Explicit addition of rigid-body motions in curved finite elements.

Several aspects of the representation of rigid-body modes in finite element displacement functions are discussed. First, a simple technique to compute six independent modes is demonstrated; it offers the possibility to estimate the extent to which the rigid modes are included in the specified interpolation functions; it also enables one to check the strain displacement relationships. Then, a procedure to find out how many and which rigid modes are present in a stiffness matrix is explained. Finally, the missing modes are explicitly added and the associated degrees of freedom are condensed out; in most cases the operation has the effect of rendering the elements incompatible. A doubly curved quadrilateral element for shells of revolution with 24° of freedom is used to illustrate these effects; several examples are solved with the element, demonstrating the advantages and drawbacks of explicitly adding rigid modes to an element.