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Solares Kochen
(1990)
Solidification of silver-germanium alloys in an amorphous matrix aboard the space station Mir
(1993)
In the study, the process chain of additive manufacturing by means of powder bed fusion will be presented based on the material glass. In order to reliably process components additively, new concepts with different solutions were developed and investigated.
Compared to established metallic materials, the properties of glass materials differ significantly. Therefore, the process control was adapted to the material glass in the investigations. With extensive parameter studies based on various glass powders such as borosilicate glass and quartz glass, scientifically proven results on powder bed fusion of glass are presented. Based on the determination of the particle properties with different methods, extensive investigations are made regarding the melting behavior of glass by means of laser beams. Furthermore, the experimental setup was steadily expanded. In addition to the integration of coaxial temperature measurement and regulation, preheating of the building platform is of major importance. This offers the possibility to perform 3D printing at the transformation temperatures of the glass materials. To improve the component’s properties, the influence of a subsequent heat treatment was also investigated.
The experience gained was incorporated into a new experimental system, which allows a much better exploration of the 3D printing of glass. Currently, studies are being conducted to improve surface texture, building accuracy, and geometrical capabilities using three-dimensional specimen.
The contribution shows the development of research in the field of 3D printing of glass, gives an insight into the machine and process engineering as well as an outlook on the possibilities and applications.
Solution of plane anisotropic elastostatical boundary value problems by singular integral equations
(1982)
There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost.
Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.