Console shapes based on the Castigliano variational principle

Abstract

The purpose of this work is to study the forms of consoles based on the Castigliano variational principle using the duality of setting problems on a conditional extremum with integral connections and comparison them with traditional forms. A sufficient condition for achieving the global extremum of the functional of the goal is the introduction of the energy principle into the procedure for solving the isoperimetric problem. The purpose of the shape determination task is to distribute the material in such a way that a global minimum of potential deformation energy is achieved under variable stresses, shape parameters and imposed constraints. In the particular case under consideration, restriction on movement are introduced without violation of the energy principle and isoperimetrically. It was found that on a console loaded at the edge with concentrated force, it is more profitable to change the width of the section (saving 33% of the material) than its height (saving 19%).