28-08-2014, 10:52 AM
Paralinear Element Technique For The Finite Element Analysis Project Report
Paralinear Element Technique.ppt (Size: 549 KB / Downloads: 16)
Introduction
Selection of Element i. e. Size and Shape of Element.
Importance of Aspect Ratio
Number of Elements increases the results.
Order of Displacement field also increases the results
But in case of Rectangular Element, large Aspect Ratio deviate the results.
Use of Para Linear Element
In this study, it is interesting to see the effect of more Aspect Ratio in Para Linear, Cubic Linear, Cubic Para Elements
Literature Review
FEM – General formulations
Triangular elements in FEM
Discretization of structures in FEM
Effect of aspect ratio in modeling
General formulations
This paper introduces a new fixed mesh structural analysis technique.
This paper first introduces the Area Ratio Based Fixed Grid (AFG) formulation.
Later on they introduces new Isoparametric Based Fixed Grid (IFG) formulation.
A fixed grid mesh is generated by discretization of a rectangular domain into equal sized rectangular elements. This creates three types of elements are shown in figure
The two dimensional isoparametric method divides boundary elements into three types depending on their inside area shape.
Quadrilateral elements
Triangular elements
pentagonal elements
Clough and Wilson (1999)
In this paper they have attempted to summarize the early research at the University of California at Berkeley from 1957 to 1970.
Significant finite element research was conducted at the University of California at Berkeley during the period 1957 to 1970.
The initial research was a direct extension of classical methods of structural analysis which previously had been restricted to one-dimensional elements.
The majority of the research conducted was motivated by the need to solve practical problems in
Ergatoudis et al (1968)
An increase of available parameters associated with an element usually leads to improved accuracy of solution.
It is possible thus to use fewer elements for the solution.
This paper concerned with a method of generating a series of elements.
This processes was easily extended to three-dimensional analysis with a basic, eight cornered element.
4 and 8 nodal quadrilaterals, both show a considerable improvement in accuracy over simpler “constant strain” element.
Triangular elements in FEM
In this paper, the problems involved the process of degeneration of quadrilateral element into triangular elements are thoroughly analyzed.
The contents include the formulation of geometry mapping induced by collapsing one side of the quadrilateral element and construction of the shape function
Effect of aspect ratio in modeling
A multiphase-field model for the description of coalescence is solved numerically using adaptive finite elements with high aspect ratio.
The unknown of the multiphase-field model are the three phase fields (solid phase1, solid phase 2, and liquid phase).
An adaptive finite element algorithm is proposed.
In order to reduce the number of mesh vertices, the generated meshes contain elements with high aspect ratio.
They introduce an error indicator.
Numerical results on two test cases (1D and 2D) show the efficiency of the method
concluslon
By studying the literature as mentioned above it is found that
the refinement of mesh and in some cases higher order displacement functions are used.
The application of
para linear,
cubic linear elements
is not seen much in the literature.
In the present study it is aimed to use the para linear element technique in finite element analysis.