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



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Submitted Jul 15, 2020
Published Aug 31, 2020
10.24018/ejeng.2020.5.8.2041

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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

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