Abstract
In this paper, I derived shape functions for a 20-nodal tri-quadratic serendipity element which consists of eight corner nodes and twelve mid-side nodes using natural coordinate system. I derived two shape function verification conditions, first verification condition sum of all the shape functions is equal to one, and second verification condition each shape function has a value of one at its own node and zero at all other nodes. For mathematical computations, I used Mathematica 9 Software.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Liu GR, Quek SS (2003) The finite element method: a practical course. Elsevier Science Ltd., Amsterdam
Wolfram Mathematica® 9 Software, Version number 9.0.0.0
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Reddaiah, P. (2021). Deriving Shape Functions for a 20-Nodal Tri-quadratic Serendipity Element and Verified. In: Rushi Kumar, B., Sivaraj, R., Prakash, J. (eds) Advances in Fluid Dynamics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-4308-1_1
Download citation
DOI: https://doi.org/10.1007/978-981-15-4308-1_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-4307-4
Online ISBN: 978-981-15-4308-1
eBook Packages: EngineeringEngineering (R0)