SHAPE OPTIMIZATION FOR FATIGUE PROBLEMS IN MECHANICAL ENGINEERING

High Cycle Fatigue (HCF) is a very important topic in mechanical engineering problems. Almost any machine part contains some changes in cross section or boreholes connected with stress concentration. It is the task of shape optimization to improve the strength of machine parts by changing the design at free boundaries. In the past, some work was done with the so-called classical stress concentration factors just to minimize the mentioned stress concentration, also for fatigue. This paper represents a more sophisticated view by including modern Continuum Damage Mechanics (CDM) to model material behavior in HCF. The central question is to design machinery parts so that maximum lifetime is obtained. The whole context for this is developed in this paper, including non-linear finite element algorithms. The paper concludes with numerical and experimental tests for the shape optimization of a notched tension bar in HCF.     

DOMAIN DECOMPOSITION WITH BEM AND FEM

The Finite Element Method and the Boundary Element Method are two different structure analysis methods with a totally different numerical character. Therefore, it makes no sense to couple these two methods pointwise at the interface. In contrast to a lot of coupling strategies in the past, in this paper a method is constructed where we have coupling of the two different methods in a weak form. As a result we can analyse the given structure with two different grids independent of each other. On this account, we see that the big advantage of the proposed method is in its ablity to couple BEM and FEM. The construction of a robust and reliable numerical algorithm depends on the adaptive control of symmetry and definiteness of the coupling matrix. Therefore, we use an iterative method for solving the boundary integral equation by expanding the Calderon projector in a Neumann series. Numerical results show the preciseness and efficiency of the method. © 1997 John Willey & Sons Ltd.