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

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

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

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 application of size, shape and topology optimisation of structural components, like fuselage panels, 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.

Course Requirements

The course requires a basic background on structural mechanics. No experience is required on numerical modelisation of structural problems.

This is a hands-on course. To take advantage of the practical sessions, it is advisable that participants bring a laptop computer with Windows or Linux operating system.


Please email the Course Coordinator to register your interest for this course and give a recommendation of suitable dates in the 1st Quarter of 2020.

Jane Chantler - This email address is being protected from spambots. You need JavaScript enabled to view it.

Once the course date is finaliased we will contact you and activate the registration form.

Some subsidies might be available for PhD students. Contact us for further information.


new forestThe New Forest is one of the UK's most popular tourist destinations and offers many attractions all year round, including picturesque forest villages as well as beautiful scenery. It is located in Southern England, spreading over 150 square miles of Hampshire. The New Forest was established as a royal hunting ground by King William I, and by the 14th century, the land was being used to produce timber for the shipbuilding industry on the south coast. Today, after nearly 1000 years, the forest is still Crown property and is administered by the Forestry Commission. Since the reign of King William I commoners have been given the right to graze their livestock, normally ponies, cattle and pigs, on Forest land where they wander freely. In the New Forest, the well-being of the animals and the special needs of the countryside are a priority. The Forest is unarguably recognised as one of the most unique and important wilderness areas in Western Europe and, because of this, it is now a National Park.

Venue and Accommodation

The course will take place at the Wessex Institute at Ashurst Lodge located in the New Forest, an outstanding National Park that borders the South Coast. Ashurst Lodge is an ideal venue for conferences, courses and seminars.  The participants can benefit from an excellent standard of accommodation, either on Campus or in various hotels or bed and breakfasts in the area.  The surroundings are equally appealing to those who enjoy walking, horse riding, cycling, sailing and fine landscapes.

For more information on how to find Ashurst Lodge and to arrange accommodation during the courses please use the information provided on the Contact Us page.

Ashurst Lodge panorama