Modeling the motion of a mechanical system consisting of deformable elastic bodies, by integrating two packages: EULER and Fidesys

In the article theoretical basis of flexible bodies' large displacement within a multibody system as well as practical experience of flexible multibody dynamics simulation with integrated computer-aided design software systems EULER and Fydesis are considered. The hypothesis of flexible body undergoing both small elastic deformations and large motion within a multibody system is used. The derivation of dynamic equations of motion of flexible bodies was first published in [3]. The derivation uses classical (linear) finite element method (FEM) and the Craig–Bampton method of FE model's matrices reduction. No additional approximations are involved, thus obtaining the most general equations in given problem definition. In the Craig–Bampton method a finite element model of a flexible body is reduced approximating small elastic deformation with a set of modes: static modes where the bound nodes' displacements equal one unit, and normal modes where the bound nodes are fixed. The full finite element model and the reduced model are prepared in Fidesys software and are transferred to EULER software to be used in a dynamics simulation as a part of a multibody system. For the flexible body's spatial motion representation a floating frame of reference is used. A floating frame of reference defines the motion of a rigid body, related to which flexible body's motion is considered as small deformations. The dynamic equation for flexible bodies are derived from Lagrange equations of the second kind. As generalized coordinates the floating frame of reference's position and the modal coordinates vector are used. The expressions for the inertial forces vector and the generalized mass matrix are derived from the expression for the kinetic energy of the body. The article also contains all the other terms of the dynamic equation and the expressions for constraint equations' components calculation.
In the article an example of real practical motion simulation for KAMAZ-5308 vehicle with taking into consideration the flexibility of the vehicle's frame is given. A finite element model of the frame with the load platform was developed to consider it's flexible deformations. The following assumptions have been adopted for simulating the vehicle: additional attachments to the frame and platform, load platform's wooden flooring are considered significantly less rigid than the basic structure; brackets for attaching the suspension and the cabin are considered very rigid in comparison with the structure itself; roundings and technological apertures are not considered. As the interface for dynamic reduction, there are 26 nodes corresponding to the places of attachment to the frame of the rest of the car — suspension, load and cabin. After the development of the finite element model in the Fidesys software, four files are created, containing the stiffness and mass matrices, model geometry, normal and static modes. The obtained model of the frame is used in the EULER software as part of a multibody system motion simulation. The model of a car with a flexible frame is used to take into account the effect of the dynamics of the car as a whole on the stress-strain state of the frame in the lane change maneuver.