A student of the Faculty of Mathematics and Physics, Department of Mathematics, prepared and defended the master's thesis in the field of Solving linear elastostatic problems with meshless methods under the supervision of a member of the project team, for which he received the faculty Prešeren prize. The work was prepared as part of the project. The author introduces the concept of a stress tensor in a mathematically correct way, derives equations of motion, and shows the existence of a unique solution. Next, he focuses to the numerical solution of the obtained equations with the meshless method. He analyses solutions of several problems and presents an example of a stress analysis in the simplified case of fretting fatigue of the material as the final result.
D.10 Educational activities
COBISS.SI-ID: 18122329In the project we are developing a general library for numerical solving of coupled systems of partial differential equations, where we strive for the highest level of coordinate free implementation that enables us to quickly adapt to new problems. Thus, we have used the library in the task "Cooling of overhead power lines in wind regimes below 0.6 m/s ", which is carried out for ELES, d.d. In the task we are dealing with the problem of natural convection in the vicinity of the transmission line, described by the Navier Stokes and the heat equation.
D.01 Chairing over/coordinating (international and national) projects
COBISS.SI-ID: 31223335In the paper the theoretical analysis of the complexity of the fretting fatigue simulation with a cyclic non-proportional load is presented. For the simulation of each cycle it is necessary to model the contact of two bodies, and crack propagation or conditions for cracks initiation. Cycles are completely consecutive, which means that the problem cannot simply be parallelized at the level of cycles, but it is necessary to use parallel computing approaches within individual solution elements. Each of the above elements requires the knowledge of the stress tensor within the considered bodies, which requires the numerical solution of the Navier Cauchy vector partial equation. Therefore, if we want to accelerate the execution of one cycle, it is necessary to successfully solve the Navier equation in a parallel, which is not trivial, due to the pronounced jumps in the stress tensor in the vicinity of the contact, and especially in the vicinity of the crack tip, where the stress tensor even diverges.
B.03 Paper at an international scientific conference
COBISS.SI-ID: 31224615