Optimization of Plane Frames with Variable Cross-Section

Nowadays, in structural engineering, many elements in structural systems are selected with variable cross-sections for some purposes. The optimization problem helps to define the suitable dimensions of elements for the optimal weight of the system under given loading and other effects. In the studies of optimization, it is applied many methods depending on the characteristics of the problem. The article uses the Gradient and graphic methods to optimize plane frames with constant and variable cross-sections. The authors established the relationship between internal forces and displacements of the element ends with different boundary conditions using force and displacement methods. With the development of technology, it is allowed to use programming software to avoid mathematical difficulties. The calculation procedure of the considered optimization problem is written in the programming software MATLAB in the article. The obtained results are compared with those of other methods to verify the applied method’s accuracy, reliability and effectiveness.