### Refine

#### Document Type

- Article (43)
- Conference Proceeding (10)
- Preprint (1)

#### Institute

- Institut für Strukturmechanik (44)
- Juniorprofessur Stochastik und Optimierung (43)
- Graduiertenkolleg 1462 (4)
- Bauhaus-Institut für zukunftsweisende Infrastruktursysteme (2)
- Professur Angewandte Mathematik (2)
- Professur Informatik im Bauwesen (2)
- Professur Modellierung und Simulation - Konstruktion (1)

#### Keywords

- Angewandte Mathematik (50)
- Stochastik (41)
- Strukturmechanik (41)
- Angewandte Informatik (9)
- Computerunterstütztes Verfahren (9)
- Building Information Modeling (6)
- Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications (6)
- Sensitivitätsanalyse (2)
- Abtastung (1)
- Adaptive sampling method (1)
- Approximation (1)
- Architektur <Informatik> (1)
- Beam-to-column connection; semi-rigid; flush end-plate connection; moment-rotation curve (1)
- Computational modeling (1)
- Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing (1)
- Dielectric materials (1)
- Finite element methods (1)
- Finite-Elemente-Methode (1)
- Fire resistance; Parameter optimization; Sensitivity analysis; Thermal properties (1)
- Frequency (1)
- Global sensitivity analysis (1)
- Impedance measurement (1)
- Least-squares support vector regression (1)
- Manufacturing (1)
- Partial differential equations (1)
- Piezoelectric materials (1)
- Resonance (1)
- Resonanz (1)
- Sampling (1)
- Stütze (1)
- Surrogate models (1)
- Thermodynamische Eigenschaft (1)
- Tragfähigkeit (1)
- Träger (1)

Many structures in different engineering applications suffer from cracking. In order to make reliable prognosis about the serviceability of those structures it is of utmost importance to identify cracks as precisely as possible by non-destructive testing. A novel approach (XIGA), which combines the Isogeometric Analysis (IGA) and the Extended Finite Element Method (XFEM) is used for the forward problem, namely the analysis of a cracked material, see [1]. Applying the NURBS (Non-Uniform Rational B-Spline) based approach from IGA together with the XFEM allows to describe effectively arbitrarily shaped cracks and avoids the necessity of remeshing during the crack identification problem. We want to exploit these advantages for the inverse problem of detecting existing cracks by non-destructive testing, see e.g. [2]. The quality of the reconstructed cracks however depends on two major issues, namely the quality of the measured data (measurement error) and the discretization of the crack model. The first one will be taken into account by applying regularizing methods with a posteriori stopping criteria. The second one is critical in the sense that too few degrees of freedom, i.e. the number of control points of the NURBS, do not allow for a precise description of the crack. An increased number of control points, however, increases the number of unknowns in the inverse analysis and intensifies the ill-posedness. The trade-off between accuracy and stability is aimed to be found by applying an inverse multilevel algorithm [3, 4] where the identification is started with short knot vectors which successively will be enlarged during the identification process.

A topology optimization method has been developed for structures subjected to multiple load cases (Example of a bridge pier subjected to wind loads, traffic, superstructure...). We formulate the problem as a multi-criterial optimization problem, where the compliance is computed for each load case. Then, the Epsilon constraint method (method proposed by Chankong and Haimes, 1971) is adapted. The strategy of this method is based on the concept of minimizing the maximum compliance resulting from the critical load case while the other remaining compliances are considered in the constraints. In each iteration, the compliances of all load cases are computed and only the maximum one is minimized. The topology optimization process is switching from one load to another according to the variation of the resulting compliance. In this work we will motivate and explain the proposed methodology and provide some numerical examples.

Safety operation of important civil structures such as bridges can be estimated by using fracture analysis. Since the analytical methods are not capable of solving many complicated engineering problems, numerical methods have been increasingly adopted. In this paper, a part of isotropic material which contains a crack is considered as a partial model and the proposed model quality is evaluated. EXtended IsoGeometric Analysis (XIGA) is a new developed numerical approach [1, 2] which benefits from advantages of its origins: eXtended Finite Element Method (XFEM) and IsoGeometric Analysis (IGA). It is capable of simulating crack propagation problems with no remeshing necessity and capturing singular field at the crack tip by using the crack tip enrichment functions. Also, exact representation of geometry is possible using only few elements. XIGA has also been successfully applied for fracture analysis of cracked orthotropic bodies [3] and for simulation of curved cracks [4]. XIGA applies NURBS functions for both geometry description and solution field approximation. The drawback of NURBS functions is that local refinement cannot be defined regarding that it is based on tensorproduct constructs unless multiple patches are used which has also some limitations. In this contribution, the XIGA is further developed to make the local refinement feasible by using Tspline basis functions. Adopting a recovery based error estimator in the proposed approach for evaluation of the model quality and performing the adaptive processes is in progress. Finally, some numerical examples with available analytical solutions are investigated by the developed scheme.