On the constraints violation in forward dynamics of multibody systems

It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio

On shear and extensional locking in nonlinear composite beams

10.1016/S0141-0296(03)00175-5Engineering Structures262151-170ENST

Review of Classical Approaches for Constraint Enforcement in Multibody Systems

A hallmark of multibody dynamics is that most formulations involve a number of constraints. Typically when redundant generalized coordinates are used, equations of motion arc simpler to derive but constraint equations are present. While the dynamic behavior of constrained systems is well understood, the numerical solution of the resulting equations, potentially of differential-algebraic nature, remains problematic. Many different approaches have been proposed over the years, all presenting advantages and drawbacks: The sheer number and variety of methods that have been proposed indicate the difficulty of the problem. A cursory survey of the literature reveals that the various methods fall within broad categories sharing common theoretical foundations. This paper summarizes the theoretical foundations to the enforcement in constraints in multibody dynamics problems. Next, methods based on the use of Lagrange's equation of the first kind, which are index-3 differential-algebraic equations in the presence of holonomic constraints, are reviewed. Methods leading to a minimum set of equations are discussed; in view of the numerical difficulties associated with index-3 approaches, reduction to a minimum set is often performed, leading to a number of practical algorithms using methods developed for ordinary differential equations. The goal of this paper is to review the features of these methods, assess their accuracy and efficiency, underline the relationship among the methods, and recommend approaches that seem to perform better than others

Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems

A hallmark of multibody dynamics is that most formulations involve a number of constraints. Typically, when redundant generalized coordinates are used, equations of motion are simpler to derive but constraint equations are present. Approaches to dealing with high index differential algebraic equations, based on index reduction techniques, are reviewed and discussed. Constraint violation stabilization techniques that have been developed to control constraint draft are also reviewed. These techniques are used in cony. unction with algorithms that do not exactly enforce the constraints. Control theory forms the basis for a number of these methods. Penalty based techniques have also been developed, but the augmented Lagrangian formulation presents a more solid theoretical foundation. In contrast to constraint violation stabilization techniques, constraint violation elimination techniques enforce exact satisfaction of the constraints, at least to machine accuracy. Finally, as the finite element method has gained popularity for the solution of multibody systems, new techniques for the enforcement of constraints have been developed in that framework. The goal of this paper is to review the features of these methods, assess their accuracy and efficiency, underline the relationship among the methods, and recommend approaches that seem to perform better than others

Theoretical and Experimental Investigation of the Nonlinear Behavior of Composite Beams

As part of the research on the aeroelasticity of helicopter blades, a nonlinear kinematic model has been developed for an initially twisted composite beam. The beam undergoes large rotations but small strains. Some non-classical effects such as transverse shear deformations and elastic couplings that arise from the anisotropic behavior of composite materials are included in the formulation. The effects of differential warping, such as that which arises when warping is constrained, are ignored; whereas warping effects, both in- and out-of-plane are retained. A finite element program has been developed on the basis of the theoretical model. This can predict static behavior as well as calculate natural frequencies and mode shapes of a rotating beam subjected to external loads. The sectional stiffnesses required for the calculations are determined using an extension of NABSA which is a two-dimensional finite element program. For validation of both the theoretical model and numerical code, calculations are compared with experimental data from published work and from the present investigation on a non-uniform torsionally soft model blade. Parametric studies are also carried out to show transverse shear effects

Evaluation of some shear deformable shell elements

10.1016/j.ijsolstr.2005.08.006International Journal of Solids and Structures43175033-505

Nonlinear composite beam model - an application to the aeroelasticity of rotors

Communication to : 20th European Rotorcraft Forum, Amsterdam (The Netherlands), october 4-7, 1994Available at INIST (FR), Document Supply Service, under shelf-number : 22419, issue : a.1994 n.139 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

Theoretical and experimental investigation of the large deflections of beams

Tire de : 'International technical specialist's meeting on rotorcraft basic research, Atlanta (GA, USA), march 25-27, 1991SIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 22419, issue : a.1991 n.35 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc