Mass and Force Lumping: An Essential Enhancement to the Intrinsic Beam Finite Element Discretization

Abstract

This paper introduces the novel application of the mass and force lumping technique to enhance the finite element discretization of the fully intrinsic beam formulation. In our aeroelastic system model, 2-D unsteady aerodynamics were incorporated alongside simple calculations for thrust and gravity. Through the central difference discretization method, the discretized system was thoroughly examined, shedding light on the advantages of the mass and force lumping approach. With the use of a first-order lumping method, we successfully reconstructed the inertia matrices, external forces, and moments. The resulting equations are more systematically structured, facilitating the extraction of a regular state-space linear system using the direct index reduction method post-linearization. Numerical results further confirm that the proposed techniques can effectively capture the nonlinear dynamics of aeroelastic systems, enabling equation reconstruction and leading to significant benefits in system order reduction and flight dynamical analysis.