Universitätsbibliothek
Weimar Open Access

Adaptive Response Surfaces for Structural Reliability of Nonlinear Finite Element Structures

Moving Least Squares-elements for stochastic crack propagation simulations coupled with stochastic finite elements

In this paper a meshless component is presented, which internally uses the common meshless interpolation technique >Moving Least Squares<. In contrast to usual meshless integration schemes like the cell quadrature and the nodal integration in this study integration zones with triangular geometry spanned by three nodes are used for 2D analysis. The boundary of the structure is defined by boundary nodes, which are similar to finite element nodes. By using the neighborhood relations of the integration zones an efficient search algorithm to detected the nodes in the influence of the integration points was developed. The components are directly coupled with finite elements by using a penalty method. An widely accepted model to describe the fracture behavior of concrete is the >Fictitious Crack Model< which is applied in this study, which differentiates between micro cracks and macro cracks, with and without force transmission over the crack surface, respectively. In this study the crack surface is discretized by node pairs in form of a polygon, which is part of the boundary. To apply the >Fictitious Crack Model< finite interface elements are included between the crack surface nodes. The determination of the maximum principal strain at the crack tip is done by introducing an influence area around the singularity. On a practical example it is shown that the included elements improve the model by the transmission of the surface forces during monotonic loading and by the representation of the contact forces of closed cracks during reverse loading.