The TRIC shell element: theoretical and numerical investigation

Abstract

The TRIC facet triangular shell element, which is based on the natural mode method, is seen under the light of the non-consistent formulation proposed by Bergan and co-workers. Under this formulation, the convergence requirements are fulfilled even with relaxed conditions on the conformity demands of the displacement shape functions. The intrinsic connection between the non-consistent formulation and the natural mode method is demonstrated, establishing thus a rigorous theoretical foundation for the TRIC element. Under the perspective of the non-consistent formulation, TRIC's convergence characteristics are established by satisfying apriori the patch test due to its inherent properties and thus guaranteeing convergence to the exact solution. Furthermore, the element's accuracy, robustness and efficiency are tested in a number of judiciously selected numerical examples on benchmark plate and shell problems, while a CPU time comparison with a pure displacement-based isoparametric shell element demonstrates its computational merits.