Description
Locking phenomena of finite elements, a numerical error in which the element behaves in an artificially stiff manner, may pose a serious problem for correct simulation of the behavior of structures, and many approaches have been devised to overcome this issue including the use of higher order elements and mixed formulations. The present study assesses the performance of linear and higher order triangular finite elements formulated with the Principle of Virtual Displacements (PVD) and Reissner’s Mixed Variational Theorem (RMVT). In particular, an a priori error analysis of the finite elements’ strain and semi-complementary energies is conducted. It is demonstrated that spurious energy terms are present in some contributions to the energy. The magnitude of the energy errors are quantified for the case of a transversely loaded plate with a known elasticity solution. For the case of displacement-based formulations of the element, the energy associated with transverse shear presents a large error, especially when the width-to-thickness ratio increases. This behavior is particularly evident in low order triangular elements, which are known to have a slow convergence rate. The case of the RMVT-based elements is very different: the error is relatively small and from the numerical investigations conducted in this study appears to be invariant with respect to the width-to-thickness ratio. Higher order elements, as expected, present better performance in both PVD and RMVT cases.
