Bücher der Reihe Mechanics and Adaptronics

The novel finite element formulations fall into the category of geometrically exact Kirchhoff-Love beams. A prominent characteristic of this category is that the absence of shear deformation is strongly enforced by removing two degrees of freedom. Further, the corresponding beam theories exhibit not only translational but also rotational degrees of freedom and their configurations thus form a non-additive and non-commutative space. Sophisticated interpolation schemes are required that need to be tested not only for locking, spatial convergence behavior, and energy conservation, but also for observer invariance and path-independence. For the three novel beam element formulations all these properties are analytically and numerically studied and confirmed, if applicable. Two different rotation parameterization strategies are employed based on the well-known geodesic interpolation used in many Simo-Reissner beams and the lesser known split into the so-called \textit{smallest rotation} and a torsional part. Application of the former parameterization results in a mixed finite element formulation intrinsically free of locking phenomena. Additionally, the first geometrically exact Kirchhoff-Love beam element is presented, which strongly enforces inextensibility by removing another degree of freedom. Furthermore, the numerical efficiency of the new beam formulations is compared to other beam elements that allow for or suppress shear deformation. When modeling very slender beams, the new elements offer distinct numerical advantages.Standard molecular dynamics simulations, which are commonly used to study polymers, suffer from a lack of a careful mathematical basis and the use of an expensive explicit time integration scheme. To circumvent these shortcomings and to be able to simulate stretching experiments on relevant time scales, the problem is described by a stochastic partial differential equation, which can be solved using the finite element method with a backward Euler temporal discretization. In detail, the polymer is represented by a Kirchhoff-Love beam with a linear elastic constitutive model. Inertial and electrostatic forces are neglected. It is deformed by a distributed load mimicking collisions with molecules of the surrounding fluid. Naturally, this load heavily fluctuates over time and space and mean values need to be computed in a Monte Carlo manner. To vastly speed up the fitting process to experimental data in a Bayesian framework, a surrogate model based on a Gaussian process is set up, which directly computes the mean values for given material parameters. The uncertainties and correlations of the material parameters are studied and compared to the literature.

This thesis works on the topic of fiber-reinforced plastics and discusses the measurement of strain with embedded sensors. Embedding sensors into a structure fundamentally poses challenges arising from the differences in mechanical properties of sensor and structure. This thesis works on the research area of Self-Sensing, where these challenges are overcome by using carbon fibers for both load-carrying and strain-sensing functions. Starting with a literature review, this thesis proposes three research hypotheses, which are targeted to describe the Self-Sensing properties of unidirectional carbon fiber reinforced plastics (CFRPs) for strain measurements. These hypotheses assume, that the electric anisotropy of the material results in a complex voltage distribution within a Self-Sensing specimen. In order to discuss this point further, a two-dimensional piezoresistivity model based on the Laplace equation is introduced. The developed model newly allows to quantify the electricpotential changes in specimens with arbitrary geometrical dimensions and electric anisotropy.Furthermore, this thesis discusses a set of experimental results on the piezoresistive properties of unidirectional CFRP made with the pultrusion process. Overall, the results of the experiments indicate that the most repeatable results are obtained for specimens with electric contacts at their cut-end. This approach allows to manufacture Self-Strain-Sensing rods with a gauge factor of approximately 1.9 that can be used in a multifunctional manner for both load-carrying and strain-sensing purposes. Furthermore, a novel measurement setup is developed, which allows to acquire the electric potential distribution on the surface of electrical conductors with very high spacial resolution. This experimental setup newly reveals that the current flow in specimens can be more complex than assumed in a two-dimensional model.

This book provides findings on the simulation of the valve dynamic to the current technological standards. Above all, it delivers a simulation based and predictive approach on the fatigue strength assessment of four-stroke heavy-duty engine valves. The demand for more efficient combustion engines with fuel flexibility goes along with increasing component requirements regarding strength and durability, while the development costs should remain low. In this context, the present book focuses on the gas exchange valves of heavy-duty engines. Especially, the valves on the exhaust side have an increased risk of fatigue failure. The aim of this book is the generation of a predictive fatigue strength assessment to strengthen the frontloading of the exhaust valve design process and to increase the reliability of the component. In the context of fatigue assessment, this book examines the loads of the exhaust valve during its working cycle. Beside the high temperature and cylinder pressure, further loads act on the exhaust valve like actuation force or an eccentric impact of the valve on the valve seat ring. Furthermore, a bold valve secondary dynamic in the form of valve bending vibrations is observed on the exhaust valves of heavy-duty engines increasing the valve load even more. The cause of this secondary dynamic is unknown. This book investigates the valve loads to get the necessary input for the fatigue strength assessment. With respect to a predictive approach, the determination of valve dynamic and valve loads is based on a multibody simulation model of the valve train. In order to deliver predictive results and a transferable method, this simulation model includes all relevant physical effects to describe the valve dynamic accurately during all valve load phases of the working cycle. With the simulation model, the root cause for the bold valve secondary dynamic is examined iteratively. The model delivers not only the cause for the valve secondary dynamic but most importantly the critical valve loads. These loads deliver the input for the fatigue strength assessment. To ensure the robustness of the load data determined by the simulation model, the sensitivity of influences on the valve load is examined. In this context geometrical misalignment, fluctuations in load data and variable engine operation points are considered. A load collective based on the variation of influences on the valve load is the result of this analysis. All the results of the influence and sensitivity study are generated with the newly developed simulation model of the valve train. Moreover, this book outlines measurements on a testbed engine. In scope of these measurements are temperature and strain measurements of the valve. The generated data validate the simulation model of the valve train. Additionally, the statistical evaluation of the data is used in the subsequent fatigue strength assessment to increase the reliability of the results.