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Squeaking in Total Hip Arthroplasty
Published in Jitendra Kumar Katiyar, Alessandro Ruggiero, T.V.V.L.N. Rao, J. Paulo Davim, Industrial Tribology, 2023
Alessandro Ruggiero, Marco De Stefano, T.V.V.L.N. Rao
The finite element method operates by decomposing the complex and continuous domain of the system into a set of numerous subdomains of variable geometric nature (finite elements) and into a set of points (nodes), solving them and reassembling the entire prostheses domain solutions.
Finite Element Analysis
Published in G. Ravichandran, Finite Element Analysis of Weld Thermal Cycles Using ANSYS, 2020
The finite element method is a numerical technique for the analysis of engineering components. In this method, the operating domain is divided into a number of subdomains called elements. The elements are connected to each other by the corner points which are called nodes. The field variable is assigned to the nodes and within each element, the field variable is assumed to vary as per linear or quadratic relationship while maintaining continuity at the nodes. The field variable is thus said to be piecewise continuous and is expressed in terms of the interpolation function or shape function for the elements and the nodal values of the field variable.
Numerical Features Used in Simulations
Published in James Fern, Alexander Rohe, Kenichi Soga, Eduardo Alonso, The Material Point Method for Geotechnical Engineering, 2019
James Fern, Alexander Rohe, Kenichi Soga, Eduardo Alonso
In classical FEM, the application of prescribed boundary conditions is simple as these can be specified directly on the boundary nodes, which coincide with the boundary of the continuum body and are well defined throughout the computation. However, the computational mesh in MPM does not necessarily align with the boundary of the material making the application of the prescribed boundary conditions more challenging. The difficulty arises when dealing with non-zero boundary conditions, including non-zero tractions and non-zero kinematic boundary conditions. Zero kinematic boundary conditions, also called fixities, can be applied at the degree of freedom of the computational grid in a similar way as in FEM. However, those conditions have to be applied to boundary nodes that might become active during computations. This is when a material point is located in the element connected to the node. Applying essential boundary conditions that are not aligned with element boundaries is not trivial. In some cases, the problem is overcome by workarounds such as introducing stiff regions or applying a moving mesh (see Section 1.8). Recently, the implicit boundary method (IBM), which was originally developed for FEM, has been extended to MPM [72]. It consists in defining a trial and test function space that will implicitly lead to the enforcement of the essential boundary conditions.
Simultaneous heat and mass enhancement in mixed convective flow of power-law fluid using hybrid nanoparticles
Published in Waves in Random and Complex Media, 2022
Abdelatif Salmi, Hadi Ali Madkhali, Shafia Rana, Sayer Obaid Alharbi, M. Y. Malik
Models are coupled and nonlinear and their exact solutions are possible. Therefore, approximate solutions are found by the implementation of FEM [18–20]. The residual equations are converted into their residual weighted integrals which are approximated by Galerkin techniques. The stiffness elements are derived and used in the assembly process, which leads to nonlinear algebraic system. This algebraic system is solved iteratively under computational tolerance . Convergence is ensured by computing mesh-free analysis. The results are used for various information about the behaviors of fluid variables. The finite element method is a powerful technique that computes convergent and accurate numerical results. This method is used in this research. Other methods can also be applied with less accuracy. The next section contains graphical and numerical data.
Numerical investigation and modelling of controllable parameters on the photovoltaic thermal collector efficiency in semi-humid climatic conditions
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
Ilias Terrab, Nor Rebah, Samir Abdelouahed, Michel Aillerie, Jean-Pierre Charles
The mesh generation is the numerical approach used to solve the partial differential equations (“Detailed Explanation of the Finite Element Method FEM” n.d). The finite element method separates a complex structure into smaller and simpler sections known as finite elements. The PV/T is meshed using the built-in environment mesh sequence as implemented in COMSOL Multiphysics. At each border, the number of mesh elements increases, leading to a more accurate heat transfer and flow calculations. Free tetrahedral settings were used to develop this model (“Detailed Explanation of the Finite Element Method FEM” n.d).
Effect of wear on frictionally excited thermoelastic instability: A finite element approach
Published in Journal of Thermal Stresses, 2020
Yijun Qiao, Michele Ciavarella, Yun-Bo Yi, Tie Wang
In general, the finite element method is a more convenient method to deal with complex geometries, boundary conditions and loadings compared to the analytical counterpart, and is therefore a preferable tool in industry applications. Although extensive research has been carried out on the aforementioned TEI problems, the study on the effect of wear was limited to the analytical approaches. An implementation of the finite element method to the wear problem is possible by following an approach similar to the classical eigenvalue formulation, with the addition of the Archard wear law.