ABSTRACT
The numerical analysis of a plate using the FEM has played an important role in engineering applications in structural engineering [1], because (1) the plate is one of the most widely used essential structural components, and (2) the FEM is so far one of the most important and robust numerical methods. In recent years, mesh-free methods have also been developed and applied to various problems for different types of plates [2]. In practical engineering applications, lower-order Reissner-Mindlin plate elements are preferred due to its simplicity, efficiency and applicability to “thick” plates. However, when applied to thin plates, these low-order plate elements often suffer from the so-called shear locking. In order to eliminate shear locking, many attempts have been made and the selective reduced integration scheme was proposed [3-6]. The idea of the selective reduced integration scheme is to split the strain energy into two parts: the bendingrelated term and the shear-related one. Two different integration rules are then used, respectively, for the bending strain energy and the shear strain energy. For example, for four-node quadrilateral elements with bilinear shape functions, the reduced integration (using a single Gauss point) is used to compute shear strain energy, while the full Gauss integration (using 2 × 2 Gauss points) is used for the bending strain energy. Such a selective reduced integration scheme is very simple, easy to apply, and works well for many cases. Unfortunately, the reduced integration often leads to rank deficiency in the stiffness matrix, which can be observed as zero-energy modes. Various improvements have also been made in the formulation, and many numerical techniques have been developed to overcome the shear locking problem, aiming to increase the accuracy and to ensure the stability of the solution, such as the mixed formulation or hybrid elements [7-17], enhanced assumed strain (EAS) methods [18-22], and assumed natural strain (ANS) methods [23-32]. Recently, the so-called DSG method [33] was proposed to overcome the shear locking problem. The DSG is somewhat similar to the ANS methods in the aspect of modifying the strains within the element, but is different in the aspect of removing collocation points. The DSG method is found to work well for elements of different orders and shapes [33].
