Area Optimization of Bending Members with Different Shapes in Terms of Pure Bending

This study focuses on the optimization of the total cross-sectional area of bending elements with different shapes under the influence of loads. The optimization process is conducted using the Grey Wolf Optimization (GWO), which is a metaheuristic algorithm implemented in the Matlab program. Bending elements offer a wide range of usage options, making simple bending analysis highly significant and applicable in various areas. Therefore, performing optimization studies and achieving designs based on structural constraints are of great importance, aiming to control material utilization at a defined level (minimizing raw material consumption), attain cross-sectional shapes with optimum areas as well as reduce costs. To determine the cross-section of elements with two distinct shapes, the algorithm assigns variables for section lengths and heights, subsequently locating the centre of gravity of the system. Following this step, the distances from the centres of each component to the axes are calculated, enabling the computation of moment of inertia for both directions. Once the moments of inertia are obtained, the bending moments and stresses are computed. Considering that the design of each section is desired based on a specific stress value, constraint checks are conducted, and the decision regarding whether to penalize or not penalize the objective function is determined, ultimately leading to achieving the minimum area for each shape. Notably, due to the variation in shapes, it is observed that each element possesses a different minimum area.