Integration Of Flexible Multibody Dynamic Analysis With Dimensional Reduction Techniques

Flexible multibody systems are becoming increasingly complex and many of their components are now made of heterogeneous, highly anisotropic composite materials. High-fidelity prediction of the three-dimensional stress field in these components involves two tasks. The first task is to predict the overall dynamic response of the system under load while taking into account the effects of three-dimensional deformation of the structural components. The second task is to determine the resulting stress field in the flexible components of the system,once the analysis is completed. The objective of this thesis is to improve the accuracy and efficiency of these two tasks by integrating multibody dynamics analysis with dimensional reduction procedures.Conceptually, all flexible components of the system could be modeled using three-dimensional finite elements, but the computational cost of such an approach is so overwhelming as to be unpractical. Consequently,beam, plate, and shell models are typically used to alleviate the computational burden. For beams and plates,Timoshenko and Reissner-Mindlin theories, respectively, are used most commonly to model flexible components.These theories are based on kinematic assumptions describing the cross-section and normal material line motions for beams and plates, respectively. While these assumptions are adequate to evaluate the kinetic energy of the structure, they cannot yield an accurate estimate of its strain energy, particularly in the presence of structures presenting complex configurations and made of anisotropic materials. Furthermore, these theories are not capable of predicting the detailed three-dimensional stress field in these complex structures, a prerequisite for strength and fatigue analyses.In this thesis, an alternative approach is followed. Beam and plate models are derived from three-dimensional elasticity theory based on novel dimensional reduction techniques. The nonlinear three-dimensional equations of beams can be decomposed into a linear two-dimensional analysis over the cross-section, referred to as “sectional analysis,” and a nonlinear, one-dimensional analysis along the beam’s span. Similarly, the linear threedimensional equations of plate and shells can be decomposed into a linear one-dimensional analysis over the normal material line, referred to as “through-the-thickness analysis,” and a linear, two-dimensional analysis over the plate and shell’s mid-surface.The geometrically exact one- or two-dimensional equations for beams or plates and shells, respectively, are assembled into the global system equations to predict overall system motion. The sectional and through-thethickness analyses provide a fully populated stiffness matrices that characterize the behavior of beams and plates or shells, respectively. The sectional stiffness matrices take into accounts the three-dimensional deformation of the beam’s cross-section or of the plates’ s normal material line. The geometrically exact beam, plate, and shell models equipped with sectional stiffness matrices obtained by sectional and through-the-thickness analyses capture three-dimensional effects of the material heterogeneity over the cross-section or through the thickness.Once the stress resultant are obtained by the multibody dynamics analysis, three-dimensional stresses at any point of the beams, plates, or shells can be evaluated using the recovery procedure resulting from the sectional or through-the-thickness analysis.This thesis is divided into two parts: the formulation of multibody dynamics based on the motion formalism and the development of dimensional reduction techniques. Beam, plate and shell models are developed,implemented, and validated within the framework of a general purpose flexible multibody dynamics code.