New slave-node constraints and element for adaptive analysis of C0 plates

In the h-type adaptive analysis, when an element is refined or subdivided, new nodes are added. Among them are the transition nodes which are the corner nodes of the new elements formed by subdivision and, simultaneously, the mid-side nodes of the adjacent non-subdivided elements. To secure displacement compatibility, the slave-node approach in which the DOFs of a transition node are constrained by those of the adjacent nodes had been used. Alternatively, transition elements which possess the transition nodes as active mid-side/-face nodes can be used. For C0 plate analyses, the conventional slave-node constraints and the previously derived ANS transition elements are implemented. In both implementations, the four-node element is the ANS element. With reference to the predictions of the transition elements, the slave-node approach not only delivers erroneous results but also fails the patch test. In this paper, the patch test failure is resolved by developing a set of new constraints with which the slave-node approach surpasses the transition-element approach. The accuracy of the slave-node approach is further improved by developing a hybrid four-node element in which the assumed moment and shear force modes are in strict equilibrium.