ABSTRACT of the Doctoral Thesis
The subject of the work is to provide contributions towards an efficient numerical analysis of the plastic collapse process of thin-walled structures. Starting from a survey on the state of research the theoretical foundations underlying the proposed algorithms are summarized. Here, besides large deformation continuum mechanics and plastic extremum and bounding principles, special emphasis is put on the derivation and description of the exact Ilyushin yield criterion, providing an important ingredient for the proposed algorithms. This plastic limit yield criterion (which is based on perfectly plastic material behaviour obeying the von Mises yield condition) provides a number of advantageous features, rendering the definition of both accurate and numerically efficient simulation tools for plastic collapse analysis of slender beams, thin plates and shells possible. Furthermore, due to the assumptions underlying the derivation of the yield surface it is fully consistent with plastic extremum and bounding principles, where it may in particular be utilized in combination with kinematics-oriented theorems, e.g. the Markov theorem or the upper bound theorem of limit analysis.
To gain more insight into the principles of the crushing phenomenon in a next step experimental results are presented and simplified analytically based collapse mechanisms proposed in the literature, which describe the quasistatic progressive buckling process of circular and multicornered prismatic profiles, are investigated in some detail. As a generalization of these simplified tools a computational model based on the upper bound theorem of limit analysis ("sequential limit analysis method") in combination with a finite element discretization is presented afterwards, which allows to study the large deformation crushing behaviour of general axisymmetric shell structures. The kinematic description is chosen such that both continuous and discontinuous plastic deformations can be considered. The large deformation process is described in an incremental manner, where each increment is solved by mathematical programming techniques. Within the framework of the application of the exact Ilyushin yield surface the power of internal forces can be taken into account very accurately. It is also shown that frictionless internal contact can be accounted for easily in the algorithm developed in this thesis. Several examples confirming the generality and suitability of this novel method for simplified plastic collapse analysis are included, too.
For conventional finite element based collapse and limit load analyses of shell structures a "full section material model", which is based on the exact Ilyushin yield criterion, is investigated afterwards. Many features considered as being essential for the definition of both a numerically stable and a computationally efficient formulation are proposed and the main difficulties concerned with the implementation are discussed. This not only includes the reformulation of standard plasticity algorithms (being required, because the exact Ilyushin yield criterion may only be stated in parametric form), but also an appropriate definition and choice of internal parameters used for the local stress update. The test examples confirm that the proposed full section material routine is in principle applicable for general finite element analyses and even has the potential of speeding up FE based limit and collapse analyses.