Radul O. Load-carrying capacity and optimal designing of bar structures taking into account general and local corrosion

Object of research - the problem of ensuring of reliability and reducing consumption of materials in bar structures that are operated in aggressive environments, providing the durability of the structures. The objective is to create a unified approach to solving problems of determination of load-carrying capacity and optimal design of corroding bar structures taking into account local corrosion in junctions of bars. Mathematical methods of analysis of processes have been applied to resolve this problem using modern computer technologies. Stressed-strained state of structures has been analyzed using finite element method. Methods of sliding tolerance and random search have been used to solve the task of optimization. In this research the new statement of problem of optimal designing of corroding bar structures has been offered. This statement includes two calculation schemes: bar structure as a whole and planar-stressed plates in places of junctions of bars. New and effective semi-analytical algorithm of solving the system of differential equations is offered and substantiated. The modified triangular finite element of variable thickness is developed for more accurate modeling of the corroding process. New algorithm of solving the task of nonlinear mathematical programming is offered and substantiated. It is based on simultaneous application of sliding tolerance method as well as the random search method for solving problems of continuous and discrete optimization. For the first time the tasks of durability determination and optimal design of bar structures have been solved in a probabilistic formulation using modified models of geometrical damage accumulation, that consider random components of corrosion process. By means of developed software new tasks of optimal designing of bar structures have been solved taking into account local corrosion in bar junctions. The analysis of numerical date is given and it shows that the optimization of size and shape of cross-sections only of bars does not allow providing given operational time of structure as a whole due to the fact that the structure may fail because of the break in junctions of bars, caused by local corrosion. Method of calculating the load-carrying capacity, durability and optimal design of corroding structures has been introduced into educational process and applied in developing of the project of reconstruction of the railway overpass of OJSC Dnipropolimermash. The developed software can be used by research organizations in investigation and designing of corroding bar structures.