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- Bruchmechanik (4) (remove)
DETERMINATION OF THE DYNAMIC STRESS INTENSITY FACTOR USING ADVANCED ENERGY RELEASE EVALUATION
(2000)
In this study a simple effective procedure practically based upon the FEM for determination of the dynamic stress intensity factor (DSIF) depending on the input frequency and using an advanced strain energy release evaluation by the simultaneous release of a set of fictitious nodal spring links near the crack tip is developed and applied. The DSIF is expressed in terms of the released energy per unit crack length. The formulations of the linear fracture mechanics are accepted. This technique is theoretically based upon the eigenvalue problem for assessment of the spring stiffnesses and on the modal decomposition of the crack shape. The inertial effects are included into the released energy. A linear elastic material, time-dependent loading of sine type and steady state response of the structure are assumed. The procedure allows the opening, sliding and mixed modes of the structure fracture to be studied. This rational and powerful technique requires a mesh refinement near the crack tip. A numerical test example of a square notched steel plate under tension is given. Opening mode of fracture is studied only. The DSIF is calculated using a coarse mesh and a single node release for the released energy computation as well a fine mesh and simultaneous release of four links for more accurate values. The results are analyzed. Comparisons with the known exact results from a static loading are presented. Conclusions are derived. The values of the DSIF are significantly larger than the values of the corresponding static SIF. Significant peaks of the DSIF are observed near the natural frequences. This approach is general, practicable, reliable and versatile.
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.
Dynamic testing for damage assessment as non-destructive method has attracted growing in-terest for systematic inspections and maintenance of civil engineering structures. In this con-text the paper presents the Stochastic Finite Element (SFE) Modeling of the static and dy-namic results of own four point bending experiments with R/C beams. The beams are dam-aged by an increasing load. Between the load levels the dynamic properties are determined. Calculated stiffness loss factors for the displacements and the natural frequencies show differ-ent histories. A FE Model for the beams is developed with a discrete crack formulation. Cor-related random fields are used for structural parameters stiffness and tension strength. The idea is to simulate different crack evolutions. The beams have the same design parameters, but because of the stochastic material properties their undamaged state isn't yet the same. As the structure is loaded a stochastic first crack occurs on the weakest place of the structure. The further crack evolution is also stochastic. These is a great advantage compared with de-terministic formulations. To reduce the computational effort of the Monte Carlo simulation of this nonlinear problem the Latin-Hypercube sampling technique is applied. From the results functions of mean value and standard deviation of displacements and frequencies are calcu-lated. Compared with the experimental results some qualitative phenomena are good de-scribed by the model. Differences occurs especially in the dynamic behavior of the higher load levels. Aim of the investigations is to assess the possibilities of dynamic testing under consideration of effects from stochastic material properties
In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.