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New triangular finite element for plates and shells

Ghazi Abu‐Farsakh (Department of Civil Engineering, Jordan University of Science and Technology, Irbid, Jordan (Received January 1987))

Engineering Computations

ISSN: 0264-4401

Article publication date: 1 February 1987

71

Abstract

A new triangular shell finite element ‘TNTE.1’ (Ten Node Triangular Element, Model 1) is presented. The formulation is based on Sanders' theory which involves the inclusion of the normal rotation Φn in the bending‐strain relations only. The element displacement functions are complete cubic polynomials for inplane displacements u and v. For out‐of‐plane displacement w, three new singular rational shape functions were added at the element corners. Thus a conforming triangular element with twenty seven degrees‐of‐freedom is obtained after eliminating the internal displacements by static condensation. The formulation of this element is new in that an integration technique is developed and applied to the element stiffness matrix and load vector. This technique is based on performing all the necessary integrations externally (i.e. outside the main computer program) and then modifying the formulation of the element matrices to account for this change. Hence, such a method allows the inclusion of higher‐order integration rules without any loss of economy, due to computer time, in the main program. Results using this element showed good agreement with other finite element and closed form solutions.

Citation

Abu‐Farsakh, G. (1987), "New triangular finite element for plates and shells", Engineering Computations, Vol. 4 No. 2, pp. 149-160. https://doi.org/10.1108/eb023694

Publisher

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MCB UP Ltd

Copyright © 1987, MCB UP Limited

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