Deriving Shape Functions for 2,3,4,5 Noded Line Element by Polynomial and Verified

P. Reddaiah

doi:https://doi.org/10.14445/22315373/IJMTT-V53P524

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 3 | Year 2018 | Article Id. IJMTT-V53P524 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P524

Deriving Shape Functions for 2,3,4,5 Noded Line Element by Polynomial and Verified

P. Reddaiah

Abstract

In this paper, I derived shape functions for 2,3,4,5 noded line element by polynomial functions, by taking natural coordinate system and also I verified two verification conditions for shape functions. First verification condition is sum of all the shape functions is equal to one and second verification condition is each shape function has a value of one at its own node and zero at the other nodes. For computational purpose I used Mathematica 9 Software[2].

Keywords

Line element, Polynomial functions, Shape functions.

References

[1] S.S. Bhavikatti, Finite Element Analysis, New Age International (P) Limited, Publishers, 2nd Edition, 2010.
[2] Mathematica 9 Software, Wolfram Research, Version number 9.0.0.0, 1988-2012.
[3] J.N.Reddy, An introduction to Finite Element Method, 2nd Edition, McGraw Hill International Editions, 1993.
[4] S.Md.Jalaludeen, Introduction of Finite Element Analysis, Anuradha Publications, 2012.
[5] P. Reddaiah, Deriving shape functions for 8-noded rectangular serendipity element in horizontal channel geometry and verified, International Journal of Mathematics Trends and Technology (IJMTT), Volume 50, Number 2 , October 2017.
[6] P. Reddaiah, Deriving shape functions for 9-noded rectangular element by using lagrange functions in natural coordinate system and verified, International Journal of Mathematics Trends and Technology (IJMTT),Volume 51, Number 6, November 2017.
[7] P. Reddaiah, Deriving shape functions for Hexahedral element by natural coordinate system and Verified, International Journal of Mathematics Trends and Technology (IJMTT), Volume 51, Number 6, November 2017.
[8] P. Reddaiah, Deriving shape functions for hexahedron element by lagrange functions and verified, International Journal of Mathematics Trends and Technology (IJMTT), Volume 51, Number 6, November 2017.
[9] P. Reddaiah, Deriving shape functions for 2,3,4,5 noded line element by lagrange functions and verified, International Journal of Mathematics Trends and Technology (IJMTT), Volume 51, Number 6, November 2017.
[10] P. Reddaiah and D.R.V. Prasada Rao, Deriving Vertices, Shape Functions for Elliptic Duct Geometry and Verified Two Verification Conditions, International Journal of Scientific & Engineering Research, Volume 8, Issue 5, May-2017.
[11] P. Reddaiah, Deriving shape functions for cubic 12- noded serendipidty family element and verified, International Journal of Creative Research Thought, Volume 5, Issue 4, November 2017.

Citation :

P. Reddaiah, "Deriving Shape Functions for 2,3,4,5 Noded Line Element by Polynomial and Verified," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 3, pp. 195-201, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P524