A review of flexible multibody dynamics for gradient-based design optimization

Design optimization of flexible multibody dynamics is critical to reducing weight and therefore increasing efficiency and lowering costs of mechanical systems. Simulation of flexible multibody systems, though, typically requires high computational effort which limits the usage of design optimization, especially when gradient-free methods are used and thousands of system evaluations are required. Efficient design optimization of flexible multibody dynamics is enabled by gradient-based optimization methods in concert with analytical sensitivity analysis. The present study summarizes different formulations of the equations of motion of flexible multibody dynamics. Design optimization techniques are introduced, and applications to flexible multibody dynamics are categorized. Efficient sensitivity analysis is the centerpiece of gradient-based design optimization, and sensitivity methods are introduced. The increased implementation effort of analytical sensitivity analysis is rewarded with high computational efficiency. An exemplary solution strategy for system and sensitivity evaluations is shown with the analytical direct differentiation method. Extensive literature sources are shown related to recent research activities.

Dynamics of a flexible body: a two-field formulation

A two-field formulation of the nonlinear dynamics of an elastic body is presented in which positions/orientations and the resulting velocity field are treated as independent. Combining a nonclassical description of elastic velocity that includes the convection velocity due to elastic deformation with floating reference axes minimizing the relative kinetic energy due to elastic deformation provides a fully uncoupled expression of kinetic energy. A transformation inspired by the classical Legendre transformation concept is introduced to develop the motion equations in canonical form. Finite element discretization is achieved using the same shape function sets for elastic displacements and velocities. Specific attention is brought to the discretization of the gyroscopic forces induced by elastic deformation. A model reduction strategy to construct superelement models suitable for flexible multibody dynamics applications is proposed, which fulfills the essential condition of orthogonality between a rigid body and elastic motions. The problem of expressing kinematic connections at superelement boundaries is briefly addressed. Two academic examples have been developed to illustrate some of the concepts presented.

Aeroelastic Response of Aircraft Wings to External Store Separation Using Flexible Multibody Dynamics

In aviation, using external stores under the wings is a common method of carrying payload or fuel. In some cases, the payload can be rigidly attached to the wing. However, stores must often be ejected during flight for aircraft, such as military type, which carry drop tanks and missiles. This may cause the wing to respond dynamically with increasing amplitudes, due to the impulsive load of ejection and the change of total mass. This is especially critical in aircraft with highly flexible wings, such as those with high aspect ratios. In this case, it is crucial to evaluate the wing response to store separation, which requires a suitable simulation environment that is able to support nonlinear and multidisciplinary analysis. To address such a need, this work presents the use of flexible multibody dynamics in the simulation of wing response to store separation. To demonstrate, a highly compliant wing was selected with a rigid body that was mounted on the wing to represent an external store. The time marching simulation of the wing before and after the store separation was presented to show the features and benefits of the method.