Romanas Karkauskas

Optimisation of geometrically non‐linear elastic‐plastic structures in the state prior to plastic collapse

Abstract A mathematical model and calculation algorithm for geometrically non‐linear structure cross‐sectional optimisation are developed. Inelastic strains in the state prior to plastic collapse are evaluated. The algorithm is obtained combining the extreme energy principle for minimum value dissipated power and mathematical programming theory in concert with a large displacement analysis. An evaluation of dissipative features by employing inelastic strains finally results in a significant reducement of structure carrying capacity resource versus accounting its elastic response only. The safety requirements of structure involve stability conditions in addition to the strength ones. Stability conditions define the minimum cross‐sectional and slenderness values of structural members. An evaluation of the above‐mentioned factors restrict a free development of plastic strains, thus an optimal structure generally is in a state prior to plastic failure. The problem is solved iteratively, as the employed values...

Optimization of elastic‐plastic geometrically non‐linear lightweight structures under stiffness and stability constraints

Abstract An actual structural design, especially that of lightweight structures, must evaluate strength, stiffness and stability constraints. A designed structure must satisfy optimality criteria. One faces known difficulties when trying to implement several from above mentioned requirements into optimization problem for further successful numerical realisation. A method to formulate the optimization problem, incorporating all above described criterions, mathematical model and algorithm to solve it numerically, taking into account the geometrically non‐linear structural behaviour are presented for truss type structure. In each optimization cycle the member forces obtained in the previous optimization cycle via elastic‐plastic non‐linear analysis procedure are employed to obtain the new optimal design values. During the optimization procedures, the tension members are assumed to be loaded up to the yield limit, compression members are assumed to be stressed up to their critical limits, the nodal displaceme...

Truss optimization under complex constraints and random loading

Abstract An actual design of light‐weight structures must evaluate strength, stiffness and stability constraints as well as the nature of external loading. A designed structure must satisfy optimality and safety criterions per prescribed maintenance period. One faces the known difficulties when trying to implement several from the above‐mentioned requirements into optimization problem for further successful numerical realisation. A method to formulate the optimization problem, incorporating all above described criterions, the mathematical model and algorithm to solve it numerically, taking into account the stochastic nature of external loading, are presented for elastic‐plastic truss‐type structure.

The Analysis of Geometrically Nonlinear Elastic-Plastic Space Frames

Abstract The establishment of the real stress-strain state of the structure is one of the most important problems for designing and undertaking the reconstruction of building constructions as well as making calculations for the purpose of optimizing cross-sections of various structural elements. This task can be achieved by analysing the structure as a geometrically nonlinear system (refusing an assumption of small displacements) and taking into consideration plastic deformations. Modern computer technologies and mathematical tools enable us to perform strength analysis of space structures and to increase the accuracy of stress-strain state analysis. The present paper develops a technique for constructing a finite element tangent matrix for the nonlinear analysis of the space frame structure aimed at determining plastic deformations. The mathematical models of the problems based on static and kinematic formulations using the dual theory of mathematical programming were created for analysis. Strength condi...