Optimização em Sistemas de Engenharia Mecânica

Objectives

Provide fundamental knowledge on optimization of mechanical structures and systems, the required methodologies and in the application of advanced simulation and optimization software, necessary for analysis and optimal design in Mechanical Engineering. Train the student in the application of computational models, namely comining finite element and optimization methodologies in the analysis and optimization of Mechanical Engineering systems.

Syllabus

Optimization: Design variables, objective function and constraints. Necessary and sufficient conditions. KKT conditions, classification of constraints, Lagrange multipliers and Post-Optimality. Mathematical programming algorithms. Transformation methods for problems with constraints: Penalty and Augmented Lagrangian. Structural optimization: Topology, shape, material and size optimization of structures and mechanical systems. Objective functions and constraints in the Optimization: Design variables, objective function and constraints. Necessary and sufficient conditions. KKT conditions, classification of constraints, Lagrange multipliers and Post-Optimality. Mathematical programming algorithms. Transformation methods for problems with constraints: Penalty and Augmented Lagrangian. Structural optimization: Topology, shape, material and size optimization of structures and mechanical systems. Objective functions and constraints in the design of mechanical structures and systems. Sensitivity analysis: finite differences and analytical derivatives. Direct differentiation and adjoint variable method. Surfaces of response. Multiobjective optimization: Pareto optimum, transformation methods and genetic algorithms. Application of optimization techniques in the design of structural mechanical components, mechanical systems, thermal problems, fluid mechanics or biomechanics.

Prerequisites

Mechanics of Materials, Solid Mechanics, Computational Mechanics.

Cross Competence Component

Critical and Innovative Thinking (Creativity and approaches to problem solving); Interpersonal Skills (Oral presentations, communication skills and teamwork); Intrapersonal Skills (Self-discipline, enthusiasm, perseverance, and self motivation). The assessment of these skills has 10% weight in the final project grade.

Programming And Computing Component

The computational homework and the final project require programming MATLAB, Python ( or other equivalent) language.

Ethical Principles

All members of a group are responsible for the group’s work In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.