No. 4. A Study on Formulation of Strain-Based Triangular Elements Manuscript Received: 10 January 2022, Accepted: 24 February 2022, Published: 15 March 2022

Main Article Content

Logah Perumal
Palanisamy Chockalingam

Abstract

This paper presents formulation of triangular elements based on strain approach. Various formulations of the strain-based elements can be seen in the literature. However, most of them do not clearly describe selection of the suitable strain fields for the elements. Therefore, in this work, some guidance for the formulation of strain-based elements are provided based on simulation results that are obtained by using several polynomial functions from Pascal’s triangle. It is seen that higher order terms in the strain functions do not always guarantee better performance for the case considered in this work.

Article Details

Section
Articles

References

D. G. Ashwell and A. B. Sabir, “Limitations of Certain Curved Finite Elements When Applied to Arches,” Int. J. Mech. Sci., vol. 13, no. 2, pp. 133–139, 1971.

D. G. Ashwell, A. B. Sabir and T. M. Roberts, “Further Studies in The Application of Curved Finite Elements to Circular Arches,” Int. J. Mech. Sci., vol. 13, no. 6, pp. 507–517, 1971.

D. G. Ashwell and A. B. Sabir, “A New Cylindrical Shell Finite Element Based on Simple Independent Strain Functions,” Int. J. Mech. Sci., vol. 14, no. 3, pp. 171–183, 1972.

M. R. Pajand, N. G. Moghaddam and M. R. Ramezani, “A New Higher-order Strain-based Plane Element,” Scientia Iranica. Trans. Civil Eng. A, vol. 26, no. 4, pp. 2258-2275, 2019.

D. Hamadi, A. Ayoub and T. Maalem, “A New Strain-based Finite Element for Plane Elasticity Problems,” Eng. Comput., vol. 33, no. 2, https://doi.org/10.1108/EC-09-2014-0181, 2016.

F. Boussem and L. Belounar, “A Plate Bending Kirchhoff Element Based on Assumed Strain Functions,” J. Solid Mech., vol. 12, no. 4, pp. 935-952, 2020.

L. Belounar and M. Guenfoud, “A New Rectangular Finite Element Based on The Strain Approach for Plate Bending,” Thin-Walled Structures, vol. 43, no. 1, pp. 47-63, 2005.

C. Rebiai, N. Saidani and E. Bahloul, “A New Finite Element Based on the Strain Approach for Linear and Dynamic Analysis,” Res. J. Appl. Sci., Eng. and Techn., vol. 11, no. 6, pp. 639-644, 2015.

L. Bouzidi, L. Belounar and K. Guerraiche, “Presentation of A New Membrane Strain-based Finite Element for Static and Dynamic Analysis,” Int. J. Structural Eng., vol. 10, no. 1, pp. 40-60, 2019.

M. R. Pajand, N. G. Moghaddam and M. Ramezani, “Strain-based Plane Element for Fracture Mechanics’ Problems,” Theoret. and Appl. Fract. Mech., vol. 108, no. 102569, 2020.

M. R. Pajand, N. G. Moghaddam and M. Ramezani, “Review of The Strain-based Formulation for Analysis of Plane Structures Part I: Formulation of Basics and The Existing Elements,” Iranian J. Num. Analy. and Optim., vol. 11, no. 2, pp. 437-483, 2021.

M. Himeur, A. Zergua and M. Guenfoud, “A Finite Element Based on the Strain Approach Using Airy’s Function,” Arabian J. Sci. and Eng., vol. 40, no. 3, pp. 719–733, 2015.

M. R. Pajand, N. G. Moghaddam and M. Ramezani, “Review of The Strain-based Formulation for Analysis of Plane Structures Part II: Evaluation of The Numerical Performance,” Iranian J. Num. Analy. and Optim., vol. 11, no. 2, pp. 485-511, 2021.

A. I. Mousa and S. M. Tayeh, “A Triangular Finite Element for Plane Elasticity with In-plane Rotation,” J. the Islamic of Gaza, vol. 12, no. 1, pp. 83-95, 2004.

S. M. Tayeh, “Newstrain-Based Triangular and Rectangular Finite Elements for Plane Elasticity Problems,” Master Thesis, The Islamic University, 2003.

M. T. Belarbi and D. Hamadi, “Presentation of Tow Sabir Element Results with Irregular Shapes,” Sci. and Techn. Knowledge, Courrier du Savoir, vol. 5, no. 5, pp. 37-43, 2004.

L. Perumal, “Integration Techniques for Two Dimensional Domains,” Int. J. Res. in Eng. and Techn., vol. 3, no. 7, pp. 487–494, 2014.

G. Dasgupta, “Integration within polygonal finite elements,” J. Aerospace Eng., vol. 16, no. 1, pp. 9–18, 2003.