš vieningų pozicijų išnagrinėtos tiek tamprių, tiek tamprių-plastinių sistemų deformacijų darnos (Sen-Venano) lygtys. Sprendžiant energinio principo apie papildomos energijos minimumą pagrindu sudarytą ekstremumo analizės uždavinį, įrodoma, kad yra tik trys nepriklausomos Sen-Venano lygtys su atitinkamai performuotomis kraštinėmis sąlygomis. Prisitaikomumo teorija nagrinėja tamprių-plastinių konstrukcijų, veikiamų kintamos-kartotinės apkrovos, būvį, pasitelkdama tiek tamprumo, tiek plastiškumo teorijų pagrindines lygtis ir priklausomybes: disertaciniame darbe pavyko, pasinaudojant Kuno ir Takerio optimalumo sąlygomis, metodiškai pagrįstai įjungti į plastinį konstrukcijų skaičiavimą liekamųjų deformacijų darnos lygtis. Taigi, disertacijoje Kuno ir Takerio sąlygos originaliai pritaikytos tamprumo teorijos lygtims įtempiais ir asociatyvinio tekėjimo dėsnio išraiškoms plastiškumo teorijoje gauti. Pasinaudojant gautaisiais rezultatais patobulinta prisitaikančių lenkiamų plokščių optimizavimo teorija ir sukurti nauji tokių uždavinių sprendimo metodai. Netiesinių uždavinių matematiniai modeliai, sudaryti taikant pusiausvirų baigtinių elementų metodą, sprendžiami iteraciniu būdu, pasitelkus Rozeno projektuojamųjų gradientų algoritmą. Darbui būdinga tai, kad matematinio programavimo teorija optimizavimo problemos nagrinėjimą lydi nuo matematinio modelio sudarymo iki... [toliau žr. visą tekstą] / Adapted perfectly elastic-plastic structure satisfies strength conditions and it is safe with respect to cyclic-plastic collapse. But it can do not satisfy its serviceability requirements, for instance, stiffness ones. Therefore, not only strength, but also stiffness conditions-constraints should be included in the discrete mathematical models of bending plate parameter or load variation bound optimization problems (exactly such problems are considered in the dissertation). Using mathematical programming not only new optimization technique of bending plates at shakedown is developed, but also relation between Kuhn-Tucker conditions and strain compatibility (Saint-Venant) equations and dependences of associative yield law of the deformable body mechanics is showed in the dissertation. Mathematical models of nonlinear problems are constructed applying method of equilibrium elements and are solved by iterations using Rosen project gradient algorithm. The feature of this research work is that the theory of mathematical programming accompanies investigation of optimization problem from the construction of the mathematical model up to its numerical solution, at the same time revealing mechanical meaning optimality criterion of applied Rosen algorithm.

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]

Darbo tikslas – tampriųjų-plastinių strypų konstrukcijų (santvaros, rėmų), veikiamų kartotinės kintamosios apkrovos, prisitaikomumo proceso ir būvio įtempių ir deformacijų analizė optimalaus konstrukcijų projektavimo kontekste. Darbo aktualumas grindžiamas prisitaikančių konstrukcijų optimizavimo uždaviniuose figūruojančių standumo sąlygų-apribojimų kokybės gerinimo būtinumu. Prisitaikančių konstrukcijų deformacijų būvis priklauso nuo apkrovimo istorijos, o poslinkių ribojimui taikoma nepakankamai tiksli Koiterio sąlyga arba liekamųjų poslinkių influentinė matrica, nepagrįstai laikant, kad plastinio deformavimo procesas yra išimtinai holonominis. Anotuojamame darbe apkrovimo istoriją siūloma įvertinti, atliekant papildomą inkrementinę deformacijų būvio analizę. Tyrimai atlikti taikant idealiai tamprių plastinių santvarų ir rėmų techniškosios skaičiavimo teorijos prielaidas (maži poslinkiai ir deformacijos). Taikomi ekstreminiai energiniai mechanikos principai, matematinio programavimo teorija ir metodai. Inkrementinės analizės matematiniai modeliai sudaryti, besikeičiančias plastines deformacijas tapatinant su distorsijomis. Taip nustatomos konkrečios apkrovimo istorijos liekamųjų poslinkių kitimo maksimalios ir minimalios reikšmės. Gautieji rezultatai panaudoti optimizavimo uždavinių sprendiniams tikslinti ir, esant būtinumui, leidžiantys keisti pradines pagrindinio optimizavimo uždavinio sąlygas. Pateikti išsamūs skaitinių eksperimentų rezultatai. / The purpose of this work is analysis of stress-deformation state of perfectly elastic-plastic shakedown structures (truss, frames) subjected to repeated variable load in the context of optimal design. Relevance of this work is based on a need of improvement of accurateness of stiffness constrains in optimization problems of structures. Stress-deformation state of shakedown structures depends on its loading history, while for the restriction of displacements inaccurate Koiter’s condition or an influence matrix of residual displacements, on the wrong supposition that the process of plastic deformation is exclusively holonomic, is used. In this work is proposed to evaluate loading history by performing an additional incremental analysis of stress-deformation state. This research was performed invoking the assumptions of technical computing theory of perfectly elastic-plastic trusses and frames (small deformations and displacements). Mechanics extremum energy principles, mathematical programming theory and methods are applied. Mathematical models of incremental analysis are composed by indentifying volatile plastic deformations with distortions. Thus particular maximum and minimum values of residual displacements are found. Obtained results are used to verify optimal design problems solutions and change the restrictions of main optimimization problem if necessary. Comprehensive results of numerical experiments presented.