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Numerical solution of the heat equation with non-linear, time derivative-dependent source term
(2010)
The mathematical modeling of heat conduction with adsorption effects in coated metal structures yields the heat equation with piecewise smooth coefficients and a new kind of source term. This term is special, because it is non-linear and furthermore depends on a time derivative. In our approach we reformulated this as a new problem for the usual heat equation, without source term but with a new non-linear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semi-implicit and a fully implicit finite volume method. We compared these two methods theoretically as well as numerically. Finally, as practical application, we simulated the heat conduction in coated aluminum fibers with adsorption in the zeolite coating. Copyright © 2010 John Wiley & Sons, Ltd.
Numerical and experimental investigation of tensile behavior of laser beam welded TRIP700 steel
(2011)
Damage of reinforced concrete (RC) frames with masonry infill walls has been observed after many earthquakes. Brittle behaviour of the masonry infills in combination with the ductile behaviour of the RC frames makes infill walls prone to damage during earthquakes. Interstory deformations lead to an interaction between the infill and the RC frame, which affects the structural response. The result of this interaction is significant damage to the infill wall and sometimes to the surrounding structural system too. In most design codes, infill walls are considered as non-structural elements and neglected in the design process, because taking into account the infills and considering the interaction between frame and infill in software packages can be complicated and impractical. A good way to avoid negative aspects arising from this behavior is to ensure no or low-interaction of the frame and infill wall, for instance by decoupling the infill from the frame. This paper presents the numerical study performed to investigate new connection system called INODIS (Innovative Decoupled Infill System) for decoupling infill walls from surrounding frame with the aim to postpone infill activation to high interstory drifts thus reducing infill/frame interaction and minimizing damage to both infills and frames. The experimental results are first used for calibration and validation of the numerical model, which is then employed for investigating the influence of the material parameters as well as infill’s and frame’s geometry on the in-plane behaviour of the infilled frames with the INODIS system. For all the investigated situations, simulation results show significant improvements in behaviour for decoupled infilled RC frames in comparison to the traditionally infilled frames.
Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.