Topology Optimization – Theory, Methods and Applications

• Understand and use existing topology optimization software for stiffness design (88- and 99-line codes)
• Modify existing codes to change boundary conditions, loads, design domains, etc.
• Understand principles for design sensitivity analysis and derive them for new objective functions
• Implement topology design of compliant mechanisms
• Understand the theory behind mathematical programming tools and implement them in topology optimization software
• Understand the newest developments in theoretical aspects of topology optimization methods
• Read and understand research papers on topology optimization
• Know the historical foundation of the topology optimization method
• Understand new applications of topology optimization in academic research and industry
• Implement topology design of dynamic problems with harmonic loads

The course focuses on theory and practice of Topology Optimization. Topics include:

• Design parametrization (composites’ homogenization, density-based interpolations, level-set, etc.)
• Sensitivity analysis (direct and adjoint methods)
• Optimization algorithms (OC-methods, mathematical programming, convex approximation schemes, stochastic optimization and other methods)
• Computational issues (checkerboards, filters, robust design, parallelization)
• Novel and emerging approaches (multiscale methods, de-homogenization, AI/ML, contact)
• Applications to structural and multi-physics problems (micro- and nano-systems, optics, wave-propagation problems, nonlinearities, material design, fluid systems)
• Industrial applications and advanced manufacturing constraints

The course is designed for Ph.D.-students and final-year graduate students being familiar with the basic concepts of the finite element method. Knowledge
corresponding to a course in FEM as well as Matlab experience is assumed.

1 full week (weekend incl.) with lectures and computer exercises

All participants are required to present a poster on the topic of their Ph.D. research work.

Maximum: 50.

Please be aware that this course has a limited number of seats available. If there are too many applicants, a pool will be created for the remainder of the qualified applicants, and they will be selected at random. You will be informed 8 days before the start of the course, whether you have been allocated a spot.