Open AccessA Review on Analysis and Development of Mathematical Formulation Interpolants for a 4 Noded Polygon using Wachspress’ Interpolation Function
Author(s) -
Deepak Kumar,
P.V. Jeyakarthikeyan
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/912/2/022055
Subject(s) - quadrilateral , interpolation (computer graphics) , matrix (chemical analysis) , discretization , mathematics , element (criminal law) , stiffness matrix , matrix function , transformation matrix , function (biology) , transformation (genetics) , finite element method , polygon (computer graphics) , computer science , algorithm , mathematical analysis , symmetric matrix , structural engineering , engineering , computer graphics (images) , physics , materials science , law , chemistry , composite material , biology , telecommunications , biochemistry , kinematics , classical mechanics , quantum mechanics , evolutionary biology , political science , animation , eigenvalues and eigenvectors , frame (networking) , gene
This paper presents a detailed view of a methodology of using Wachspress’ Interpolation Function for the analysis and development of Interpolants by means of a mathematical formulation for a 4 Noded Element i.e. A 4 Noded Quadrilateral Element which has been already addressed by Stephane P.A. Bordas, Sundararajan Natarajan in their research work from where the authors have took have inspiration and worked for advancement. Here a 4 Noded Quadrilateral is taken for analysis and is sub divided into 4 equal Quadrilaterals using Smoothed Finite Element Analysis (SFEM) and the respective coordinates of the discretized element will be same as the local coordinates of the parent element without and coordinate transformation. Once it is done then we form the C Matrix (Shape function Values Matrix) which remains constant. Here we consider the line that connects two nodes and using that we will use to generate the Wachspress’ Interpolants. Later on multiplication of the B Matrix (First Derivative Matrix) with the C Matrix, D Matrix (Material Matrix) and the Area Matrix we can find the Element Stiffness Matrix and later the results will be validated with that of an already existing generic example.