Description: Polymeric resin fibre reinforced materials (FRP´s or composite materials) are being used increasingly for structural applications where properties such as high strength, high stiffness and low weight are determining design parameters. The driving force behind the development and application of these materials has been the demands posed by the aerospace industry, but the use of advanced composite materials is expanding rapidly to other industrial sectors as well. Pertinent examples of this include applications for ship structures, automotive and train applications, wind turbine blades and civil engineering applications including bridge structures.

Objectives and Contents:
The purpose of the course is to present the participants with a general overview and an introduction to recent advances and modern techniques for analysis and gradient based design optimization of advanced laminated composite structures. The following topics will be treated:
• Laminae and laminates: fiber and resin materials, modelling of the laminae, classical lamination theory (CLT), shear-deformation plate theories
• Fracture and failure of composite materials - focus on failure criteria and their use
• Finite element analysis of laminated composite structures with focus on shell and solid shell formulations
• Introduction to basic concepts of gradient based structural optimization
• Parameterization choices for laminated composites (continuous fiber angles and thicknesses, lamination parameters, Discrete Material Optimization (DMO), Discrete Material and Thickness Optimization (DMTO), etc.)
• Efficient methods of Design Sensitivity Analysis for gradient based structural optimization
• Inclusion of manufacturing constraints
• Gradient based design optimization of laminated composite structures for linear and nonlinear problems including buckling problems

Course Language:
The course will be given in English.

Teaching Material:
Lecture notes will be made available for registered course attendees.
Furthermore, a Matlab skeleton script for analysis and design optimization of laminated composite plates using isoparametric finite elements is provided as basis for part of the assignments.

Course Format and Work Load:
The course will consist of a condensed session comprised of 5 full days of lectures, work on assignments, and discussions at AAU. After the course session the course participants (PhD students) are expected to solve and submit homework assignments. Diplomas will be issued on the basis of course participation and evaluation of homework assignments, and entitle Ph.D. students to 5 ECTS, corresponding to 140 hours of work load.


Participants are expected to have a basic knowledge in mechanics of solids corresponding to undergraduate level (mechanical, aero, civil and ship/maritime engineering). The course is aimed specifically at Ph.D. students, but the course is also recommended for industrial engineers and engineering scientists. University staff and final year M.Sc. students are welcome as well. University staff, M.Sc. students and participants from industry may be exempted from the homework assignments and the course evaluation/examination. Course assignments are based on Matlab scripts, and it is expected that participants have Matlab installed (preferably version 2017b or later). 

Earlier Events:

The course has been held biannually since 2004 to 2014 as "Analysis and Design Optimisation of Laminated Composite Structures". However, since 2016 the course has been revised such that more focus is put on gradient based methods for the design optimization part, and the course assignments have thereby also been changed significantly.

New deadline for registration: 6 August 2020.

Course participation is free for national Ph.D. students and university staff. Participants from industry will be charged DKK 12,500 (DKK 2,500 pr. ECTS). International Ph.D. students and university staff get a discount of 90% and will be charged DKK 1,250.

If you are from outside Aalborg University and you wish to enroll in one of our PhD courses, you must create a profile. This is done by clicking on "create new account" and filling out the form.

For further information please contact Professor Erik Lund, Phone (+45) 9940 9312, E-mail:

Professor Erik Lund,

In collaboration with
DCAMM, Danish Center for Applied Mathematics and Mechanics (

Erik Lund, Johnny Jakobsen and Esben Lindgaard
Department of Materials and Production, Aalborg University

New course dates: 17-21 August 2020

Place: Department of Materials and Production, Aalborg University, Fibigerstræde 16, DK-9220 Aalborg, Denmark.

ECTS: 5.0

Number of seats: 30

Important information concerning PhD courses: We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.