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Prisitaikomumo teorija, nagrinėjanti tampriai plastiškas konstrukcijas, veikiama kintamosios kartotinės apkrovos, leidžia judamąją apkrovą traktuoti kaip atskirą kartotinai kintančių jėgų atvejį. Apkrovai leidžiama „judėti“ bet kuria konstrukcijos dalimi: nuo tilto vidurio, grįžti atgal, vėl į priekį – taip universaliai įvertinama apkrovimo istorija, kuri yra lemiamas faktorius, nagrinėjant plastines deformacijas patiriančios konstrukcijos įtempių ir deformacijų būvį. Straipsnyje atskleista galimybė taikyti prisitaikomumo teorijos metodus, sudarant teorinius santvarų optimizavimo uždavinių matematinius modelius ir juos sprendžiant. Nagrinėjama idealiai tampriai plastinė žinomos geometrijos santvara, veikiama judamosios apkrovos. Sudaryti minimalaus tūrio santvaros ar ją veikiančios apkrovos maksimizavimo uždavinių matematiniai modeliai. Modeliuose įvertinamos ne tik konstrukcijos stiprumo (prisitaikomumo) ir standumo sąlygos, bet ir stabilumo netekimo galimybė esant plastinei santvaros darbo stadijai. Pasiūlyti nauji sprendimo algoritmai, pateikti skaitiniai strypų lankstinės santvaros, veikiamos judamosios apkrovos, optimizavimo uždavinių pavyzdžiai. Tyrimai atlikti, darant mažų poslinkių prielaidą., in English. The shakedown theory, which analyses elastic-plastic constructions, subjected by variable repeated load, enables treating moving load as a separate type of variable repeated load. The load is allowed to „move“ at any part of the construction: from the middle of the bridge, to turn back, again move ahead – in this manner loading history is universally evaluated and it is a crucial factor, considering stress-deformation state of structures under plastic deformations. This paper reveals a possibility to apply methods of shakedown theory for creation and solution of theoretical optimization mathematical models of trusses. The perfectly elastic-plastic loaded by moving load truss is considering. The mathematical models of the minimal volume truss or it acting load maximization problems are created. There are evaluating not only strength (shakedown) and rigidity restrictions, but also stability restriction in case of plastic state of truss in models. There is proposed new solution algorithms and introduced numerical examples of truss optimization in case of moving load. The results are valid for the small displacement assumptions.

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]

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]

Perfectly elastic-plastic truss of known geometry adapted to variable repeated load (only its lower and upper variation bounds are prescribed) is considered. Non-linear mathematical models of truss minimum volume problem are formulated. Not only strength and stiffness constraints are included in problem formulations, but also possible bar buckling is taken into account. As during volume minimization stiffness of truss elements is changing, non-linear optimization problem is solved step-by-step. Solution algorithm allows the evaluation of bar unloading phenomenon, which often occurs during shakedown process. The technique is illustrated by numerical example of pin-joined bar system calculation. The results are valid for the small displacement assumptions.