Tamprių-plastinių prisitaikančių sistemų optimizacija su standumo ir stabilumo sąlygomis

Abstract

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 considered in shakedown theory. Applying the classical Melan and Koiter theorems, it is possible to analyse only simple systems at shakedown by elementary methods. Meanwhile for civil engineering, calculation of any complexity elastic–plastic structures subjected by variable repeated load is relevant. Growing number of scientific works dedicated to adapted structure calculation shows importance of these researches. Solution of structure optimization problems at shakedown is difficult as stress–strain state of dissipative systems depends on loading history. Not only general point of adapted structure analysis and optimization theory is solved in dissertation, but also new methods and algorithms of bar–structure optimization are presented. Also new potential, which is provided by connections between mathematical programming and extremum energy principles, are shown for formulation of analysis and optimization problems of shakedown theory and their numerical solution. It is shown application possibilities of strain compatibility equations for formulation of new mathematical models of residual displacement variation bound calculation problems. Technique of bar–structure optimization is implemented: new non–linear mathematical models for frames (under strength and stiffness constraints) and trusses (with stability conditions (EC3)) optimization problems, solution algorithms, numerical experiments are carried out. Technique of incremental analysis for unloading phenomenon fixation is created; numerical experiment is carried out for bending plate with von Mises yield conditions.