Shape design sensitivity analysis and optimization of spatially rotating objects

Abstract

Shape design sensitivity analysis (DSA) and optimization of spatially rotating objects is presented in this paper. Design sensitivity expressions are derived using a continuum DSA method for spatial objects rotating with angular velocity and angular acceleration, based on three definitions of the finite element mass matrix: consistent, lumped, and diagonalized. The design sensitivity expression derived using a diagonalized element mass matrix, which is consistent with the finite element analysis (FEA) method used in ANSYS, is implemented, although the method can work with other FEA codes, such as MSC/NASTRAN or ABAQUS. Since the continuum DSA method is used, sensitivity information can be computed outside the FEA codes by postprocessing finite element data. Rotating block and turbine blade examples are presented to validate the proposed DSA method. The turbine blade example is optimized using an integrated optimization module of the Design Sensitivity Analysis and Optimization (DSO) tool developed at the University of Iowa. The integrated module consists of ANSYS, MSC/NASTRAN, or ABAQUS for FEA; Design Optimization Tool (DOT) for nonlinear programming; and DSA and design model update programs developed in DSO.