A numerical approach for the computation of dispersion relations for plate structures using the Scaled Boundary Finite Element Method

In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.     

A novel approach to mode-tracing in SBFEM-simulations: Higher-order Taylor- and Padé approximation

This contribution presents the study of strange phenomena in wave mode representations of waveguides. For this study the waveguides are computed by means of the Scaled Boundary Finite Element Method (SBFEM). Different approaches of mode tracing are used to identify the characteristics of the resulting wave modes. Higher order differentials of the underlying eigenvalue problem are the basis for these approaches. The main idea behind this mode tracing approach is to reduce the cubic computation time to solve the eigenvalue problem for each frequency of interest. This study identifies potentially critical frequency regions and attempts to formulate a solution process. The fascinating effects at critical frequencies are displayed and a suggestion for a stabilization for the solution process is made. This study bases its conclusion on a numerical viewpoint. Main aspects in this study include high order differentials of the eigenvalue problem and the corresponding Taylor and Padé approximations for the eigenvalue problem as a whole. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Carbon nanotube sidewall functionalization with carbonyl compounds--modified Birch conditions vs the organometallic reduction approach

Covalent addition reactions turned out to be one of the most important functionalization techniques for a structural alteration of single walled carbon nanotube (SWCNT) scaffolds. During the last years, several reaction sequences based on an electrophilic interception of intermediately generated SWCNT(n-) carbanions, obtained via Birch reduction or by a nucleophilic addition of organometallic species, have been developed. Nevertheless, the scope and the variety of potential electrophiles is limited due to the harsh reaction conditions requested for a covalent attachment of the functional entities onto the SWCNT framework. Herein, we present a significant modification of the reductive alkylation/arylation sequence, the so-called Billups reaction, which extends the portfolio of electrophiles for covalent sidewall functionalization to carbonyl compounds--ketones, esters, and even carboxylic acid chlorides. Moreover, these carbonyl-based electrophiles can also be used as secondary functionalization reagents for anionic SWCNT intermediates, derived from a primary nucleophilic addition step. This directly leads to the generation of mixed functional SWCNT architectures, equipped with hydroxyl or carbonyl anchor groups, suitable for ongoing derivatization reactions. A correlated absorption and emission spectroscopic study elucidates the influence of the covalent sidewall functionalization degree onto the excitonic transition features of carbon nanotubes. The characterization of the different SWCNT adducts has been carried out by means of Raman, UV-vis/nIR, and fluorescence spectroscopy as well as by thermogravimetric analysis combined with mass spectrometry and X-ray photoelectron spectroscopy analysis.     

Integrated planning of transportation and recycling for multiple plants based on process simulation

By-products accrue in all stages of industrial production networks. Legal requirements, shortening of primary resources and their increasing prices make their recycling more and more important. For the re-integration into the economic cycle the scope of common supply chain management is enlarged and so-called closed-loop supply chains with adapted and new planning tasks are developed. In process industries this requires a detailed modelling of the recycling processes. This is of special relevance for operational planning tasks in which an optimal usage of a given production system is envisaged. This contribution presents an integrated planning approach for a real-world case study from the zinc industry to achieve such an adequate process modelling. We consider the planning problem of a company that operates four metallurgical recycling plants and has to allocate residues from different sources to these recycling sites. The allocation determines the raw material mix used in the plants. This blending has an effect on the transportation costs and the costs and revenues of the individual technical processes in the recycling plants. Therefore in this problem transportation and recycling planning for multiple sites have to be regarded in an integrated way. The necessary detailed process modelling is achieved by the use of a flowsheet process simulation system to model each recycling plant individually. The models are used to derive linear input–output functions by multiple linear regression analyses. These are used in an integrated planning model to calculate the decision-relevant input and output flows that are dependent upon the allocation of the residues to the recycling sites. The model is embedded in a decision support system for the operational use. An example application and sensitivity analyses demonstrate and validate the approach and its potentials. The approach is transferable to other recycling processes as well as to other processes in process industries.