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The 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.

The paper presents a mathematical model for bar cross-sectional optimization of steel structureunder strength, stiffness and stability constraints. The theory of mathematical programming of extremum energy principles has been used for developing the introduced model. Solving a non-linear mathematical problem is subject to the MatLab programming environment. Because of the existing relationship between elastic response values and the optimized parameters of the structure, the problem has been calculated iteratively. The calculation algorithm has been applied to a frame with a truss span. The framing structure has been discretized by finite bar elements. The minimum volume of the structure that has not reached full plastic collapse but its individual members have experienced plastic deformation has been designed. According to the obtained optimal project, standard tube profiles have been chosen. Santrauka Straipsnyje pateikiamas plieninių rėminių konstrukcijų strypų skerspjūvių optimizavimo uždavinio matematinis modelis, kuris leidžia įvertinti konstrukcijos stiprumo, standumo ir stabilumo reikalavimus. Optimizavimo uždavinio matematiniam modeliui sudaryti taikoma matematinio programavimo teorija ir ekstreminiai energiniai principai. Netiesiniam matematiniam programavimo uždaviniui spręsti taikoma MatLab programavimo aplinka. Dėl ryšio tarp konstrukcijos tampraus atsako dydžių ir optimizuojamų parametrų uždavinys sprendžiamas iteracijų būdu. Skaičiavimo algoritmas pritaikytas plokščiajam vieno tarpatramio rėmui su santvara. Rėminė konstrukcija diskretizuojama strypiniais baigtiniais elementais. Nustatytas minimalus konstrukcijos tūris, kai konstrukcija dar nepasiekusi visiško plastinio suirimo, tačiau atskiri jos elementai jau yra patyrę plastines deformacijas. Pagal gautąjį optimalų planą – strypų ribines įrąžas – parenkami standartiniai dėžiniai profiliuočiai.

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Abstract. This paper deals with the results of analytic, experimental and numerical investigation of the hollow and solid concrete-filled steel tubular simple beams. Overall interaction between the external thin-walled circular steel shell and the internal concrete core significantly increases the bending resistance, ductility and durability of such beams in comparison with the steel or concrete flexural members. The circular steel tubes have been chosen for investigation taking into account the simplicity of manufacture of concretefilled CHS by simple casting, or especially for forming the hollow concrete cores by centrifuging. The great torsional capacity of tubular members as well as great local buckling capacity of wall of CHS of concrete-filled members were taken into account too. For calculation of the bending resistance of such members two methods have been applied: one recommended by EC4, and, second, method of design based on the test data. Furthermore, obtained design results were compared to determine their interrelationship and with the results of carried out natural and numerical testing. Results of carried out investigation have proved sufficiently great durability and reserve of bending resistance of hollow and solid concrete-filled steel tubular simple beams. There is presented giving better agreement developed method for design of hollow and solid concrete-filled circular steel tubular simple beams based on test data what allows recommending the developed method to use in design practice.