Optimal design of cylindrical tanks with hard shell cover

Abstract

The article considers  parametric optimization of cylindrical fuel tanks with hard coating shells. In the designing and constructing of industrial tanks for the preservation of oil and chemical products in the region where seismic loading occurs, it is very important to analyze all combinations of loads that affect to the structures, and it is important to choice the optimal solusion of such conctraction. As a rule, such reservoirs are divided: underground and ground. Ground tanks are divided into: tanks with a floating lid, and with a lid that is rigidly fixed. Tanks are considered only shell structures, without additional stiffening ribs.

To solve the problems of parametric optimization, we consider the mathematical method of gradient descent, which was proposed by Rosen. The purpose of the method is to find the optimal solution for the structure using the input data through iterations design variables, and constraints that are superimposed on the response of the construction. The gradient descent method involves without preliminary selection of the structural cross-section of the construction and its modeling, which, taking into account the incoming data, leads to methods of connecting the structure to the hard disk of the earth or other structures, as well as to objective reasons.

Two versions of the calculated spatial models of fuel tanks were constructed using the finite element method. External static and dynamic loads in the form of seismic were set, since the construction of reservoirs is considered in seismically active regions of Ukraine. Using the new technique, design variables were set in the form of a shell thickness of 1 to 100 mm and Mises stress limits of 260 MPa and displacements along the X, Y, Z, 15 mm axes. The objective function is the mass of the fuel tank. Tank options differ in the geometry of the lid. For the first option - conical, for the second option - segmented. All geometric parameters, the number and type of finite elements, fixing conditions and types of loading are the same. The optimization cycles for calculating in two variants are 20. The objective function was built on the optimization cycles. The diagrams showed that the weight of the melted tank with a conical cover is 155.2 tons, for a fuel tank with a segment cover 187.5 tons. Thus, the fuel tank with a conical cover weighs 32.3 tons less than with a segment cover, and the maximum  stresses by Mises and displacement along the axes X, Y, Z, is inacceptable limits. We can conclude that a fuel tank with a conical cover of rigid fastening is a better option.