Algorithm for building structures optimization based on Lagrangian functions
A review of modern algorithms and optimization programs is presented, based on which it is concluded that there is no application software in the field of optimal design of building structures. As part of solving this problem, the authors proposed numerical optimization algorithms based on conditionally extreme methods of mathematical programming. The problem of conditional minimization is reduced to a problem of an unconditional extreme using two modified Lagrange functions. The advantage of the proposed methodology is a wide range of convergence, the absence of requirements for convexity of functions on an admissible set of variation parameters, as well as high convergence, which can be achieved by adjusting the parameters of the objective and constraint functions. Verification of the developed methodology was carried out by solving a well-known example of ten-bar truss optimization. A comparison of the results obtained by other sources with the copyright ones confirmed the effectiveness of the presented algorithms. As an example, the problems of optimizing the cross-section of a steel beam have also been solved. Automation of the algorithms is performed in mathematical package MathCAD, which allows you to visually trace the sequence of commands, as well as obtain graphs that reflect the state of the task at each iteration. Thus, the authors obtained an original methodology for solving the optimization problem of flat bar structures, which can be extended to solve the problem of optimal design of general structures, where the optimality criterion is defined as material consumption, and the given structural requirements are presented as constraint functions.