Over the last decade, the demand for offshore power cables has increased significantly due to, in particularly, the emergence of offshore wind. Despite this growth, industry-wide rules and guidelines to analyse fatigue during cable installation operations are yet to be developed, even though fatigue can become an important parameter in the installation design.  In similar offshore operations, e.g. installation of pipelines or umbilicals, fatigue is assessed based on fundamental fatigue theory like rainflow counting, S-N curves and Miner's rule and therefore these principles form the basis of analysis in this research. However, submarine power cables consist of numerous layers of different materials that result in complex cable cross-sections. The fatigue behaviour of the cross-sectional elements due to external loads has been investigated to determine a maximum stand-by time during installation operations. In this regard, a cross-sectional analysis was performed to establish the stress-strain response of the individual cable components to the global cable deformations. For bending behaviour, the analysis was shown to be consistent with existing test data. However, this type of data is scarce and the analysis was based on a limited sample size. Moreover, geometrical cross-sectional data of submarine cables is rarely provided by suppliers and hence several assumptions were made in the analysis. For future work, it is recommended to develop in-house test data of cables such that the cross-sectional model can be accurately verified and improved. The cross-sectional stresses were implemented in a fatigue assessment model, in which the local stresses were calculated based on the output of global modelling software OrcaFlex and subsequently analysed with rainflow counting and Miner's rule. The model was applied to three cable types and it was found hat lead, used for cable sheaths, is the critical cable component in terms of fatigue. When no lead is used in the power cable, the conductors are the critical component. Furthermore, for mild loading scenarios, i.e. waves with significant wave heights H_s≤1.5 m, the model yields components infinite life for all cable components. For higher load cases, i.e. H_s≥2.5m, the model showed that fatigue mitigation measures are required to stay within the fatigue budget. Several mitigation methods were implemented, from which it was found that increasing the layback length of the cable combined with adjusting the vessel heading to favourable conditions most effectively reduces fatigue damage as all load cases with H_s=2.5 m resulted in maximum stand-by times of t_sb≥ 125days. However, for higher loading scenarios, i.e. Hs=4 m, all researched mitigation measures were insufficient to stay within fatigue budget. For future work, it is therefore recommended to improve the mitigation measures such that severe load cases can be survived. Lastly, the wave conditions were simulated as JONSWAP waves. These simulations are time-consuming and therefore not many loading scenarios were modelled. It is recommended to research methods to approximate wave conditions with regular waves, as the duration of OrcaFlex simulations will decrease exponentially. An increase in number of load cases will result in more accurate limit states for the cable components.   ... Read more

In proton therapy the development of dose calculation methods is of great importance
to optimize the dose. In this work a method is presented to solve the Fokker-Planck
transport equation using ray-tracing techniques and nite element methods.
The idea of the method is dividing the Fokker-Planck equation in two seperate equa-
tions, one without scattering and the other with scattering. The result of the unscat-
tered equation is then used to function as source for the second one. The equations
are discretized in all free variables: space, angle and energy. The spatial domain is
discretized such that each spatial element has its own angular and energy mesh. The
main solution technique is the discontinuous Galerkin (dG) method in combination
with ray-tracing techniques.
The results from the ray-tracing method for calculating the unscattered dose correspond
to known physical phenomena. The method for Gaussian sampling however shows a
great sensitivity to the number of sampling beams used and yields consistent results
only for a numer of sampling beams in the order of 103.
In future work the sampling needs to be done by using the quadrature method, which
results in a smaller error and uses only 4 sampling beams, resulting in a more favorable
computation time. ... Read more