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The numerical analysis of 4-On-Pillars technique using meshless methods
Published in J. Belinha, R.M. Natal Jorge, J.C. Reis Campos, Mário A.P. Vaz, João Manuel, R.S. Tavares, Biodental Engineering V, 2019
K.F. Vargas, G.A.R. Caldas, J. Belinha, R.M. Natal Jorge, P.A.G. Hernandez, A. Ozkomur, R. Smidt, M.M. Naconecy, L.E. Schneider
One of the most popular numerical tool used is the Finite Element Method (FEM) (Zienkiewicz & Taylor, 1994), which can be used to predict the biomechanical behaviour of implants, prostheses and bone remodelling. FEM is recognized and commonly used in many fields of engineering and science. It is characterized by the problem domain discretization into small elements connected through nodes. Such discretization comprises the creation of the mesh, the elements, their respective nodes and definition of boundary conditions (Geng, Tan, & Liu, 2001) (Alencar et al., 2017). This numerical method allows to solve engineering problems for which it is difficult to obtain an exact analytical solution. Additionally, it allows to save time, minimizing the costs of scientific research. Furthermore, the virtual simulation of bio-tissue avoids the use of experimental tests in animals. (Holmes, Grigsby, Goel, & Keller, 1992) (Brunski, 2014) (Bordin, Bergamo, Fardin, Coelho, & Bonfante, 2017). However, FEM has some limitations, mostly related to the generation of the element mesh, which represents most of the computational cost of the complete FEM analysis. Therefore, this is a mesh-dependent discretization method and the solution is directly influenced by the element mesh arrangement (C. Tavares, Belinha, Dinis, & Jorge, 2015).
Review of Numerical Methods
Published in Yongjie Jessica Zhang, Geometric Modeling and Mesh Generation from Scanned Images, 2018
Numerical methods did not start with the advent of computers. In old days, people used abacuses, slide rules (a mechanical analog computer) and log tables. Gradually, digital computation received more attention as computers became more powerful. A computer can speed up the computation significantly and reduce the risk of error. In general, a numerical method is a powerful tool that solves problems that are not tractable analytically, especially for nonlinear equations, partial differential questions and complex engineering problems. See Table 2.1 for the detailed comparison between analytical solution and numerical solution.
Extreme Waves Excited by Radiation Impact
Published in Shamil U. Galiev, Extreme Waves and Shock-Excited Processes in Structures and Space Objects, 2020
The examined problems in the two-dimensional axisymmetric formulation were solved numerically using an explicit Lagrange algorithm. Comparison of the calculated results with the data obtained in experiments made it possible to verify the numerical method used. As a result of automatic rearrangement of the numerical mesh all types of fracture formed in dynamics could be examined.
2D and 3D soil finite/infinite element models: modelling, comparison and application in vehicle-track dynamic interaction
Published in International Journal of Rail Transportation, 2023
Zheng Li, Lei Xu, Dongli Wang, Zengjian Niu, Yongsheng Zhao, Wei Liu, Xinsheng Zhan
Regarding numerical method, it is mainly conducted from viewpoint of the time domain analysis. For its wide applicability, numerical method can solve most problems in engineering. Gardien and Stuit [14] developed a 3D propagation half-model for tunnel to investigate the response spread through soil surrounding the tunnel. Ju [15] developed a full-scale vehicle-road soil FEM model and made a comparison on the numerical and field experimental results. Zhai [16] proposed a train-track-ground dynamic model to predict the soil ground vibrations induced by high-speed trains, in which the integrated model considered a complicated wheel-rail relationship. Besides, it was validated by the experiments in situ. Furthermore, a 3D VTS model founded by LY-DYNA (Refs [8,17]) was introduced to analyse the vehicle-induced vibrations of pile-soil structure and seismic metamaterials.
Optimal Allocation and Hourly Scheduling of Capacitor Banks Using Sine Cosine Algorithm for Maximizing Technical and Economic Benefits
Published in Electric Power Components and Systems, 2019
Abdelazeem A. Abdelsalam, Hany S. E. Mansour
Several optimization techniques have been proposed in the former decades. A literature review about C-Bs allocation techniques is presented in [5]. The optimal C-Bs allocation techniques can be categorized as follows; analytical methods, numerical methods, heuristic methods, and meta-heuristic methods. In the analytical methods, some approximation had been done in order to reduce the computation procedure and the objective function was formulated with aim of maximizing the reduction of power losses. Also the famous “two-thirds” rule for C-B placement was suggested and that means "to achieve the maximum power loss reduction, the C-Bs should be connected at a position two-thirds of the distance along the total feeder length with rating equals to two-thirds of the maximum reactive load". A numerical method is based on an approach by which mathematical problems are formulated so that they can be solved numerically. Numerical programing techniques are iterative techniques utilized for maximizing (or minimizing) the objective function of decision variables. The values of the decision variables must also satisfy a set of constraints. With the availability of large memories and faster computing processors, the utilization of numerical methods in power system has increased [6].
Numerical assessment of the effect of different end-plates on the performance of a finite-height Savonius turbine
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2021
Mohsen Goodarzi, Salaheddin Salimi
Generally, a numerical method must be validated by a set of reliable data. In the present study, a particular Savonius turbine, which was analyzed by Ferrari et al. (2017), was simulated to validate the prescribed numerical method. Note that the simulated rotor has the same geometry of that was studied by Ferrari et al. (2017). The most important dimensionless parameter describing the mechanical performance of the wind turbine is the torque coefficient. It is defined as (Ferrari et al. 2017)