In mechanical engineering we are usually concerned with dynamically loaded constructions, i.e. machinery parts. In this paper a new idea for high-cycle fatigue behavior working with the two-grid method is presented, using one grid on the microlevel and the other one for the meso-level. While on the meso-level the behavior of the construction in high-cycle fatigue is nearly linear, however on the micro-level there are defects and microcracking with small plastic zones around the crack tips. Using a homogenization technique. we develop an energy release rate formulation on the mico-grid. from which the evolution equation for increasing damage arises. The new idea is now to define the damage at the meso-level depending on the damage at the micro-level, while controlling the stress redistribution by a modified locally coupled analysis. This leads to a new concept for shape optimization of mechanical engineering problems using the sequential quadratic programming technique. The theoretical and numerical results are controlled by experiments using a hydropulser machine. For high quality steel an increase of lifetime by a factor of about 3 was achieved for our shape optimized notched structures compared with the ones possessing classical circular cut-outs. Therefore we can say that this concept offers a new possibility for lifetime increasement of mechanical engineering structures.
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