Higher-order linked interpolation in triangular thick plate finite elements

Abstract

Purpose – 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. Design/methodology/approach – 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. Findings – 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. Originality/value – 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.