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AbstractThe paper focuses on the optimization of a perfectly elastic-plastic truss under repeated variable load. The improved mathematical model of truss volume minimization problem with strength, stiffness and stability constraints is presented. The assumptions of the calculation methods of the truss-like structures and the shakedown theory are applied. The evaluation of the stability of elements under compression is based on EC3 requirements and related to plastic deformations in the shakedown process to correct the interpretation of the stability constraints in mathematical programming problems. In the optimization problem, truss displacements are evaluated according to different reliability levels of the ultimate and serviceability limit states of EC. The proposed methodology is illustrated with a numerical example. The results are valid for the assumption of small displacements.

SantraukaDarbe pateikiama simetriškai apkrauto lėkšto sferinio kevalo saugos ribinio būvio analizė. Konstrukcijos fizikiniai parametrai, forma, matmenys, apkrova ir jos pridėjimo vieta ir kryptis yra žinomi. Nagrinėjamas tamprusis ir idealiai tamprus plastinis kevalas, pasitelkiant ekstreminį energetinį principą randami tikrieji įtempių ir deformacijų būviai. Tampraus būvio analizės uždavinio matematinis modelis formuluojamas taikant virtualių jėgų principą, o ribinės apkrovos nustatymo uždavinio matematinis modelis formuluojamas kaip netiesinis matematinio programavimo uždavinys.

ABSTRACTThe design of optimal elastic-plastic steel frames is improved by a new treatment of rigidity and yield conditions for a finite element under uniform load. It allows avoiding an investigation of loading history, herewith not increasing elements number, in case of nonlinear physical model of material. Also, structure's minimal volume is obtained using a new dispersion estimation methodology of the real cross-sections geometrical characteristics. The designing is implemented using MATLAB© environment toolbox « JWM SAOSYS Toolbox v0.42 » created by the authors.

SantraukaPrisitaikomumo teorija, nagrinejanti tampriai plastiškas konstrukcijas, veikiama kintamosios kartotines apkrovos, leidžia judamaja apkrova traktuoti kaip atskira kartotinai kintančiu jegu atveji. Apkrovai leidžiama “judeti” bet kuria konstrukcijos dalimi: nuo tilto vidurio, grižti atgal, vel i prieki ‐ taip universaliai ivertinama apkrovimo istorija, kuri yra lemiamas faktorius, nagrinejant plastines deformacijas patiriančios konstrukcijos itempiu ir deformaciju būvi. Straipsnyje atskleista galimybe taikyti prisitaikomumo teorijos metodus, sudarant teorinius santvaru optimizavimo uždaviniu matematinius modelius ir juos sprendžiant. Nagrinejama idealiai tampriai plastine žinomos geometrijos santvara, veikiama judamosios apkrovos. Sudaryti minimalaus tūrio santvaros ar javeikiančios apkrovos maksimizavimo uždaviniu matematiniai modeliai. Modeliuose ivertinamos ne tik konstrukcijos stiprumo (prisitaikomumo) ir standumo salygos, bet ir stabilumo netekimo galimybe esant plastinei santvaros darbo stadijai. Pasiūlyti nauji sprendimo algoritmai, pateikti skaitiniai strypu lankstines santvaros, veikiamos judamosios apkrovos, optimizavimo uždaviniu pavyzdžiai. Tyrimai atlikti, darant mažu poslinkiu prielaida.

ABSTRACTThe theory of mathematical programming is used, composing improved mathematical models of nonlinear load-oriented problem for frames at shakedown under stiffness constrains and performing its numerical experiment. Mathematical model of load variation bounds optimization problem contains strength and stiffness constrains. Complementary slackness conditions of mathematical programming prohibit taking into account the dechargable phenomena in some cross-sections, therefore analysis of residual deformation compatibility equations are performed, using linear mathematical programming. An elastic perfectly-plastic frame is considered. The results are valid for the small displacement assumptions.

AbstractIncremental method for shakedown analysis of the elastic perfectly plastic structures is based on the extremum energy principles and non-linear mathematical programming approach. Residual force increment calculation problem is developed applying minimum complementary deformation energy principle. The Rozen project gradient and equilibrium finite element methods were applied for solution. The Rozen optimality criterion (Kuhn-Tucker conditions) ensures compatibility of residual strains and allows plastic strain and residual displacement increment calculation without dual problem solution. The possibility to fix the structure cross-section unloading phenomenon during shakedown process was developed. The proposed technique is illustrated by annular bending plate residual force and deflection calculation examples, when the von Mises criterion is taken into account.

AbstractThe adapted plate load optimization problem is formulated applying the non-linear mathematical programming methods. The load variation bounds satisfying the optimality criterion in concert with the strength and stiffness requirements are to be identified. The stiffness constraints are realized via residual displacements. The dual mathematical programming problems cannot be applied directly when determining actual stress and strain fields of plate: the strained state depends upon the loading history. Thus the load optimization problem at shakedown is to be stated as a couple of problems solved in parallel: the shakedown state analysis problem and the verification of residual deflections bounds. The Rozen project gradient method is applied to solve the cyclically loaded non-linear shakedown plate stress and strain evaluation and that of the load optimization problems. The mechanical interpretation of Rozen optimality criterions allows to simplify the shakedown plate optimization mathematical model and solution algorithm formulations.

AbstractThe study describes how in Lithuania (mostly in Vilnius) during some past decades a new trend of investigations in structural mechanics thanks to Aleksandras Čyras' (1927–2001) research and organisational activities has been developed. The main distinguished features of the trend are: application of mathematical programming, and especially the duality theory, to the optimization of elastic-plastic and other structures, formulation of mathematical models of structural mechanics problems, elaborating algorithms and programmes for their solution. The advantages of the research results are shown, a large information concerning the publication of the results and the evolution of investigations initiated by A. Čyras are presented.