A New Quadratic Membrane Element

2004 ◽  
Vol 261-263 ◽  
pp. 537-542
Author(s):  
Shui Lin Wang ◽  
Xia Ting Feng ◽  
Xiu Run Ge
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Quadratic Function ◽  
High Accuracy ◽  
Displacement Function ◽  
Test Problems ◽  
Interpolation Function ◽  
Membrane Element ◽  
Quadrilateral Element

In finite element method, the order of complete polynomial of the interpolation function is related to the number of nodes in the element. This paper presents a four-node quadrilateral element with quadratic function on it. The presented displacement functions maintain C0-continuity. Meanwhile, the element stiffness matrix is derived from the displacement functions. Test problems show that high accuracy can be achieved by the use of the new displacement function on the element.

The Finite Element Model Study of the Pre-Twisted Euler Beam

2012 ◽  
Vol 446-449 ◽  
pp. 3615-3618
Author(s):  
Ying Huang ◽  
Chang Hong Chen ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Displacement Function ◽  
Interpolation Function ◽  
Euler Beam ◽  
Systematic Analysis ◽  
Element Stiffness Matrix ◽  
Straight Beam

Based on the traditional mechanical model of straight beam, the paper makes a systematic analysis and research on the pre-twisted Euler beam finite element numerical model. The paper uses two-node model of 12 degrees of freedom, axial displacement interpolation function using 2-node Lagrange interpolation function, beam transverse bending displacements (u and υ) still use the cubic displacement, bending with torsion angle displacement function using cubic polynomial displacement function. Firstly, based on the author previous literature on the flexure strain relationship, the paper deduces the element stiffness matrix of the pre-twisted beam. Finally, by calculating the pre-twisted rectangle section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Euler beam element stiffness matrix has good accuracy.

Accelerating Vector Iteration Methods

1986 ◽  
Vol 53 (2) ◽  
pp. 291-297 ◽  
Author(s):  
M. Papadrakakis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Iterative Methods ◽  
Conjugate Gradient ◽  
Test Problems ◽  
Convergence Properties ◽  
Dynamic Relaxation ◽  
Element Level ◽  
Iteration Methods ◽  
Partial Elimination

This paper describes a technique for accelerating the convergence properties of iterative methods for the solution of large sparse symmetric linear systems that arise from the application of finite element method. The technique is called partial preconditioning process (PPR) and can be combined with pure vector iteration methods, such as the conjugate gradient, the dynamic relaxation, and the Chebyshev semi-iterative methods. The proposed triangular splitting preconditioner combines Evans’ SSOR preconditioner with a drop-off tolerance criterion. The (PPR) is attractive in a FE framework because it is simple and can be implemented at the element level as opposed to incomplete Cholesky preconditioners, which require a sparse assembly. The method, despite its simplicity, is shown to be more efficient on a set of test problems for certain values of the drop-off tolerance parameter than the partial elimination method.

Development of Bifurcation Analysis Method for Rate Dependent Materials

2019 ◽  
Vol 794 ◽  
pp. 220-225
Author(s):  
Daiki Towata ◽  
Yuichi Tadano
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bifurcation Analysis ◽  
Stiffness Matrix ◽  
Computational Method ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Tangent Stiffness Matrix ◽  
Rate Dependent ◽  
Element Method

In this study, a novel numerical method to analyze the bifurcation problemof a rate dependent material using the finite element method is proposed. The consistent stiffness matrix, which is required for a bifurcation analysis using the finite element method, for a rate dependent material is generally hard to compute, therefore, a computational method to calculate the tangent stiffness matrix based on a numerical differential is introduced so that exact bifurcation analyses for the rate dependent material can be conducted. A numerical example of the proposed method is demonstrated, and the adequacy of the proposed method is discussed.

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