# Refined Mixed Finite Element Model For Analysis of Bar Member

 International Journal of Civil Engineering © 2022 by SSRG - IJCE Journal Volume 9 Issue 7 Year of Publication : 2022 Authors : Kamal S Patel, G D Ramtekkar 10.14445/23488352/IJCE-V9I7P101
##### How to Cite?

Kamal S Patel, G D Ramtekkar, "Refined Mixed Finite Element Model For Analysis of Bar Member," SSRG International Journal of Civil Engineering, vol. 9,  no. 7, pp. 1-5, 2022. Crossref, https://doi.org/10.14445/23488352/IJCE-V9I7P101

##### Abstract:

The mixed finite element method allows the stress field to be the primary and displacement variable. The variation of these primary variables is selected in the problem domain and then solved with the minimization of the total potential energy. Unlike other mixed finite element formulation which uses mixed variation principle like Hellinger-Reissner’s variational principle, which is based on the stationarity principle, the present formulation is based on the minimization principle; hence it gives a stable algorithm. The developed formulation is applied to solve the cantilever bar member subjected to varying axial load. The result was compared with the closed-form analytical solution and displacement-based finite element formulation. The present formulation gives accurate results for the stress value with only one element compared to the threeelement based on displacement-based formulation.

##### Keywords:

Mixed-finite element, Minimization of total potential energy principle, Bar element, Refined solution, HR principle.

##### References:

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