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An Efficient Solution Method for Multibody Systems with Loops Using Multiple Processors

This paper describes a multibody dynamics algorithm formulated for parallel implementation on multiprocessor computing platforms using the divide-and-conquer approach. The system of interest is a general topology of rigid and elastic articulated bodies with or without loops. The algorithm divides the multibody system into a number of smaller sets of bodies in chain or tree structures, called "branches" at convenient joints called "connection points", and uses an Order-N (O (N)) approach to formulate the dynamics of each branch in terms of the unknown spatial connection forces. The equations of motion for the branches, leaving the connection forces as unknowns, are implemented in separate processors in parallel for computational efficiency, and the equations for all the unknown connection forces are synthesized and solved in one or several processors. The performances of two implementations of this divide-and-conquer algorithm in multiple processors are compared with an existing method implemented on a single processor.

Multibody dynamics

An Application of Flexible Multibody Simulations to Space Launch Systems Liftoff Pad Separation and Umbilical Disconnect

A flexible multibody dynamics approach is applied to the Space Launch System (SLS) liftoff Coupled Loads Analysis (CLA), enabling the inclusion of a large array of component nonlinearities with extreme computational efficiency. The nonlinearities include the cryogenic induced preloads due to the large rotations of the aft struts connecting the Core Stage (CS) to the boosters, the contact/separation and potential re-contact at the booster aft skirt to Mobile Launcher(ML) interface, contact/separation and potential re-contact at the ML/extensible columns interfaces, secondary disconnect of the CS umbilicals including the LOX and LH2 Tail Service Mast Umbilicals (TSMUs), and the disconnect of the upper stage umbilical, the Interim Cryogenic Propulsion Stage Umbilical (ICPSU). The ICPSU disconnect involves algorithms simulating the winch motors reeling lanyard ropes, the nonlinear modeling of ropes and hoses, the disconnect and capture of multiple umbilical ground plates by catch-nets (geometrically nonlinear models), and the large rotations of the ML gantry in order to track clearances between the lifting SLS vehicle and umbilicals rotating out of the way. The flexible multibody dynamics framework utilized for these simulations provided a systematic and efficient framework for adding complex nonlinearities at the system level which would have otherwise not been possible in standard CLAs or would have to be treated by separate local analyses thereby not accounting for the coupled system behavior.

Application

Seamless Integration of Multibody and Orbital Dynamics to Support Human Spaceflight Simulations

At the NASA Johnson Space Center (JSC), modeling capability requirements are often driven by the need to simulate upcoming mission scenarios for analysis, procedures development, and training. In preparation for free-flyer vehicle capture, maneuvers, and release, it was determined that the multibody dynamics capabilities provided by MBDyn and the orbital dynamics capabilities supplied by JEOD needed to be merged to properly simulate the dynamic behaviors expected on-orbit. After initial attempts to combine the two packages proved cumbersome, it was decided that a more refined solution was required to facilitate the interface between these two packages. The resulting interface software package was named MBJEOD. The primary design goals for this new package were to leave MBDyn and JEOD untouched, to simplify and clarify simulation initialization for users, and to support any topology or on-orbit operational scenario that future missions might require. This paper provides a detailed overview of MBJEOD and the approach taken to seamlessly integrate the multibody dynamics of MBDyn with the orbital dynamics of JEOD. Additional attention is given to the numerical considerations required for MBJEOD and the simplifying assumptions leveraged to provide for real-time simulation needs. Verification and validation are addressed and current MBJEOD applications at the NASA JSC are discussed.

modeling

Seamless Integration of Multibody and Orbital Dynamics to Support Human Spaceflight Simulations

