Overcoming liabilities of foreignness : expanding to Africa as a foreign Venture Capitalist

Venture Capital firms face additional risks and challenges when investing in start-ups in foreign markets because of the increased geographical, institutional, and cultural distance to potential investment targets resulting in Liabilities of Foreignness. Despite these challenges, there are increasing numbers of cross-border investments in the African market. This dissertation explores the drivers of the increasing interest in African start-ups and how foreign investors are overcoming the liabilities of foreignness. The exploratory study uses a qualitative research approach in the form of semi-structured interviews with 12 active investors in Africa. The results highlight the numerous drivers of the growing African Venture Capital market and the different internationalization strategies applied by foreign investors. Moreover, foreign investors in Africa must adapt their traditional investment process to local conditions. Foreign investors use additional risk assessment signals the deal evaluation and not only invest in later rounds, but also place more emphasis on entrepreneurial characteristics and the expertise of local co-investors. Additionally, foreign investors conduct extensive risk analysis of potential macro-economic scenarios potentially impacting local business models. Post-investment activities by foreign investors are strategic by providing an international context to local African start-ups. This thesis adds to existing literature on internationalization of VC firms with a focus on the African continent.As empresas de Capital de Risco enfrentam riscos e desafios adicionais quando investem em start-ups em mercados estrangeiros devido ao aumento da distância geográfica, institucional e cultural em relação a potenciais alvos de investimento, resultando em Liabilities of Foreignness. Apesar destes desafios, há um número crescente de investimentos transfronteiriços no mercado africano. Esta dissertação explora os motores do crescente interesse nas empresas africanas em fase de arranque e a forma como os investidores estrangeiros estão a ultrapassar as Liabilities of Foreignness. O estudo exploratório utiliza uma abordagem de investigação qualitativa sob a forma de entrevistas semi-estruturadas com 12 investidores activos em África. Os resultados destacam os numerosos motores do crescente mercado africano de capital de risco e as diferentes estratégias de internacionalização aplicadas pelos investidores estrangeiros. Além disso, os investidores estrangeiros em África devem adaptar o seu processo de investimento tradicional às condições locais. Os investidores estrangeiros utilizam avaliações de risco adicionais para assinalar a avaliação do negócio e não só investem em rondas posteriores, mas também colocam mais ênfase nas características empresariais e na perícia dos co-investidores locais. Além disso, os investidores estrangeiros conduzem uma análise de risco extensiva de potenciais cenários macroeconómicos com potencial impacto nos modelos empresariais locais. As actividades pós-investimento dos investidores estrangeiros são estratégicas, proporcionando um contexto internacional às empresas locais africanas em fase de arranque. Esta tese vem juntar-se à literatura existente sobre internacionalização de empresas de capital de risco com enfoque no continente africano

Simulation of Fluid Structure Inte actions by using High Order FEM and SPH

The investigation of fluid structure interactions is crucial in many areas of science and technology. This study presents a robust methodology for studying fluid structure interactions, which is characterized by high convergence behavior and is insensitive to distortion and stiffening effects. Therefore, the Smoothed Particle Hydodynamicy is coupled with the high order FEM. After various coupling methods for linear and quadratic elements from the literature have been described, a variant with higher-value approach functions is implemented. The two methods can be meshed independend without loss of accuracy. After successful validation, it is shown that only a few finite elements are necessary to obtain a convergent solution. The presented method is promising especially for thin-walled structures where significantly fewer degrees of freedom are required than for linear elements

Wave Propagation Analysis using High-Order Finite Element Methods: Spurious Oscillations excited by Internal Element Eigenfrequencies

From a computational point of view, the numerical analysis of ultrasonic guided waves is still a very demanding task. Because of the high-frequency regime both a fine spatial and temporal discretization is required. To minimize the numerical costs, efficient and robust algorithms ought to be developed. One promising idea is therefore to focus on high-order finite element methods (ho-FEM).The current article investigates the behavior of the p-version of the finite element method (p-FEM) and the spectral element method (SEM) with respect to the existence of spurious oscillations in the solution. Convergence studies have shown that it is possible to observe non-physical oscillations under certain conditions. These parasitic vibrations, however, significantly deteriorate the accuracy of the simulation. For this reason, we analyse this phenomenon in detail and propose solutions to avoid its occurrence.Without loss of generality, we employ a two-dimensional plane strain model to derive a guideline as to how to avoid these spurious oscillations, placing a special emphasis on the relation between the element size, the polynomial degree of the high-order shape functions and the excitation frequency.Our results show that accurate simulations are possible if the model is generated according to the proposed methodology. Moreover, the implementation of the guideline into an existing finite element software is straightforward; these properties turn the method into a useful tool for practical wave propagation analyses

Discrete modeling of fiber reinforced composites using the scaled boundary finite element method

A numerical method for the discrete modeling of fiber reinforced composites based on the scaled boundary finite element method (SBFEM) is proposed. A unique feature of this method is that the meshes of the matrix, aggregates, in general volumetric entities can be generated independently of the fibers which are treated as truss elements. To this end, a novel embedding method is developed which connects the mesh of the matrix consisting of scaled boundary polytopes to the fibers. This approach ensures that conforming matrix and fiber meshes are achieved. The computed stiffness matrices for both components are then simply superimposed using the nodal connectivity data. Since volume elements can be intersected by fibers at arbitrary locations, it is of paramount importance to be able to generate polytopal elements which is one unique feature of the chosen SBFEM implementation. An advantage of this procedure is that no interface constraints or special elements are required for the coupling. Furthermore, it is possible to account for random fiber distributions in the numerical analysis. In this contribution, a perfect bonding between the matrix and fibers is assumed. By means of several numerical examples, the versatility and robustness of the proposed method are demonstrated

