Modelling Seminar 2021

In this pro­ject, a pro­duced spring is to be auto­mati­cally com­pared with the pre­vious­ly pro­duced CAD de­sign. A 3D scan of the man­ufac­tured com­po­nent served as the data basis. The stu­dents of the Elite Grad­uate Pro­gram "Scientific Computing" had to de­velop a pro­ce­dure to com­pare this cloud of sur­face points with the CAD plan. They first re­con­structed a dis­tance func­tion using radial basis func­tions and a suita­ble adapted de­sign file of the spring. The scan points can be in­serted into this func­tion and their devia­tion de­ter­mined. The stu­dents had to use effi­cient data struc­tures and algo­rithms for the im­ple­men­tation since the data sets were very large.

The objec­tive of this topic was to simu­late the mo­tion of a ship hit head-on by light waves in oth­er­wise rela­tively calm con­di­tions. The dy­nam­ics of the sur­rounding water, mod­eled by the Reynolds-aver­aged Na­vier-Stokes equa­tion was han­dled by soft­ware pro­vided by the indus­try part­ner.
One group was to simu­late the free mo­tion of the ship, which was to be mod­eled as a rigid body. The re­sulting sys­tem of ordi­nary dif­feren­tial equa­tions of mo­tion was solved us­ing the Newmark meth­od.
The sec­ond group had the task of fixing the ship to the bot­tom by means of an an­chor chain and simu­lating the movement thus re­strict­ed. First, the stu­dents had to set up a dy­namic model of an elas­tic chain, which acted as an an­chorage of the ship to the sea­bed. The next step was to im­ple­ment a so­lution pro­ce­dure for the de­veloped par­tial dif­feren­tial equa­tion. For this pur­pose, they used a suita­ble meth­od for the dis­creti­sation of time and a finite ele­ment ap­proach for the spa­tial dis­creti­sa­tion.

Even under con­stant oper­ating con­di­tions, the rota­tional speed of roll­ing ele­ments in bear­ings is not con­stant. When enter­ing the load zone, they are accel­er­ated, out­side they are de­celer­ated. In order to take these veloc­ity changes into ac­count in qua­si-stat­ic simu­la­tions, a meth­od for the fast ap­prox­imation of ordi­nary peri­odic dif­feren­tial equa­tions had to be de­veloped. For this pur­pose, the stu­dents com­bined a Fou­rier series ap­prox­imation with a fix-point itera­tion.

Text: Max­imili­an Bau­er, Coor­dina­tor of the Elite Gradauate Pro­gram "Sci­en­tific Com­puting", and Thomas Rau, su­pervi­sor of the mod­elling semi­nar.