Geometry and mass optimization of box-shape beams with non-linear walls for local buckling due to bending

This article explores the possibility of optimizing geometry and mass of a beam based on the conditions for ensuring local buckling. The subject of the study is a box-shaped beam with non-linear walls. This type of beam is unpopular because it has not been studied properly. This fact only indicates its novelty. However, researches and experiments prove that this type of beam is superior to current types of beams in terms of local buckling. This indicates relevance of further research and use of beams with non-linear walls in structures, where local stability is the main aspect in choosing the geometric dimensions of the beam. To optimize this type of beam, a numerical experiment was performed by using the finite element method in ANSYS. The experiment confirmed the possibility of geometric optimization with maintaining similar performance of local stability. The results of this study are obtained formulas. The first formula is required to find the local buckling stresses of box-shaped beams with optimized non-linear walls. This formula was found by approximating the results of a numerical experiment using the least squares method in a MathCAD. The second formula is required to find benefit in mass when using optimized geometry.