New stiffened plate elements based on the absolute nodal coordinate formulation

In this study, several new stiffened plate element models are proposed based on the absolute nodal coordinate formulation. The stiffened plate elements with different geometrical continuity conditions and performances are developed by a full parametrized plate element and three different beam elements of absolute nodal coordinate formulation. The effect of stiffener is incorporated by internally constraining the stiffener displacement fields to the relevant plate displacement fields. The displacement compatible conditions of plate and stiffener are investigated to obtain the transformation matrix of nodal coordinates. The mass and stiffness of a stiffener is reflected at all the nodes of the plate element in which it is placed. Accordingly, the stiffener can be positioned anywhere within the plate element along lines of local coordinates and need not necessarily be placed on nodal lines, which gives a great flexibility in the choice of mesh size. The stiffened plate elements also achieve a better continuity condition with the slope constraint equations. Static, dynamic, and free vibration analyses are conducted to validate the proposed elements and to study the performance of the stiffeners. The results show that the new elements can be applied to describe mechanical behaviors of stiffened structures in both static and dynamic situations. The effects of the dimension of cross section and the number of stiffeners are also numerically investigated for both linear and nonlinear deformation problems.