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Smoothed Finite Element Methods for Nonlinear Solid Mechanics Problems: 2D and 3D Case Studies
(2016)
The Smoothed Finite Element Method (SFEM) is presented as an edge-based and a facebased techniques for 2D and 3D boundary value problems, respectively. SFEMs avoid shortcomings of the standard Finite Element Method (FEM) with lower order elements such as overly stiff behavior, poor stress solution, and locking effects. Based on the idea of averaging spatially the standard strain field of the FEM over so-called smoothing domains SFEM calculates the stiffness matrix for the same number of degrees of freedom (DOFs) as those of the FEM. However, the SFEMs significantly improve accuracy and convergence even for distorted meshes and/or nearly incompressible materials.
Numerical results of the SFEMs for a cardiac tissue membrane (thin plate inflation) and an artery (tension of 3D tube) show clearly their advantageous properties in improving accuracy particularly for the distorted meshes and avoiding shear locking effects.
Engineers are of particular importance for the societies of tomorrow. The big social challenges society has to cope with in future, can only be mastered, if engineers link the development and innovation process closely with the requirements of people. As a result, in the frame of the innovation process engineers have to design and develop products for diverse users. Therefore, the consideration of diversity in this process is a core competence engineers should have. Implementing the consideration of diverse requirements into product design is also linked to the development of sustainable products and thus leads to social responsible research and development, the core concept formulated by the EU.
For this reason, future engineers should be educated to look at the technical perspectives of a problem embedded in the related questions within societies they are developing their artefacts for. As a result, the aim of teaching engineering should be to prepare engineers for these requirements and to draw attention to the diverse needs in a globalized world.
To match the competence profiles of future engineers to the global challenges and the resulting social responsibility, RWTH Aachen University, one of the leading technical universities in Germany, has established the bridging professorship “Gender and Diversity in Engineering” (GDI) which educates engineers with an interdisciplinary approach to expand engineering limits. The interdisciplinary teaching concept of the research group pursues an approach which imparts an application oriented Gender and Diversity expertise to future engineers. In the frame of an established teaching concept, which is a result of experiences and expertise of the research group, students gain theoretical knowledge about Gender and Diversity and learn how to transfer their knowledge into their later field of action.
In the frame of the conference the institutional approach will be presented as well as the teaching concept which will be introduced by concrete course examples.
A further development of the Added-Mass-Method allows the combined representation of the effects of both soil-structure-interaction and fluid-structure interaction on a liquid-filled-tank in one model. This results in a practical method for describing the dynamic fluid pressure on the tank shell during joint movement. The fluid pressure is calculated on the basis of the tank's eigenform and the earthquake acceleration and represented by additional masses on the shell. The bearing on compliant ground is represented by replacement springs, which are calculated dependent on the local soil composition. The influence of the shear modulus of the compliant soil is clearly visible in the pressure curves and the stress distribution in the shell. The acceleration spectra are also dependent on soil stiffness. According to Eurocode-8 the acceleration spectra are determined for fixed soil-classes, instead of calculating the accelerations for each site in direct dependence on the soil composition. This leads to unrealistic sudden changes in the system's response. Therefore, earthquake spectra are calculated for different soil models in direct dependence of the shear modulus. Thus, both the acceleration spectra and the replacement springs match the soil composition. This enables a reasonable and consistent calculation of the system response for the actual conditions at each site.
Near-Earth asteroid 99942 Apophis provides a typical example for the evolution of asteroid orbits that lead to Earth-impacts after a close Earth-encounter that results in a resonant return. Apophis will have a close Earth-encounter in 2029 with potential very close subsequent Earth-encounters (or even an impact) in 2036 or later, depending on whether it passes through one of several so-called gravitational keyholes during its 2029-encounter. Several pre-2029-deflection scenarios to prevent Apophis from doing this have been investigated so far. Because the keyholes are less than 1 km in size, a pre-2029 kinetic impact is clearly the best option because it requires only a small change in Apophis' orbit to nudge it out of a keyhole. A single solar sail Kinetic Energy Impactor (KEI) spacecraft that impacts Apophis from a retrograde trajectory with a very high relative velocity (75-80 km/s) during one of its perihelion passages at about 0.75 AU would be a feasible option to do this. The spacecraft consists of a 160 m x 160 m, 168 kg solar sail assembly and a 150 kg impactor. Although conventional spacecraft can also achieve the required minimum deflection of 1 km for this approx. 320 m-sized object from a prograde trajectory, our solar sail KEI concept also allows the deflection of larger objects. In this paper, we also show that, even after Apophis has flown through one of the gravitational keyholes in 2029, solar sail Kinetic Energy Impactor (KEI) spacecraft are still a feasible option to prevent Apophis from impacting the Earth, but many KEIs would be required for consecutive impacts to increase the total Earth-miss distance to a safe value. In this paper, we elaborate potential pre- and post-2029 KEI impact scenarios for a launch in 2020, and investigate tradeoffs between different mission parameters.