Mass optimization of a compressed cylindrical shell with limited life

Abstract

A new optimization model is proposed to design corrosion-affected structures with limited life. The optimization problem is stated as a nonlinear-programming problem. The mass of the structure is minimized. The design is considered optimal when physical wear and obsolescence arrive simultaneously. A smooth cylindrical shell compressed in the longitudinal direction is used to illustrate the model Keywords: smooth cylindrical shell, limited life, optimal design, corrosive medium Introduction. Thin-walled shell structures are used in many branches of mechanical engineering and construction. Quite often such structures are affected by a corrosive medium. Such a medium has a variety of effects on the behavior of shells. In most cases, just the surface layer of the shell is attacked, with corrosion products adsorbed on the surface as compact or loose formations. This affects the load-bearing capacity and performance of shells. Of considerable interest is the behavior of an optimal-design shell in a corrosive medium: What processes cause redistribution of the material among different structural members? How is the corrosion allowance determined if one of the objectives is reliable operation of the shell during a predefined service life? and How should the objective function and constraints be defined in formulating mathematical-programming problems? Among other questions are: How should a structure be designed so that its physical wear and obsolescence would arrive simultaneously? and which corrosion-damage and optimization models should be used to this end? Answers to these and other questions are especially important for the chemical industry where technologies are changed quite frequently, old technologies become economically unviable, and new technologies require fundamentally new equipment. This situation dictates a new strategy of search optimization: design a structure with limited life. The life of structures, in particular shells or shell-frame systems in media with a high concentration of chemically active substances, is determined by the corrosion allowance, which when exhausted brings the structure into a limiting state followed by failure.Optimization of corrosion-attacked structures with allowance for their life has recently been addressed in a number of studies. In particular, issues of durability of smooth and reinforced cylindrical shells in the optimal-design problem were considered in [1][2][3][4]18]. Further development of these studies was in more accurate simulation of corrosion processes and application of efficient problem-solving methods. Several versions of the optimization problem for structures interacting with corrosive media were analyzed in [5], where it was suggested to allow for durability by using the service life as one of the varied parameters. Optimal-design problems were solved both analytically and numerically. In the former case, use was made of the Kuhn-Tucker conditions and the Lagrangian multiplier method. In the latter case, the choice of one numerical method or another depend...