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Institute
- Fachbereich Medizintechnik und Technomathematik (187) (remove)
A 3D finite element model of the female pelvic floor for the reconstruction of urinary incontinence
(2014)
A generalized shear-lag theory for fibres with variable radius is developed to analyse elastic fibre/matrix stress transfer. The theory accounts for the reinforcement of biological composites, such as soft tissue and bone tissue, as well as for the reinforcement of technical composite materials, such as fibre-reinforced polymers (FRP). The original shear-lag theory proposed by Cox in 1952 is generalized for fibres with variable radius and with symmetric and asymmetric ends. Analytical solutions are derived for the distribution of axial and interfacial shear stress in cylindrical and elliptical fibres, as well as conical and paraboloidal fibres with asymmetric ends. Additionally, the distribution of axial and interfacial shear stress for conical and paraboloidal fibres with symmetric ends are numerically predicted. The results are compared with solutions from axisymmetric finite element models. A parameter study is performed, to investigate the suitability of alternative fibre geometries for use in FRP.
A new in vitro tool to investigate cardiac contractility under physiological mechanical conditions
(2019)
An optimization method is developed to describe the mechanical behaviour of the human cancellous bone. The method is based on a mixture theory. A careful observation of the behaviour of the bone material leads to the hypothesis that the bone density is controlled by the principal stress trajectories (Wolff’s law). The basic idea of the developed method is the coupling of a scalar value via an eigenvalue problem to the principal stress trajectories. On the one hand this theory will permit a prediction of the reaction of the biological bone structure after the implantation of a prosthesis, on the other hand it may be useful in engineering optimization problems. An analytical example shows its efficiency.
This work is an attempt to answer the question: How to use convex programming in shakedown analysis of structures made of materials with temperature-dependent properties. Based on recently established shakedown theorems and formulations, a dual relationship between upper and lower bounds of the shakedown limit load is found, an algorithmfor shakedown analysis is proposed. While the original problem is neither convex nor concave, the algorithm presented here has the advantage of employing convex programming tools.
Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element-based formulation of ES-FEM and FS-FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element-based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS-FEM applications found in the literature. Shape functions for non-simplex 3D elements are proposed in order to apply FS-FEM to any standard finite element.