A continuous multiphase model for liquid metal batteries

Liquid metal batteries (LMBs) are a promising alternative for large-scale stationary energy storage for renewable applications. Using high-abundance electrode materials such as Sodium and Zinc is highly desirable due to their low cost and excellent cell potential. LMBs undergo multiple complex mass transport dynamics and as a result, their operation limits and other critical parameters are not fully understood yet. In this work, a multiphase numerical model was developed to resolve electrode and electrolyte components in 1D and simulate the discharge process of a Na-Zn battery including the interfacial displacement of the molten metal electrodes. The variation in electrolyte composition was predicted throughout the process, including the species distribution and its effect on the cell conductivity and capacity. Volume change and species redistribution were found to be important in predicting the maximum theoretical capacity of the cell when neglecting convective phenomena

Simulation of potential and species distribution in a Li||Bi liquid metal battery using coupled meshes

In this work a 1D finite volume based model using coupled meshes is introduced to capture potential and species distribution throughout the discharge process in a lithium bismuth liquid metal battery while neglecting hydrodynamic effects, focusing on the electrochemical properties of the cell and the mass transport in electrolyte and cathode. Interface reactions in the electrical double layer are considered through the introduction of a discrete jump of the potential modelled as periodic boundary condition to resolve interfacial discontinuities in the cell potential. A balanced-force like approach is implemented to ensure consistent calculation at the interface level. It is found that mass transport and concentration gradients have a significant effect on the cell overpotentials and thus on cell performance and cell voltage. By quantifying overvoltages in the Li Bi cell with a mixed cation electrolyte, it is possible to show that diffusion and migration current density could have counteractive effects on the cell voltage. Furthermore, the simulated limiting current density is observed to be much lower than experimentally measured, which can be attributed to convective effects in the electrolyte that need to be addressed in future simulations. The solver is based on the open source library OpenFOAM and thoroughly verified against the equivalent system COMSOL multiphysics and further validated with experimental results

Anisotropic hierarchic finite elements for the simulation of piezoelectric smart structures

Abstract Purpose -Piezoelectric actuators and sensors are an invaluable part of lightweight designs for several reasons. They can either be used in noise cancellation devices as thin-walled structures are prone to acoustic emissions, or in shape control approaches to suppress unwanted vibrations. Also in Lamb wave based health monitoring systems piezoelectric patches are applied to excite and to receive ultrasonic waves. The purpose of this paper is to develop a higher order finite element with piezoelectric capabilities in order to simulate smart structures efficiently. Design/methodology/approach -In the paper the development of a new fully three-dimensional piezoelectric hexahedral finite element based on the p-version of the finite element method (FEM) is presented. Hierarchic Legendre polynomials in combination with an anisotropic ansatz space are utilized to derive an electro-mechanically coupled element. This results in a reduced numerical effort. The suitability of the proposed element is demonstrated using various static and dynamic test examples. Findings -In the current contribution it is shown that higher order coupled-field finite elements hold several advantages for smart structure applications. All numerical examples have been found to agree well with previously published results. Furthermore, it is demonstrated that accurate results can be obtained with far fewer degrees of freedom compared to conventional low order finite element approaches. Thus, the proposed finite element can lead to a significant reduction in the overall numerical costs. Originality/value -To the best of the author's knowledge, no piezoelectric finite element based on the hierarchical-finite-element-method has yet been published in the literature. Thus, the proposed finite element is a step towards a holistic numerical treatment of structural health monitoring (SHM) related problems using p-version finite elements

High order transition elements: The xNy-element concept -- Part I: Statics

Advanced transition elements are of utmost importance in many applications of the finite element method (FEM) where a local mesh refinement is required. Considering problems that exhibit singularities in the solution, an adaptive hp-refinement procedure must be applied. Even today, this is a very demanding task especially if only quadrilateral/hexahedral elements are deployed and consequently the hanging nodes problem is encountered. These element types, are, however, favored in computational mechanics due to the improved accuracy compared to triangular/tetrahedral elements. Therefore, we propose a compatible transition element - xNy-element - which provides the capability of coupling different element types. The adjacent elements can exhibit different element sizes, shape function types, and polynomial orders. Thus, it is possible to combine independently refined h- and p-meshes. The approach is based on the transfinite mapping concept and constitutes an extension/generalization of the pNh-element concept. By means of several numerical examples, the convergence behavior is investigated in detail, and the asymptotic rates of convergence are determined numerically. Overall, it is found that the proposed approach provides very promising results for local mesh refinement procedures.Comment: 51 pages, 44 figures, 4 table

The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometries

We present a tetrahedral finite cell method for the simulation of incompressible flow around geometrically complex objects. The method immerses such objects into non-boundary-fitted meshes of tetrahedral finite elements and weakly enforces Dirichlet boundary conditions on the objects’ surfaces. Adaptively-refined quadrature rules faithfully capture the flow domain geometry in the discrete problem without modifying the non-boundary-fitted finite element mesh. A variational multiscale formulation provides accuracy and robustness in both laminar and turbulent flow conditions. We assess the accuracy of the method by analyzing the flow around an immersed sphere for a wide range of Reynolds numbers. We show that quantities of interest such as the drag coefficient, Strouhal number and pressure distribution over the sphere are in very good agreement with reference values obtained from standard boundary-fitted approaches. We place particular emphasis on studying the importance of the geometry resolution in intersected elements. Aligning with the immersogeometric concept, our results show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis. We demonstrate the potential of our proposed method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor