Optimization in engineering problems

Abstract

This thesis addresses the application of optimization methods to engineering design problems, focusing on structural systems. It reviews linear programming (LP), nonlinear programming (NLP), and multi-objective optimization techniques. Four case studies are solved: (1) a scaffolding support system (LP); (2) a beam design problem (NLP); (3) a truss design problem (NLP); and (4) a water-tank column design with competing objectives (minimize mass, maximize natural frequency). For each problem, equilibrium equations and constraints are derived from mechanics, and the optimization model is implemented in MATLAB and Python. The results yield optimal designs under given constraints, with engineering insights drawn from load distribution, weight reduction, and vibration analysis. All computational results (numerical from python and graphical from MATLAB) agree, validating the formulations. Overall, the thesis demonstrates how combining optimization algorithms with mechanics principles can yield effective structural designs.

This thesis addresses the application of optimization methods to engineering design problems, focusing on structural systems. It reviews linear programming (LP), nonlinear programming (NLP), and multi-objective optimization techniques. Four case studies are solved: (1) a scaffolding support system (LP); (2) a beam design problem (NLP); (3) a truss design problem (NLP); and (4) a water-tank column design with competing objectives (minimize mass, maximize natural frequency). For each problem, equilibrium equations and constraints are derived from mechanics, and the optimization model is implemented in MATLAB and Python. The results yield optimal designs under given constraints, with engineering insights drawn from load distribution, weight reduction, and vibration analysis. All computational results (numerical from python and graphical from MATLAB) agree, validating the formulations. Overall, the thesis demonstrates how combining optimization algorithms with mechanics principles can yield effective structural designs.