Solutions for the common problem of path planning in an abstract environment have been extensively studied in many scientific disciplines. However, many explored techniques assume the environment does not change and that there is a complete and detailed overview of this examined space. In addition, many path planning methods need to derive a specific graph structure from the environment representation and it can be often very difficult to obtain this structure in some real applications.In our paper, we introduce a general model for the real-time path planning in a dynamic environment and provide a hybrid technique that combines a graph and grid representation of the examined space. The proposed path planning method uses an adaptive mesh for its graph part to provide the capability of the assimilation to the changing environment.The presented method offers faster times for the path retrieval than the classical raster based approaches and works in a dynamic environment where the conventional graph based techniques fail. On the other hand, there are still some higher memory requirements of the proposed solution due to the necessary raster representation of the examined environment.

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The analytical mould of the solution in the radial direction permits precision stress intensity factors to be derived in the scaled boundary finite element method, namely, directly from the definition, and consequently no particular crack-tip interpretation such as refining the crack-tip mesh or employing singular elements, is indispensable. Besides, anisotropic material characteristics can be treated effortlessly. In this analysis, the Frobenius approach in the frequency domain to the solution of the governing differential equations of the SBFEM is used to simulate variable dynamic fracture problems. The complex frequencyresponse functions are calculated. Thereafter, the dynamic stress intensity factors are squarely taken from the response functions out. That is ensued by a fast Fourier transform of the transient load and a later inverse transform to derive the time history of DSIFs.A mixed-mode crack growth simulation was developed. At first, a domain is divided into some subdomains. Since the dimensions and shapes of subdomains can be flexibly changed and only the domain boundaries or common edges between subdomains are discretized in the SBFEM, a remeshing routine such as a straightforward one as in BEMs was set up with minimum mesh variances while the universality and flexibleness of the FEM is preserved.

Significant progress has been made in the last years towards understanding the short and long – term performances of fibre reinforced cementitious materials and this has resulted in a number of novel and innovative uses. One of the main problems concerns the great quantity of random parameters– the placement of fibres, their orientation and quantity in a determined section etc. In consequence, full – probabilistic methods could be recommended for the analysis and evaluation of FRC. It can be assumed that for some structures probabilistic parameters derived from actual material tests could be used. A series of 9 specimens with the same reinforcement was used for a standard 4-point bending test. Using the obtained results, probabilistic normal distributions for the necessary input data were defined. The diagram of the experiment can then be recalculated probabilistically using the method SBRA. The ductility of the material can be expressed energetically. The final result is a histogram of the flexural toughness of the specimen that can be used for further calculations and evaluations.