Numerische Einspieluntersuchungen mechanischer Komponenten mit begrenzt kinematisch verfestigendem Materialverhalten

• Numerical shakedown analysis of mechanical components with limited kinematical hardening

Simon, Jaan-Willem; Weichert, Dieter (Thesis advisor)

Aachen : Publikationsserver der RWTH Aachen University (2011)
Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2011

Abstract

The determination of shakedown loads of mechanical systems is of crucial importance in construction engineering, particularly in case of varying thermo-mechanical loading. In order to obtain realistic results, the consideration of limited kinematical hardening is necessary. Especially for large-scale engineering structures this is a difficult task because these lead to optimization problems with large numbers of variables and constraints. In this work, the new algorithm IPSA is presented, which has been developed for shakedown analysis of mechanical components made of von Mises-materials. The underlying mathematical formulation is based on the static shakedown theorem by Melan. The resulting optimization problem is solved via the interior point method, where the solution strategy is specifically problem-tailored for the von Mises yield criterion. In a first step, the validation is carried out for structures of elastic- perfectly plastic materials subjected to two independent thermo-mechanical loadings. Here, the accuracy of IPSA is shown by comparison to results from literature as well as from the programs Lancelot, IPOPT and IPDCA. In addition, it is shown that the algorithm is characterized by high efficiency. In the worst case, the needed running time is reduced by the factor 8, in the best one by a factor of about 300 even. Moreover, both the theoretical derivation and the implementation are extended for the case of an arbitrary number of loadings is presented in this work. The methodology is shown by application to a square plate with circular hole subjected to three loads, which vary independently of each other. The presented results in the three-dimensional loading space are the first of this kind. Finally, an extension is given for the consideration of limited kinematical hardening. This is based on the two-surface model proposed by Weichert and Gross-Weege, which allows for an easy embedding of the hardening into the shakedown theorem. As in the perfectly plastic case, the interior point method is used for the solution of according optimization problem. The algorithm is validated using four examples, where the results are in agreement with those taken from literature where applicable.