Parallel Finite Element Framework for Rotorcraft Multibody Dynamics and Discrete Adjoint Sensitivities

Abstract

A parallel finite element framework for high-fidelity structural dynamic analysis and gradient evaluation using the discrete adjoint method is presented. The framework is intended to be used for gradient-based design optimization of flexible multibody dynamic systems such as rotorcraft. The formulation of governing equations, the treatment of kinematic constraints, and the evaluation of functionals of interest and their derivatives are addressed. A minimal set of routines needed to implement the discrete adjoint method is proposed. The governing equations are integrated in time using a diagonally implicit Runge–Kutta method for second-order systems of equations. The formulation of the corresponding time-dependent discrete adjoint equations are presented and are numerically verified using the complex-step method. A verification of the dynamics, an assessment of parallel scalability of the analysis and derivative evaluation techniques, and a demonstration of the design capability are presented.