Moving least-squares finite element method

2007 ◽  
Vol 221 (9) ◽  
pp. 1019-1036 ◽  
Author(s):  
M Musivand-Arzanfudi ◽  
H Hosseini-Toudeshky
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Three Dimensional ◽  
Meshless Methods ◽  
Computational Method ◽  
Computational Time ◽  
Moving Least Squares ◽  
Shape Functions ◽  
Element Method

A new computational method here called moving least-squares finite element method (MLSFEM) is presented, in which the shape functions of the parametric elements are constructed using moving least-squares approximation. While preserving some excellent characteristics of the meshless methods such as elimination of the volumetric locking in near-incompressible materials and giving accurate strains and stresses near the boundaries of the problem, the computational time is decreased by constructing the meshless shape functions in the stage of creating parametric elements and then utilizing them for any new problem. Moreover, it is not necessary to have knowledge about the full details of the shape function generation method in future uses. The MLSFEM also eliminates another drawback of meshless methods associated with the lack of accordance between the integration cells and the problem boundaries. The method is described for two-dimensional problems, but it is extendable for three-dimensional problems too. The MLSFEM does not require the complex mesh generation. Excellent results can be obtained even using a simple mesh. A technique is also presented for isoparametric mapping which enables best possible mapping via a constrained optimization criterion. Several numerical examples are analysed to show the efficiency and convergence of the method.

Application of the Vector Finite Element Method to 3D Magnetohydrodynamics

2003 ◽  
Author(s):  
Masaaki Matsumoto ◽  
Takahiko Tanahashi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Magnetic Flux ◽  
Flux Density ◽  
Three Dimensional ◽  
Magnetic Flux Density ◽  
Shape Functions ◽  
Vector Finite Element Method ◽  
Vector Finite Element ◽  
Element Method

It is well known that the vector finite element method is one of the powerful tools for solving electromagnetic problems. The vector shape functions that are consist of the facet and the edge vector shape functions have a lot of characteristics. One of them is automatic conservation of the magnetic flux density in analyzing the Induction equations without iterative correction. In the present paper the vector finite element method is applied to the problems of magnetohydrodynamics. Three-dimensional natural convection in a cavity under a constant magnetic field is analyzed numerically using the GSMAC finite element method for flow field and temperature field and the vector finite element method for the Induction equations. The computational results are good agreement with those obtained using B method that is one of the iterative methods to satisfy the solenoidal condition for the magnetic flux density of the Induction equations.

Applying the Galerkin Least Squares Finite Element Method for Solving Stirred Tank Velocity Fields

2002 ◽  
Author(s):  
Kevin J. Bittorf
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Three Dimensional ◽  
Flow Fields ◽  
Stirred Tank ◽  
Pharmaceutical Chemical ◽  
Cfd Validation ◽  
Stirred Tank Reactors ◽  
Element Method

The Galerkin Least Squares finite element solver, in conjunction with the Spalart-Allmaras turbulence closure model, is used to solve the RANS based equations for flow fields in stirred tank reactors. This GLS finite element method is well established in the aerospace industry and presently is being validated for flow fields used in industrial processes that are commonly found in the pharmaceutical, chemical, food, and personal products industries. The CFD results, computed in the commercial package ORCA, compared well with experimental data attained for the dominating macro flow structures in an axial and radial impeller stirred tanks. The CFD quantitatively predicts the two and three-dimensional wall jet structures that govern the bulk flow in a stirred tank and are responsible for blending, solid suspension, and macro-flow. This area of experimentation provides an initial basis for CFD validation for bulk flows in stirred tank reactors.

Considerations on Finite-Element Method Application in Pavement Structural Analysis

1996 ◽  
Vol 1539 (1) ◽  
pp. 96-101 ◽  
Author(s):  
Yoon-Ho Cho ◽  
B. Frank McCullough ◽  
José Weissmann
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Theory Model ◽  
Primary Objective ◽  
Computational Time ◽  
Flexible Tool ◽  
Traffic Loading ◽  
Pavement Structures ◽  
Element Method

Finite-element models have been applied extensively to the design and analysis of pavement structures. Three types of models have been used to study multilayered pavement structures: plane strain, axisymmetric, and three-dimensional (3-D). The applicability of each these three models and their disadvantages and advantages are discussed. Within the research community, an issue frequently raised about the application of the finite-element method (FEM) to pavement structures is the dependence of the solution on the simplifications that are introduced to reduce computational time and mesh configurations and element size, type, and aspect ratio. This issue is discussed extensively with the primary objective of comparing the solutions derived from FEM models with those from classic mechanistic models. The FEM solutions were derived with a commercial software package, ABAQUS, which is designed as a flexible tool for the implementation of FEM. The solution from the BISAR layered theory model for the traffic loading results was chosen for comparisons with the FEM solution. The 3-D and axisymmetric FEM models yielded results suitable for the traffic loading analysis.

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