Implementation of an optimization algorithm using modified Lagrange functions on the example of a steel hinge-rod system

An example of the optimal design of a steel truss with the use of modified Lagrange functions is considered. To solve the problem, it is necessary to select the cross-sectional areas of the truss at a given interval by minimizing its volume, provided that the regulatory requirements for strength and rigidity are met. The external diameters of the sections of the truss elements vary. A detailed algorithm for solving the problem is presented. The algorithm is implemented in the mathematical package MathCAD, which allows you to visually trace the sequence of commands, as well as receive graphs reflecting the state of the problem at each iteration.