Mixed Finite Element Matrix for Plate Bending Analysis Using Weighted-Residual Integral and Weak Formulation

Abdarrhim Mohammed Ahmed and Saleh Y. Barony
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Abdarrhim Mohammed Ahmed: Basic Science Department, College of Electronics Technology / Bani-walid, Libya
Saleh Y. Barony: Department of Civil Eng., School of Engineering, Libyan Academy of Graduate Studies, Tripoli, Libya

European Journal of Engineering and Technology Research, 2020, vol. 5, issue 8, 990-999

Abstract: The Conventional Finite Element Method for the analysis of plate bending based on a the principle of stationarity of total potential energy which is well known as Stiffness Formulation , using a variety of conformal and no-conformal elements was widely applicable in early of numerical solutions for such problems , later in order to improve the efficiency of such solutions , a more general and flexible formulation called Mixed Formulation based on variational principles which can be regarded as an extension of the Stiffness principle become important alternative. The explicit stiffness matrix for plate bending was given in the most if it`s not in all literatures so the reader can easy follow the solving procedure for such problems and verifying any published results , however such like-matrix (Augmented Matrix) in case of mixed formulation not given , at least for simple elements in the literatures as well as concerned researches . This quietly leads to some difficulties concerning the verification as well as understanding the published results. The main objective of this paper is to introduce this matrix in abbreviated size followed by a applicability through a some detailed examples for some bending models. The derived matrix will be helpful subject of research work in addition to , reveals a very good feeling with understanding and verification the published results in plus to comparing with the analytical solutions of different plate bending problems as the reader can do that.

Keywords: Finite Element Method; Plate Bending; Plate BendingWeak Formulation (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:epw:ejeng0:v:5:y:2020:i:8:id:62041

DOI: 10.24018/ejeng.2020.5.8.2041

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