A New Approach to Automatic Generation of all Quadrilateral Mesh for Finite Element Analysis

This paper presents a new mesh generation method for a convex polygonal domain. We first decompose the convex polygon into simple sub regions in the shape of triangles. These simple regions are then triangulated to generate a fine mesh of triangular elements. We propose then an automatic triangular to quadrilateral conversion scheme. Each isolated triangle is split into three quadrilaterals according to the usual scheme, adding three vertices in the middle of the edges and a vertex at the barrycentre of the element. To preserve the mesh conformity a similar procedure is also applied to every triangle of the domain to fully discretize the given convex polygonal domain into all quadrilaterals, thus propagating uniform refinement. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. Examples are presented to illustrate the simplicity and efficiency of the new mesh generation method for standard and arbitrary shaped domains. We have appended MATLAB programs which incorporate the mesh generation scheme developed in this paper. These programs provide valuable output on the nodal coordinates ,element connectivity and graphic display of the all quadrilateral mesh for application to finite element analysis

An Explicit Finite Element Integration Scheme for Linear Eight Node Convex Quadrilaterals Using Automatic Mesh Generation Technique over Plane Regions

This paper presents an explicit integration scheme to compute the stiffness matrix of an eight node linear convex quadrilateral element for plane problems using symbolic mathematics and an automatic generation of all quadrilateral mesh technique , In finite element analysis, the boundary problems governed by second order linear partial differential equations,the element stiffness matrices are expressed as integrals of the product of global derivatives over the linear convex quadrilateral region. These matrices can be shown to depend on the material properties and the matrix of integrals with integrands as rational functions with polynomial numerator and the linear denominator (4+ ) in bivariates over an eight node 2-square (-1 ).In this paper,we have computed these integrals in exact and digital forms using the symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme is illustrated by computing the Prandtl stress function values and the torisonal constant for the square cross section by using the eight node linear convex quadrilateral finite elements.An automatic all quadrilateral mesh generation techniques for the eight node linear convex quadrilaterals is also developed for this purpose.We have presented a complete program which automatically discritises the arbitrary triangular domain into all eight node linear convex quadrilaterals and applies the so generated nodal coordinate and element connection data to the above mentioned torsion problem. Key words: Explicit Integration, Gauss Legendre Quadrature, Quadrilateral Element, Prandtl’s Stress Function for torsion, Symbolic mathematics,all quadrilateral mesh generation technique

A New Approach to an all Quadrilateral Mesh Generation over Arbitrary Linear Polygonal Domains for Finite Element Analysis

This paper describes a scheme for finite element mesh generation of a convex, non-convex polygon and multiply connected linear polygon. We first decompose the arbitrary linear polygon into simple sub regions in the shape of polygons.These subregions may be simple convex polygons or cracked polygons.We can divide a nonconvex polygon into convex polygons and cracked polygons We then decompose these polygons into simple sub regions in the shape of triangles. These simple regions are then triangulated to generate a fine mesh of triangular elements. We propose then an automatic triangular to quadrilateral conversion scheme. Each isolated triangle is split into three quadrilaterals according to the usual scheme, adding three vertices in the middle of the edges and a vertex at the barrycentre of the element. To preserve the mesh conformity a similar procedure is also applied to every triangle o f the domain to fully discretize the given convex polygonal domain into all quadrilaterals, thus propagating uniform refinement. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. The proposed scheme has been realized as computer programs and a number of examples have been included to demonstrate the technique. Although the paper describes the scheme as applied to planar domains, it could be extended to three dimensions as well

Numerical Approach for Evaluation of Surface Integrals in Polygonal Domain by Gauss Legendre Quadrature and Generalized Gaussian Quadrature Method

We present a new approach for the numerical  integration of arbitrary functions over polygonal region, by applying two kinds of quadrature method Gauss Legendre quadrature  and Generalized Gaussian quadrature method, the polygonal region is divided into arbitrary triangles, the sides of each triangle is noted as equation of straight line by joining two end vertices, this approach is used to further reduces the integral equations, numerical integration of rational and irrational functions are approximated computationally, we illustrate several numerical examples to shows the accuracy of the present method&nbsp

Multi-Objective Optimization in Electric Discharge Machining of Aluminium Composite

This paper involves the optimization of input process parameters in Electric Discharge Machining of Aluminium hybrid Metal Matrix Composite. Aluminium AlSi10Mg alloy reinforced with 9 %wt. alumina and 3 %wt. graphite particles fabricated through liquid metallurgy route was used for machining. Experiments were conducted in an Electric Discharge Machine and the influence of input process parameters such as Peak current, Pulse-on time and Flushing pressure during machining of aluminium composite was studied. The objective was to obtain a minimum surface roughness with minimum tool wear rate and maximum material removal rate. Multi-objective optimization of the input process parameters was performed by employing Artificial Neural Network and Genetic Algorithm hybrid optimization technique. The results obtained provide a pareto-optimal solution set that offers a set of non-dominated solutions that can be used in a practical situation by a decision maker