Three-Dimensional Finite Element Formulation and Scalable Domain Decomposition for High Fidelity Rotor Dynamic Analysis

This paper implements and analyzes a dual-primal iterative substructuring method, that is parallel and scalable, for the solution of a three-dimensional finite element dynamic analysis of helicopter rotor blades. The finite element analysis is developed using isoparametric hexa- hedral brick elements. Particular emphasis is placed on the formulation of the inertial terms that are unique to rotary wing structures. The scalability of the solution procedure is studied using two prototype problems – one for steady hover (symmetric) and one for transient forward flight (non-symmetric) – both carried out on up to 48 processors. In both hover and forward flight, a linear speed-up is observed with number of processors, up to the point of substructure optimality. Substructure optimality and the range of linear speed-up are shown to depend both on the problem size as well as a corner based global coarse problem selection. An increase in problem size extends the linear speed-up range up to the new substructure optimality. A superior coarse problem selection extends the optimality to a higher number of processors. The method also scales with respect to problem size. The key conclusion is that a three-dimensional finite element analysis of a rotor can be carried out in a fully parallel and scalable manner. The careful selection of substructure corner nodes, that are used to construct the global coarse problem, is the key to extending linear speed-up to as high a processor number as possible, thus minimizing the solution time for a given problem size.