Incompatible Displacement Models

Publisher Summary This chapter introduces incompatible displacement modes at the element level in order to improve element accuracy. One of the main causes of inaccuracies in lower-order finite elements is their inability to represent certain simple stress gradients. The same basic method of introducing incompatible displacement modes in order to improve the bending properties can be used in three dimensions. The first eight are the standard compatible interpolation functions. The last three are incompatible and are associated with linear shear and normal strains. The nine incompatible modes are eliminated at the element stiffness level by static condensation. As the three-dimensional element degenerates to the same approximation as in the two-dimensional element, the same improvement in accuracy is obtained. This element has been found to be extremely effective in the analysis of massive three-dimensional structures subjected to bending. One element in the thickness direction of arch dams or thick pipe joints has been found to be adequate.