Use of constraint matrices in the finite element method and the stress analysis of complex rotating structures

The development of a method which allows different element types to be used in different parts of a complex structure with the help of equations of constraint has led to an economic means of finite element analysis of complex rotors by the most economic one of all the element types capable of representing the conditions in each segment reasonably well. One radial flow rotor, one curved blade doubly shrouded rotor, and one doubly shrouded rotor with hollow stiffened blades have been analysed using the technique called the "Constraint Matrix Method". Satisfactory results have been obtained in the first two cases and partially satisfactory results in the last case. The method has been used in order to enforce inter-element displacement continuity in finite element formulation of structures and in the development of a triangular plate bending element stiffness matrix in which the initial nodes with the same number of degrees of freedom per node are replaced by a set of nodes with different number of degrees of freedom for different nodes necessary for achieving inter-element displacement continuity. A three-dimensional solid finite element. stiffness matrix has also been developed in terms of cylindrical coordinates based.on the "mixed" method of analysis.