PhD Courses in Denmark

Introduction to and hands-on experience with the method of topology optimization

A student who has met the objectives of the course will be able to:

• 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