Parametric Optimization of Thin-Walled 3D Beams with Perforation Based on Homogenization and Soft Computing.

Area of Science:

• Mechanical Engineering
• Materials Science
• Computational Mechanics

Background:

• Automated and digitized production enables complex thin-walled beam cross-sections with high precision.
• Optimization opportunities now extend beyond dimensions to include bending angles and openings along the beam length.
• Multi-criteria optimization is necessary, balancing stiffness (compressive, bending, shear) with production cost and weight.

Purpose of the Study:

• To propose a comprehensive procedure for optimizing open thin-walled beams with varying cross-sections and openings.
• To develop and apply algorithms for traditional and soft computing optimization.
• To introduce a novel numerical homogenization method for efficient analysis.

Main Methods:

• Utilizing the finite element method (FEM) without requiring full computational stress analyses.
• Implementing a shell-to-beam homogenization procedure based on equivalent strain energy between 3D RVE and beam representations.
• Developing algorithms for traditional and soft computing optimization.

Main Results:

• A complete optimization procedure for thin-walled beams with open sections and longitudinal openings is established.
• The method bypasses the need for solving systems of equations in FEM, except for building the stiffness matrix.
• The numerical homogenization procedure enables rapid optimization.

Conclusions:

• The proposed procedure offers a fast and efficient method for optimizing various open thin-walled beam sections.
• The technique is versatile and can be readily implemented in development environments like MATLAB.
• This approach facilitates the design of optimized thin-walled beams with improved performance characteristics.