A least squares finite element method with high degree element shape functions for one-dimensional Helmholtz equation

2006 ◽  
Vol 73 (1-4) ◽  
pp. 76-86 ◽  
Author(s):  
Carlos E. Cadenas ◽  
Javier J. Rojas ◽  
Vianey Villamizar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Helmholtz Equation ◽  
Least Squares ◽  
Shape Functions ◽  
One Dimensional ◽  
High Degree ◽  
Element Shape ◽  
Element Method

The Inversion of Concrete Thermal Conductivity Using Least Squares Finite Element Method

2015 ◽  
Vol 723 ◽  
pp. 460-463
Author(s):  
Shao Jun Huo ◽  
Fu Guo Tong ◽  
Gang Liu
Keyword(s):  
Thermal Conductivity ◽  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Annular Region ◽  
Internal Temperature ◽  
One Dimensional ◽  
Order Of Magnitude ◽  
Steady State Heat ◽  
Element Method

This paper adopted the least squares of finite element method to calculate the thermal conductivity of concrete in annular region according to the internal temperature of concrete in one-dimensional steady-state heat conduction. The concrete in annular region was divided into several kinds of materials along the radius when computing thermal conductivity. The results that the ratios of the thermal conductivity of different radius are no more than one order of magnitude prove that the least squares finite element method has a high precision.

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.

scholarly journals Finite Element Analysis of Thermoelastic Contact Stability

1994 ◽  
Vol 61 (4) ◽  
pp. 919-922 ◽  
Author(s):  
Taein Yeo ◽  
J. R. Barber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Eigenvalue Problem ◽  
Linear Perturbation ◽  
Dimensional System ◽  
The Finite Element Method ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
Element Method

When heat is conducted across an interface between two dissimilar materials, theimoelastic distortion affects the contact pressure distribution. The existence of a pressure-sensitive thermal contact resistance at the interface can cause such systems to be unstable in the steady-state. Stability analysis for thermoelastic contact has been conducted by linear perturbation methods for one-dimensional and simple two-dimensional geometries, but analytical solutions become very complicated for finite geometries. A method is therefore proposed in which the finite element method is used to reduce the stability problem to an eigenvalue problem. The linearity of the underlying perturbation problem enables us to conclude that solutions can be obtained in separated-variable form with exponential variation in time. This factor can therefore be removed from the governing equations and the finite element method is used to obtain a time-independent set of homogeneous equations in which the exponential growth rate appears as a linear parameter. We therefore obtain a linear eigenvalue problem and stability of the system requires that all the resulting eigenvalues should have negative real part. The method is discussed in application to the simple one-dimensional system of two contacting rods. The results show good agreement with previous analytical investigations and give additional information about the migration of eigenvalues in the complex plane as the steady-state heat flux is varied.

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