Anwendung direkter Methoden zur industriellen Berechnung von Grenzlasten mechanischer Komponenten
Mouhtamid, Said; Weichert, Dieter (Thesis advisor)
Aachen : Publikationsserver der RWTH Aachen University (2007, 2008)
Dissertation / PhD Thesis
There are many industries producing or operating safety-critical structures under heavy loading conditions. Many of these structures or structural components behave ductily and undergo plas-tic deformations under severe loading or under some normal operating conditions. Their life-time may be determined by fatigue failure or incrementally increasing deformations due to plasticity. A better understanding of the behaviour of such structures under complex loading conditions may considerably improve their design. In fact, the direct industrial need for end-users of a validated design and assessment method is to improve structural design and the process in run / repair / replace / change operation decision-making. There is a strong industrial need to extend both industrial activities to complex structures (i.e. realistic geometry, complex loading, advanced material modelling,…). A realistic description of the corresponding material response may require rather sophisticated constitutive models. In combination with well-known numerical tools such as the finite element method, it is in principle possible to study the behaviour of structures by performing a series of incremental elastic-plastic analyses. However, for complex loading histories, the required numerical expense of this kind of procedure may be very high. Furthermore, an accumulation of errors cannot be excluded in principle. On the other hand, direct methods, namely statical and kinematical limit and shakedown analy-sis, provide elegant and efficient methods for the prediction of the long-term behaviour of such structures under arbitrary complex loading independent of the number of loading cycles. The lower bound direct method leads to a problem of non-linear mathematical programming in con-junction with finite element methods. The considered problem is a convex non-linear optimisa-tion problem with constraints which necessitates for the engineering applications a very large number of optimisation variables and a large amount of computer memory. To solve this large-scale problem with a reasonable computer time, we propose to apply the interior point with DC regularisation algorithm (IPDCA). Numerical examples show the efficiency and the robustness of IPDCA in comparison with standard code LANCELOT.