Adjoint sensitivity analysis of flexible multibody systems in differential-algebraic form. (February 2020) - Azari Nejat, Ali; Moghadasi, Ali; Held, Alexander
Highlights: The strengths and weaknesses of an adjoint sensitivity analysis of flexible multibody systems based on the equations of motion in differential algebraic form are outlined and compared to an alternative procedure based on ordinary differential equations. In both procedures, flexible multibody systems are modeled using the floating frame of reference formulation. A detailed discussion of an application example shall sensitize the reader to the computational efforts and issues connected to relevant parts of the procedures. Analyzing the obtained results, this work shall help the reader to choose the more convenient procedure for the purpose of gradient based structural optimization of flexible multibody systems. Abstract: In the analysis and optimization of flexible multibody systems, an efficient sensitivity analysis can be performed using the adjoint variable method. Thereby, the procedure strongly depends on the equations of motion, which can be formulated either by minimal or by redundant coordinates yielding in turn a system of ordinary or differential-algebraic equations. In the current work, redundant coordinates are used to set an adjoint system for the sensitivity analysis of flexible multibody systems with kinematic loops, which are modeled using the floating frame of reference formulation. The procedure is tested by computing the structural gradient for the flexible crank of a slider-crank mechanism and compared with a reference procedure, where the adjoint system is formulated using minimal coordinates.