MATLAB Implementation of Structural Optimization Using Penalty Function Method

In modern engineering, structural optimization programs serve as powerful tools that can enhance structural performance by optimizing design parameters. The penalty function method is a widely-used optimization algorithm that incorporates constraint handling by adding penalty terms to the objective function. The combination of these tools effectively solves nonlinear programming problems, resulting in more optimized design solutions. From a code implementation perspective, MATLAB provides an ideal environment for structural optimization through its optimization toolbox and matrix computation capabilities. Key implementation aspects include: defining the objective function with penalty terms that increase when constraints are violated, using MATLAB's fmincon or fminunc functions for unconstrained optimization after penalty transformation, and implementing iterative penalty parameter updates to ensure convergence. Research demonstrates that employing structural optimization programs with penalty function methods significantly improves engineering design efficiency and accuracy while reducing costs and risks. The MATLAB implementation typically involves creating functions for objective evaluation, constraint handling, and penalty parameter adjustment, utilizing built-in optimization solvers with proper configuration of algorithm options like tolerance settings and maximum iterations.