Abstract
This paper demonstrates finite element procedure for two-dimensional axisymmetric domains. For many engineering applications like structural engineering, aerospace engineering, geo-mechanics etc., the solution domain and boundary conditions are axisymmetric. Henceforth, we can illuminate just the axisymmetric part of the solution domain that gives the data of the entire domain. This paper demonstrates the effectiveness of using MATLAB programming demonstrated by Persson et.al (2004) as the initial mesh for discretization of axisymmetric domains for higher order meshing. Further, solving some class of partial differential equations using finite element method with nodal relation given by subparametric transformations Rathod et.al (2008). In this paper a cubic order curved triangular meshing for some of the domains like ellipse and circle are demonstrated. These in turn finds its applications in the fields like stress analysis in mechanical engineering, torsion twist (shear strength) analysis in civil engineering, evaluation of stress intensity factor for quarter elliptical crack in pressure vessels in equipment industry etc,. The output data from the meshing scheme like meshing of the domain, nodal position, element connectivity and boundary edges are been used in the finite element procedures. The efficiency of the method is achieved by p-refinement scheme i.e., fixing the number of elements and increasing the polynomial order.
Highlights
The mathematical models where developed in order to analysis the physical phenomenon that depicts the system with specific assumptions and simplifications
It is tedious to obtain the analytical solution for problems involving complex material properties and boundary conditions; we resort to numerical methods that provide approximate but acceptable solution
The major advantages of using finite element method (FEM) are generalized computer program can be developed to analyse various problems and it can handle any complex geometry with the given boundary conditions
Summary
The mathematical models where developed in order to analysis the physical phenomenon that depicts the system with specific assumptions and simplifications. In paper [4, 5] the use of isoparametric transformations by parabolic or cubic arcs to match the curved boundaries using curved triangular elements where developed. The difficulty arising in solving such an integral of an arbitrary curved boundaries can be overcome by the use of subparametric transformations by parabolic or cubic arcs for higher order curved triangular elements developed in the works [6, 7]. Numerous computer programming exist which executes meshing of two-dimensional (2D) geometries using straight edges, especially triangular elements. Persson and Gilbert [1] have presented a simple and efficient MATLAB meshing code for linear order straight edged triangular elements. The implementation of the MATLAB code [1] for finite element procedures upto cubic order for straight edged elements is provided in the works of John Coady [9].
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