Stress Stiffening and Dynamics Stress Computation in Flexible Multibody Dynamics: Formulation

Abstract

A formulation for the dynamics of flexible multibody systems is presented in this paper. This formulation relies on the use of floating reference frames to describe the configuration of the multibody system. Component flexibility is described in terms of the finite element deformation coordinates. The equations of motion are derived through the generalized d’Alembert principle, and the resulting set of differential-algebraic equations are reduced to ordinary differential equations through the use of the augmented Lagrangian penalty method. Modal reduction is utilized to reduce the dimension of the deformation coordinates. Stiffening effects is included through the use of a stress stiffening matrix, which is computed efficiently as a linear combination of constant stress stiffness matrices with time-dependent scalar coefficients. The same formulation is used to devise an efficient method for computing the dynamic stresses which include the effects of inertia due to gross motion and elastic deformation.