Shape functions and the accuracy of arch finite elements.

AIAA Journal ◽  
1973 ◽  
Vol 11 (3) ◽  
pp. 287-291 ◽  
Author(s):  
ISAAC FRIED
Keyword(s):  
Finite Elements ◽  
Shape Functions

A study of mixed-mode composite delamination using enriched interface elements

2013 ◽  
Vol 117 (1195) ◽  
pp. 959-967
Author(s):  
I. Guiamatsia ◽  
J. K. Ankersen ◽  
L. Iannucci
Keyword(s):  
Finite Elements ◽  
Analytical Solution ◽  
Elastic Foundation ◽  
Displacement Field ◽  
Mixed Mode ◽  
Crack Tip ◽  
Shape Functions ◽  
Interface Elements ◽  
Minimum Element ◽  
Element Size

Abstract This paper examines the performance of enriching the shape functions of interface finite elements in the prediction of mixed-mode delamination. Enriching second-order interface and solid elements with the analytical solution of a beam on elastic foundation problem yields the correct displacement field ahead of the crack tip. Despite the enrichment being fixed at elements nodes, resulting in non-traceability of the crack tip location, the strategy is shown to perform consistently well, increasing the minimum element size from the typical 0·5mm to 5mm, for a range of classical mixed-mode bending (MMB) specimens.

Finite Element Modeling of Dynamic Behavior of Some Basic Structural Members

1992 ◽  
Vol 114 (1) ◽  
pp. 3-9 ◽  
Author(s):  
R. C. Engels
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Finite Element Modeling ◽  
Mass Matrix ◽  
Matrix Approach ◽  
Structural Members ◽  
Shape Functions ◽  
Generalized Coordinates ◽  
Stiffness Matrices ◽  
Consistent Mass Matrix

A method is described to model the dynamics of finite elements. The assumed modes method is used to show how static shape functions approximate the element mass distribution. The deterioration of the modal content of a model can be linked to the neglect of interface restrained assumed modes. Restoration of a few of these modes leads to higher accuracy with fewer generalized coordinates compared to the standard consistent mass matrix approach. Also, no need exists for subdivision of basic elements such as rods and beams. The mass and stiffness matrices for several basic elements are derived and used in demonstration problems.

scholarly journals Exact and efficient interpolation using finite elements shape functions

2009 ◽  
pp. 307-331
Author(s):  
Gustavo H.C. Silva ◽  
Rodolphe Le Riche ◽  
Jérôme Molimard ◽  
Alain Vautrin
Keyword(s):  
Experimental Data ◽  
Finite Elements ◽  
Degrees Of Freedom ◽  
Mesh Size ◽  
Large Data ◽  
Fe Model ◽  
Shape Functions ◽  
Natural Choice ◽  
Data Points ◽  
Bounding Boxes

The comparison of finite elements (FE) and experimental data fields have become ever more prevalent in numerical simulations. Since FE and experimental data fields rarely match, the interpolation of one field into the other is a fundamental step of the procedure. When one of the fields comes from FE, using the existing FE mesh and shape functions is a natural choice to determine mesh degrees of freedom at data point coordinates. This makes no assumptions beyond those already made in the FE model. In this sense, interpolation using element shape functions is exact. However, crude implementations of this technique generally display a quadratic computation complexity with respect to mesh size and number of data points, which is impractical when large data fields must be compared repeatedly. This document aims at assembling existing numerical procedures to improve the interpolation efficiency. With a combination of cross-products, bounding-boxes and indexing methods, the resulting algorithm shows linear computation cost, providing significant improvement in efficiency.

scholarly journals Extended Penalty Coefficients For Elimination The Locking Effects In Moderately Thick Beam And Plate Finite Elements

2014 ◽  
Vol 60 (3) ◽  
pp. 367-385
Author(s):  
W. Gilewski
Keyword(s):  
Finite Elements ◽  
Strain Energy ◽  
Consistency Condition ◽  
Shape Functions ◽  
Exact Integration ◽  
The Third ◽  
Rectangular Element ◽  
Thick Beam ◽  
Independent Parameters ◽  
Linear Shape

AbstractThe present paper is dedicated to presentation and energy verification of the methods of stabilization the strain energy by penalty coefficients. Verification of the methods is based on the consistency and ellipticity conditions to be satisfied by the finite elements. Three methods of stabilization are discussed. The first does not satisfy the above requirements. The second is consistent but cannot eliminate parasitic energy terms. The third method, proposed by the author, is based on the decomposition of the element stiffness matrix. The method can help to eliminate locking of the finite elements. For two-noded beam element with linear shape functions and exact integration a stabilized free of locking (and elliptical) element is received (equivalent to reduced integration element). Two plate finite elements are analyzed: four-noded rectangular element and DSG triangle. A new method of stabilization with the use of four independent parameters is proposed. The finite elements with this kind of stabilization satisfy the consistency condition. In the rectangular element it was not possible to eliminate one parasitic term of energy which appears during the procedure. For DSG triangle all parasitic terms of energy are eliminated. The penalty coefficients depends on the geometry of the triangle.

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