A new stiffened plate element for the analysis of arbitrary plates

In spite of the large number of finite elements developed so far, most of these lack in generality, and are found to be inadequate and inefficient in some way or other, when it comes to analyzing plates of arbitrary geometrical configurations. So far the isoparametric element has been the most successful among available elements because of its ability to model a curved boundary successfully. However, the shear-locking problem inherent in the isoparametric element makes it unsuitable for analyzing thin plates of arbitrary shapes. Though research has been conducted using reduced integration and stabilization to overcome the problem, the formulations either do not converge to the correct solution in the thin-plate limit or they make the stiffness matrix a singular one. In this paper, a four-noded stiffened plate element is developed. This has the advantages and elegance of an isoparametric element in modelling arbitrary shaped plates, but without the disadvantage of shear-locking phenomena. Though this element is a high-order element, only the usual degrees of freedom have been considered, and performance is superior to that of the low-order ones. The stiffened plate element has the feature of accommodating the arbitrary shape of the plate geometry, and the stiffener modelling has been done in a general manner, with the stiffener lying anywhere with arbitrary orientation, and not necessarily following the nodal lines. The new element has been successfully used for the static, free vibration and stability analyses of arbitrary bare and stiffened plates. The results are found to agree quite satisfactorily with those of previous investigators.