For efficient dynamic simulation of mechanical and aerospace systems, the use of different sets of coordinate types may be necessary. The components of multibody systems can be rigid, flexible or very flexible and can be subject to contact forces. Examples of challenging problems encountered when multibody systems are considered are crashworthiness, problems of cables used in rescue operations and heavy load handling, belt drives, leaf spring system design, tire deformations, large deformation of high-speed rotors, stability problems, and contact problems. Most large displacement problems in structural mechanics are being solved using incremental solution procedures. On the other hand, general purpose flexible multibody computer tools and methodologies in existence today are not, in general, capable of systematically and efficiently solving applications that include, in addition to rigid bodies and bodies that undergo small deformations, bodies that experience very large deformations. The objective of this paper is to discuss the development of new computational algorithms, based on non-incremental solution procedures, for the computer simulation of multibody systems with flexible components. These new algorithms that do not require special measures to satisfy the principles of work and energy and lead to optimum sparse matrix structure can be used as the basis for developing a new generation of flexible multibody computer programs. The proposed non-incremental algorithms integrate three different formulations and three different sets of generalized coordinates for modeling rigid bodies, flexible bodies with small deformations, and very flexible bodies that undergo large deformations. The implementation of a general contact model in multibody algorithms is also presented as an example of mechanical systems with non-generalized coordinates. The kinematic equations that describe the contact between two surfaces of two bodies in the multibody system are formulated in terms of the system-generalized coordinates and the non-generalized surface parameters. Each contact surface is defined using two independent parameters that completely determine the tangent and normal vectors at an arbitrary point on the body surface. In the contact model presented in this study, the points of contact are determined on line during the dynamic simulation by solving the non-linear differential and algebraic equations of the constrained multibody system. The augmented form of the equations of motion expressed in terms of the generalized coordinates and non-generalized surface parameters is presented in this paper.
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