Nonlinear optimization of plane frames with variable section stiffness of columns using Lagrange multiplier method

Abstract

The optimization problem of structures has an important role and significant meaning. In order to determine the appropriate dimensions or shapes of structure elements for optimal volume of material under the effect of certain loading or with the given sizes of elements the structures can be subjected maximum loading. This paper presents the nonlinear optimization problem of weight of plane frames with variable section stiffness of columns according to the criteria of strength, stiffness and stability with the help of numerical method. The nonlinear optimization problem is solved by the Lagrange multiplier method. The procedure of calculation of nonlinear optimization of plane frames with variable section stiffness of columns is established and implemented using Mathcad calculation programming software.