Trihedral lattice supports geometry optimization according to the stability criterion

The study proposes a technique for optimizing trihedral lattice tower structures from the condition of maximum critical load. Towers with a cross section of elements in the form of round pipes are considered. The load is represented by a horizontal concentrated force at the upper end of the tower, simulating the operation of a wind turbine. A constraint on the constancy of the mass of the structure is introduced. The variable parameters are the width of the tower, which varies in height, the height of the panels, the external diameters of the cross-section of the chords and lattice. The solution of the nonlinear optimization problem is performed in the MATLAB environment using the Optimization Toolbox and Global Optimization Toolbox packages. A tower of constant width is taken as the initial approximation. The calculation of the critical load is performed by the finite element method in a linear formulation by solving the eigenvalue problem. To solve the nonlinear optimization problem, the interior point method, the pattern search method and the genetic algorithm are used. The efficiency of the listed methods is compared. It has been found that the interior point method is the most efficient. The critical load for the optimal tower compared to the tower of constant width with the same mass increased by 2.3 times.