This paper presents an approach toward the integration of 3D stress computation with the tools used for the simulation of flexible multibody dynamics. Due to the low accuracy of the floating frame of reference approach, the the multibody dynamics community has turned its attention to comprehensive analysis tools based on beam theory. These tools evaluate sectional stress resultants, not 3D stress fields. The proposed approach decomposes the 3D problem into two simpler problems: a linear 2D analysis of the cross-section of the beam and a nonlinear, 1D of the beam. This procedure is described in details. For static problems, the proposed approach provides exact solutions of three-dimensional elasticity for uniform beams of arbitrary geometric configuration and made of anisotropic composite materials. While this strategy has been applied to dynamic problems, little attention has been devoted to inertial effects. This paper assesses the range of validity of the proposed beam theory when applied to dynamics problems. When beams are subjected to large axial forces, the induced axial stress components become inclined, generating a net torque that opposes further rotation of the section and leading to an increased effective torsional stiffness. This behavior, referred to as the Wagner or trapeze effect, cannot be captured by beam formulations that assume strain components to remain small, although arbitrarily large motions are taken into account properly. A formulation of beam theory that includes higher-order strain effects in an approximate manner is developed and numerical examples are presented. The “Saint-Venant problem” refers to a three-dimensional beam loaded at its end sections only. The “Almansi-Michell problem” refers to a three-dimensional beam loaded by distributed body forces, lateral surface tractions, and forces and moments at its end sections. Numerical examples of beams subjected to distributed loads will be presented and compared with 3D finite element solutions.
Iterative Coordinate Reduction Algorithm of Flexible Multibody Dynamics Using a Posteriori Eigenvalue Error Estimation
