### 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)

We propose an enhanced iterative scheme for the precise reconstruction of piezoelectric material parameters from electric impedance and mechanical displacement measurements. It is based on finite-element simulations of the full three-dimensional piezoelectric equations, combined with an inexact Newton or nonlinear Landweber iterative inversion scheme. We apply our method to two piezoelectric materials and test its performance. For the first material, the manufacturer provides a full data set; for the second one, no material data set is available. For both cases, our inverse scheme, using electric impedance measurements as input data, performs well.

In this paper we present an inverse method which is capable of identifying system components in a hydro-mechanically coupled system, i.e. for fluid flow in porous media. As an example we regard water dams that were constructed more than hundred years ago but which are still in use. Over the time ageing processes have changed the condition of these dams. Within the dams fissures might have grown. The proposed method is designed to locate these fissures out of combined mechanical and hydraulic measurements. In a numerical example the fissures or damaged zones are described by a smeared crack model. The task is now to identify simultaneously the spatial distribution of Young’s modulus and the hydraulic permeability due to the fact, that in regions where damages are present, the mechanical stiffness of the system is reduced and the permeability increased. The inversion is shown to be an ill-posed problem. As a consequence regularizing methods have to be applied, where the nonlinear Landweber method (a gradient type method combined with a discrepancy principle) has proven to be an efficient choice.

We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.

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.

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.