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OPTIMAL SUBPARAMETRIC FINITE ELEMENT METHOD FOR ELLIPTIC PDE OVER CIRCULAR DOMAIN

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초록

This paper gives us an insight into the usefulness of the proposed method in Finite Element Analysis (FEM) for solving an el- liptic Partial Di erential Equation (PDE) over circular domain. We are using quadratic and cubic order curved triangular elements to solve the problem of stress concentration on a circular plate, which is governed by Poisson's equation. The proposed FEM solution matches very well with the exact solution. This shows the eciency and effectiveness of the method in various mechanical applications.

Abstract

This paper gives us an insight into the usefulness of the proposed method in Finite Element Analysis (FEM) for solving an el- liptic Partial Di erential Equation (PDE) over circular domain. We are using quadratic and cubic order curved triangular elements to solve the problem of stress concentration on a circular plate, which is governed by Poisson's equation. The proposed FEM solution matches very well with the exact solution. This shows the eciency and effectiveness of the method in various mechanical applications.

참고문헌 (12)

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  3. H. T. Rathod, "Synthetic Division Based Integration of Rational Functions of Bivariate Polynomial Numerators with Linear Denominators over a Unit Triangle <TEX>$0{\leq}{\xi},{\eta}{\leq}1,{\xi}+{\eta}{\leq}1$<", TEX> in the Local Parametric Space (<TEX>${\xi},{\eta}$<, Comput. Meth. Appl. Mech. Eng., pp.2000, 181[DOI]
  4. H. T. Rathod, "An Explicit Integration Scheme Based on Recursion for the Curved Triangular Finite Elements", Comput. Struct., 80, pp.43~76 (2002)[DOI]
  5. H. T. Rathod, "These of Parabolic Arcs in Matching Curved Boundaries by Point Transformations for some Higher Order Triangular Elements", Fin. Elem. Anal. Des., 44, pp.920~932 (2008)[DOI]
  6. K. V. Nagaraja, "Optimal Sub parametric Finite Elements for Elliptic Partial Differential Equations Using Higher Order Curved Triangular Elements", Int., J. for comp. methods in Eng. Sci. and Mechanics, 15, pp.83~100 (2014)[DOI]
  7. K. V. Nagaraja, "Optimal Subparametric Finite Elements for the Computation of Cutoff Wave numbers in Waveguides", AIP Conference Proceedings (2016)
  8. V. Kesavulu Naidu, "Finite Element Solution of Darcy-Brinkman Equation for Irregular Cross-Section Flow Channel Using Curved Triangular Elements", Procedia Engineering, 127, pp.301~308 (2015)[DOI]
  9. O.C. Zienkiewicz, "The Finite Element Method in Structural and Continuum Mechanics" (1967), McGraw-Hill
  10. O.C. Zienkiewicz, "The Finite Element Method: Its Basis and Fundamentals" (2005), Elsevier
  11. J. N. Reddy, "an Introduction to the Finite Element Method" (2005), Tata McGraw-Hill
  12. H. T. Rathod, "Gauss Legendre quadrature over a triangle", J. Indian Inst. Sci., 84, pp.183~188 (2004)

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