Citation

Koh, Wei Hao and Perumal, Logah and Kok, Chee Kuang (2024) Formulating strain-based quadrilateral membrane finite elements with drilling rotations. Applications in Engineering Science, 19. p. 100188. ISSN 2666-4968

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Abstract

Membrane finite elements with drilling degrees of freedom have sparked interest in many research works since they can be conveniently combined with plates to form shell elements. This study presents two non-conforming strain-based four-node quadrilateral membrane elements, SBQ13 and SBQ13E, for static analysis. SBQ13 partially satisfies the equilibrium equations, while SBQ13E completely fulfils the force balance equations. Both elements carry drilling rotations at each node. One difficulty when formulating quadrilateral elements is the singularity in the transformation matrix, which is addressed in this study by utilising the properties of singular matrices. Both quadrilateral elements were tested in several benchmark problems. It has been found that both elements passed the higher-order patch test but failed the constant stress patch test. Nevertheless, SBQ13 produced accurate responses in most numerical tests, but SBQ13E unreasonably overestimated the solution. Solving the eigenvalue problem revealed that the SBQ13E element has a near-zero energy deformation mode, which might explain the anomaly. Although fulfilling equilibrium does not always enhance solution accuracy, it is essential to overcome volumetric locking. Apart from the newly developed elements, this paper presents several new ideas that may apply to strain-based element formulations

Item Type:	Article
Uncontrolled Keywords:	Strain-based quadrilateral finite element, Corrective coefficients
Subjects:	T Technology > TA Engineering (General). Civil engineering (General) > TA329-348 Engineering mathematics. Engineering analysis
Divisions:	Faculty of Engineering and Technology (FET)
Depositing User:	Ms Nurul Iqtiani Ahmad
Date Deposited:	01 Aug 2024 02:59
Last Modified:	01 Aug 2024 02:59
URII:	http://shdl.mmu.edu.my/id/eprint/12704

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