Higher-order linked interpolation in triangular thick plate finite elements

Dragan Ribarić (Faculty of Civil Engineering, University of Rijeka, Rijeka, Republic of Croatia)
Gordan Jelenić (Faculty of Civil Engineering, University of Rijeka, Rijeka, Republic of Croatia)

Engineering Computations

ISSN: 0264-4401

Publication date: 25 February 2014



In this work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of displacement-based higher-order triangular plate finite elements and test their performance.


Starting from the analogy between the Timoshenko beam theory and the Mindlin plate theory, a family of triangular linked-interpolation plate finite elements of arbitrary order are designed. The elements are tested on the standard set of examples.


The derived elements pass the standard patch tests and also the higher-order patch tests of an order directly related to the order of the element. The lowest-order member of the family of developed elements still suffers from shear locking for very coarse meshes, but the higher-order elements turn out to be successful when compared to the elements from literature for the problems with the same total number of the degrees of freedom.

Research limitations/implications

The elements designed perform well for a number of standard benchmark tests, but the well-known Morley's skewed plate example turns out to be rather demanding, i.e. the proposed design principle cannot compete with the mixed-type approach for this test. Work is under way to improve the proposed displacement-based elements by adding a number of internal bubble functions in the displacement and rotation fields, specifically chosen to satisfy the basic patch test and enable a softer response in the bench-mark test examples.


A new family of displacement-based higher-order triangular Mindlin plate finite elements has been derived. The higher-order elements perform very well, whereas the lowest-order element requires improvement.



The results shown here have been obtained within the scientific Project No. 114-0000000-3025: “Improved accuracy in non-linear beam elements with finite 3D rotations” financially supported by the Ministry of Science, Education and Sports of the Republic of Croatia.


Ribarić, D. and Jelenić, G. (2014), "Higher-order linked interpolation in triangular thick plate finite elements", Engineering Computations, Vol. 31 No. 1, pp. 69-109. https://doi.org/10.1108/EC-03-2012-0056

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