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Guidelines for practical use of nonlinear finite element analysis
Published in Paulo B. Lourenço, Angelo Gaetani, Finite Element Analysis for Building Assessment, 2022
Paulo B. Lourenço, Angelo Gaetani
Linear triangular and tetrahedral elements do not suffer hourglassing issues. However, in some applications, their behaviour is stiffer than quadrilateral or hexahedral elements, and the final displacements may be underestimated, especially when bending occurs. The reason lays on the fact that these elements have constant strain, thus stress. Consequently, equilibrium is satisfied by means of underestimated nodal displacements, with consequences on the assessment of strain and stress. The shortcoming is usually avoided by using multiple elements that better approximate the expected stress distribution. It is worth reminding that averaging or smoothing the results may help visualizing the otherwise piecewise constant results. However, as shown in Section 5.4, it is recommended to compare averaged and unaveraged results to look for inaccuracies, together with a check of mesh convergence (see Section 5.2.4). Consequently, triangular (two-) and tetrahedral (three-dimensional) meshing (often done automatically by software codes) should be compensated by a larger number of elements needed, that in turn affects the computational costs. The analyst should consider these two aspects when choosing quadrilateral or triangular, hexahedral or tetrahedral elements. If possible, quadrilateral or hexahedral elements should be preferred, in the case of linear analysis. However, in the case of large models with complex geometry, a fine mesh with triangular or tetrahedral elements is likely to be the best option.
Image-Based Triangular and Tetrahedral Meshing
Published in Yongjie Jessica Zhang, Geometric Modeling and Mesh Generation from Scanned Images, 2018
Poorly shaped elements influence the convergence and stability of finite element simulations, therefore it is critical to generate meshes with good quality. First we need to define proper criteria to measure the quality of various types of meshes. For triangular meshes, a popular metric is the aspect ratio defined as 2 * rin/rout, where rin is the radius of the inscribed circle and rout is the radius of the circumcircle. For tetrahedral meshes, people choose various mesh quality functions to measure them; for example, the dihedral angle [144], the ratio of the element diameter such as the longest edge over the in-radius [150], the edge ratio of the longest edge over the shortest edge in a tetrahedron, the Joe-Liu parameter [244] and a minimum volume bound. With these measures, the mesh quality can be judged by checking the worst, mean and best mesh quality, as well as the distribution of elements in terms of their quality metrics or the histograms.
Computational Electromagnetics
Published in Parveen Berwal, Jagjit Singh Dhatterwal, Kuldeep Singh Kaswan, Shashi Kant, Computer Applications in Engineering and Management, 2022
Parveen Berwal, Jagjit Singh Dhatterwal, Kuldeep Singh Kaswan, Shashi Kant
Tetrahedral meshes have the benefit of ensuring that curved surfaces are well approximated. The only drawback is that such a mesh is not suitable for time-domains: The corresponding matrix multiplication (for any number method) can be solved in frequency-domains efficiently but are ineffective for time-domain algorithms because of their non-diagonal properties. It must be emphasized, finally, that tetrahedral numerical solution is not a trivial operation.
Numerical simulation of indirect contact phase-change cooling system with R1234yf/R152a mixed refrigerant for battery thermal management
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2023
Yujia Kang, Chunhua Zhang, Jing Ma, Ke Yang
The geometric model in Figure 3 is imported into the Meshing. The single battery, thermal conductive sheet, and cold plate are set as solid domains, while the refrigerant flow area is set as a fluid domain. Since the BTM models are regular shapes, hexahedral meshes can be used in this case. Hexahedral meshes discretize continuous space into cubic elements consisting of six planes. The meshing results are shown in Figure 6. The advantage of using hexahedral meshes is that the shape is simple and has better mathematical properties when the shape of an object is relatively regular, which improves numerical stability and accuracy. Compared with other mesh types, such as tetrahedral meshes, hexahedral meshes have a more compact structure and higher efficiency in numerical calculations. This is relatively easy to process and store in computer programs, which is particularly important for complex simulation and optimization problems.
Recognition and decomposition of rib features in thin-shell plastic parts for finite element analysis
Published in Computer-Aided Design and Applications, 2018
Jiing-Yih Lai, Ming-Hsuan Wang, Pei-Pu Song, Chia-Hsiang Hsu, Yao-Chen Tsai
Mold flow analysis is commonly used in injection molding to assist in designing injection molds as well as setting the process parameters. In mold flow analysis, it is necessary to convert the computer-aided design (CAD) model into solid meshes so that the solver can perform computations. Traditionally, tetrahedral meshes are used because they are easy to generate automatically, but this type of mesh is of the lowest quality compared with other types (e.g., pyramid, prism, or hexahedron). Hexahedral meshes are highly preferable to tetrahedral meshes for their greater accuracy, convergence, and application specificity. However, hexahedral meshes are inherently trickier to generate because they require the careful decomposition of the CAD model, which is usually complex and challenging even for well-trained CAE engineers. The generation of entirely hexahedral meshes on a CAD model may be difficult, but a hybrid combination of hexahedral and prismatic meshes is possible and can solve the problems of tetrahedral meshes.
Image-based finite-element modeling of the human femur
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2020
Cristina Falcinelli, Cari Whyne
The second step in geometry-based FE mesh generation is meshing of the segmented bone geometry (Schileo et al. 2007; Grassi et al. 2012). The use of unstructured meshes is most commonly employed, in particular tetrahedral meshes. The choice of tetrahedral elements is related to their ability to better fit complex computational domains (e.g. curved geometries, acute angles) (Spears et al. 2001; Wirtz et al. 2003; Perillo-Marcone et al. 2004; Cheung et al. 2005) and the ease of automatic meshing compared to hexahedral elements (Ramos and Simões 2006). Different shape functions, linear (four-noded) or quadratic (ten-noded), can be used to approximate the displacement field over each element. Quadratic elements admit a parabolic displacement field over each element enabling stress and strain to vary linearly over each element. Conversely, individual linear elements exhibit a constant value of strain and stress. The choice of shape function is problem dependent; higher order elements increase the computational requirements of the model. In analyzing the biomechanics of the human femur under compressive loading, Polgar et al. (2001) demonstrated that ten-noded quadratic tetrahedral elements provide more accurate FE modeling results (maximum principal stress error <5%) compared to four-noded linear tetrahedral elements. However, in modeling contact or crack initiation and propagation (e.g. when the phase field method is used), linear elements avoid problems seen with quadratic shape functions (e.g. convergence problems, volumetric locking) (Perillo-Marcone et al. 2004; Completo et al. 2007; Dopico-González et al. 2010; Shen et al. 2019).