This short course provides the participants with the main tools to optimise the design of engineering structures. As designers, we are always looking for the best structure that satisfies a set of design constraints. Today, we have efficient mathematical algorithms and powerful finite element analysis software, which can be combined to allow the designer to achieve the optimum structural design, without increasing the development cycle and reducing manufacturing costs.

The goal of this course is to present the fundamental concepts of structural optimisation from an applied point of view and to provide the participants with enough autonomy to formulate and solve a general structural optimisation problem for themselves. The course combines brief lectures, for the explanation of the basic concepts, with hands-on workshops using spreadsheets, Python programming, and the commercial software Altair Optistruct, to solve selected application examples.

Course Programme

The course will be organised in six sessions during three days with the following topics and schedule:

Day 1 - Tuesday 13th July

Session 1

  • Introduction to design optimisation
    The design processes. Types of structural optimisation problems. Formulation of the optimisation problem. Graphical optimisation. Optimality criteria design. Brief history of structural optimisation.

  • Graphical solution of optimisation problems
    Drawing the design region. Identification of the optimum design and the active constraints. Numerical optimisation tool.

Session 2

  • Linear programming
    Introduction. Formulation of linear programming problems. Standard form of a linear problem. The Simplex method. Dual problems in linear programming.

  • Hands-on workshop: Python for optimisation problems in engineering
    Python programming for engineering and science. Basic scientific libraries in Python: Numpy, Scipy and matplotlib. Data structures and performance.

  • Hands-on workshop: Solving linear programming problems with Python
    The Simplex method implementation in Python. Linear programming problems in engineering. Application examples with Python.

Day 2 - Wednesday 14th July

Session 1

  • Unconstrained methods of design optimisation
    Introduction. Conjugate directions method. Gradient-based methods. Newton’s method. Quasi-Newton methods.

  • Hands-on workshop: Solving unconstrained optimisation problems with Python
    Unconstrained optimisation problems in engineering. Implementation of unconstrained optimisation methods in Python. The Scipy.optimize library.

Session 2

  • Engineering applications of structural optimisation
    Civil and aeronautical engineering structures.

  • Hands-on workshop: Structural optimisation with Altair Optistruct (Part I)
    Definition of the design variables, constraints and objective function. Constraint screening concept. Convergence parameters. Execute the optimisation process. Applications to bar and shell structures.

Day 3 - Thursday 15th July

Session 1

  • Constrained optimisation methods for design optimisation
    Introduction. Sequential unconstrained methods: penalty functions. Method of feasible directions. Sequential quadratic programming.

  • Hands-on workshop: Solving constrained optimisation problems with Python
    Constrained optimisation problems in engineering. Constrained optimisation methods in Python. Application examples.

Session 2

  • Hands-on workshop: Structural optimisation with Altair Optistruct (Part II)
    Postprocessing results. Create user constraints. Problems with constraints from different structural analyses (static, frequency, buckling, …). Multi-model optimisation.

Course Presenters

Dr Jacobo Díaz has been Associate Professor of Structural Mechanics at the University of A Coruña since 2004, where he teaches courses on finite element analysis, optimum design of structures and mechanics of plates and shells. His research interests are focused on structural and multidisciplinary design optimisation, design for crashworthiness and numerical modelling of structural adhesives and advanced composite materials. As a researcher, he is co-author of more than 50 publications and has worked in several research projects funded by the Spanish Government and EU. He maintains regular collaborations with industry and has been guest researcher at TU Delft (Aerospace Structures and Materials Department) where he worked in the analysis and design of composite materials with non-conventional architectures. Dr Díaz is Senior Member of the American Institute of Aeronautics and Astronautics (AIAA) and serves as a regular reviewer for scientific journals and conferences.

Dr Aitor Baldomir has been Associate Professor of Structural Mechanics at the University of A Coruña since 2008. He has collaborated with Airbus in structural analysis and optimisation of aeronautical structures in the A380, A350, A30x and A320neo programmes. The main contributions in these works were the application of size, shape and topology optimisation of structural components, like fuselage panels, the internal structure of S19, or secondary structures like the support of the APU. He has published 20 papers in international journals indexed in JCR in the field of civil and aerospace structures and more than 40 conference papers. He also collaborated in two European research projects: MAAXIMUS (Seventh Framework Programme) and STRATOFLY (Horizon 2020). Currently, his research lines are the optimization of structures considering partial collapses, and optimization of structures subject to random and epistemic uncertainty. He is AIAA member since 2011.