Jürgen Zechner

Fast isogeometric boundary element method based on independent field approximation

Abstract An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology are demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.

A simple approach to the numerical simulation with trimmed CAD surfaces

Abstract In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its simplicity and ease of implementation into existing Finite Element (FEM) or Boundary Element (BEM) software. The method is first verified with classical test examples in structural mechanics. Then two practical applications are presented one using the FEM, the other the BEM, that show the applicability of the method.

Stable isogeometric analysis of trimmed geometries

Abstract We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The construction for non-uniform knot vectors is presented. The properties of extended B-splines are examined in the context of interpolation, potential, and linear elasticity problems and excellent results are attained. The analysis is performed by an isogeometric boundary element formulation using collocation. It is argued that extended B-splines provide a flexible and simple stabilization scheme which ideally suits the isogeometric paradigm.

Playing a game in civil engineering - The Internal Force Master for Structural Analysis

The goal of our research work was to find out whether in-depth learning of complex theoretical engineering knowledge at higher education level could be improved by the use of online games. In this context we addressed the research question to what extent online games contribute to the students learning outcome. The corresponding online game was used for the first time during a lecture on Structural Analysis at bachelors level with 159 students of the third semester. We used a pre-/post-test design with questionnaires and an independent online tracking. As a result we can point out that playing the game did not increase the learning outcome per se and the didactical scenario should be reconsidered. Nevertheless, the usage of the game for learning purposes was underlined by the oral feedback given which says that students enjoyed playing the game more than learning in a traditional way.

INTEGRATION OF DESIGN AND ANALYSIS THROUGH BOUNDARY INTEGRAL EQUATIONS

The direct integration of Computer Aided Geometric Design (CAGD) models into a numerical simulation improves the accuracy of the geometrical representation of the problem as well as the efficiency of the overall analysis process. In this work, the complementary features of isogeometric analysis and boundary integral equations are combined to obtain a coalescence of design and analysis which is based on a boundary-only discretization. Following the isogeometric concept, the functions used by CAGD are employed for the simulation. An independent field approximation is applied to obtain a more flexible and efficient formulation. In addition, a procedure is presented which allows a stable analysis of trimmed geometries and a straightforward positioning of collocation points. Several numerical examples demonstrate the characteristics and benefits of the proposed approach. In particular, the independent field approximation improves the computational efficiency and reduces the storage requirements without any loss of accuracy. The proposed methodology permits a seamless integration of the most common design models into an analysis of linear elasticity problems.