A method for solving problems of bending rod optimization taking corrosion into account

Abstract

The article offers and justifies a method for solving a problem of optimal design of bent rods exposed to aggressive media. The problems of such class have special place among the problems of optimal design, which is explained by the fact that modeling corrosion deformation in structural elements requires solving not only the equations of solid mechanics, but also the system of differential equations describing the accumulation of geometric damage and including stress functions. The authors analyze existing approaches to solving these problem and problems of these approaches. On the basis of this analysis a fundamentally different approach to solving some problems of optimal design of bending rod elements that function in aggressive media is proposed, the statement of a problem, the numerical solution of which requires much less computational cost, and the result is the same as for the traditional problem statement, is proposed and justified. The authors consider a problem of vector optimization by two criteria: minimum area and perimeter of a cross-section at the time of exhaustion of the bearing capacity. The objective function includes the weight coefficient , taking into account the influence of cross-sectional perimeter. A modified scheme for solving the optimization problem is created, which involves a module for one-dimensional optimization by parameter . The proposed method is based on the assumption that there is only one value of the coefficient of perimeter influence, for which the solutions of problems in both traditional and new statements coincide. To compare these results correctly, it is necessary for a cross-section to be represented in both statements by a set of rectangular fragments both at an initial time and at a time corresponding to the limit state, so the model of corroding equivalent crosssection is used. A numerical illustration demonstrates almost complete coincidence of the solutions for both problem statements. At the same time utilization of developed method allows reducing the computational cost by several orders of magnitude compared to traditional methods for solving problems of this class.