At the NASA Johnson Space Center (JSC), modeling capability requirements are often driven by the need to simulate upcoming mission scenarios for analysis, procedures development, and training. In preparation for free-flyer vehicle capture, maneuvers, and release, it was determined that the multibody dynamics capabilities provided by MBDyn and the orbital dynamics capabilities supplied by JEOD needed to be merged to properly simulate the dynamic behaviors expected on-orbit. After initial attempts to combine the two packages proved cumbersome, it was decided that a more refined solution was required to facilitate the interface between these two packages. The resulting interface software package was named MBJEOD. The primary design goals for this new package were to leave MBDyn and JEOD untouched, to simplify and clarify simulation initialization for users, and to support any topology or on-orbit operational scenario that future missions might require. This paper provides a detailed overview of MBJEOD and the approach taken to seamlessly integrate the multibody dynamics of MBDyn with the orbital dynamics of JEOD. Additional attention is given to the numerical considerations required for MBJEOD and the simplifying assumptions leveraged to provide for real-time simulation needs. Verification and validation are addressed and current MBJEOD applications at the NASA JSC are discussed.

modeling

Modeling and Verification of Lumped-Parameter, Multibody Structural Dynamics for Offshore Wind Turbines

This paper presents the modeling and verification of multibody structural dynamics for offshore wind turbines. The flexible tower and support structure of a monopile-based offshore wind turbine are modeled using an acausal, lumped-parameter, multibody approach that incorporates structural flexibility, soil-structure interaction, and hydrodynamic models. Simulation results are benchmarked against alternative modeling approaches, demonstrating the model's ability to accurately capture both static and dynamic behaviors under various wind and wave conditions while maintaining computational efficiency. This work provides a valuable tool for analyzing key structural characteristics of wind turbines, including eigenfrequencies, mode shapes, damping, and internal forces.

17 WIND ENERGY

Applications of Multibody for Everybody (M4E) in Marine Energy

Multibody for Everybody (M4E) is an open-source symbolic dynamics modeling framework designed to automate the derivation of equations of motion and simulation of constrained multibody systems using the joint coordinate formulation.

16 TIDAL AND WAVE POWER

Constrained multibody system dynamics: An automated approach

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

Kamman, J. W.

Multibody transport concept

Two baseline aircraft are configured in this study. The multibody aircraft has two fuselage bodies located at approximately 28% wing semispan. The single-body aircraft is configured in such a way as to provide a reference base with which the multibody aircraft can be compared. The aircraft are sized to provide the lowest direct operating cost configuration when transporting 771,620 lbs. over a distance of 3,500 nautical miles at a cruise speed of Mach 0.80. The aircraft are assumed to operate in the years 1990-1995, thus allowing for the incorporation of those technologies expected to be mature and available for production usage in 1985. In comparison with the single-body aircraft, the two-body aircraft shows reductions of 8.9% in wing weight, 7.7% in structural weight, 13.5% in block fuel weight, and 11.3% in direct operating cost.

Moore, J. W.

Approaches and possible improvements in the area of multibody dynamics modeling

A wide ranging look is taken at issues involved in the dynamic modeling of complex, multibodied orbiting space systems. Capabilities and limitations of two major codes (DISCOS, TREETOPS) are assessed and possible extensions to the CONTOPS software are outlined. In addition, recommendations are made concerning the direction future development should take in order to achieve higher fidelity, more computationally efficient multibody software solutions.

Lips, K. W.

Enhanced element-specific modal formulations for flexible multibody dynamics

The accuracy of current flexible multibody formalisms based on assumed modes is examined in the context of standard spacecraft motions involving structural components undergoing both slow and fast overall translational and rotational motions as well as small deformations. Limitations of current techniques in treating: (1) element-specific coupling behavior of large motion and small deformation, and (2) motion-induced structural stiffness variations, are noted. The roles of nonlinear and linear elastic structural theories in accurately predicting transient large-displacement dynamic behavior of flexible multibody systems are examined in detail. Coupling effects between deformation and overall motion are carefully scrutinized in the context of assumed-mode discretization techniques. Consistently linearized beam, plate, and shell formulations involving in-plane stretch variables are proposed and shown to yield very accurate simulation results and extremely fast modal convergence for most motions involving small strains. In some particular cases, however, in which membrane stiffness dominates bending stiffness, a nonlinear strain formulation is required in order to capture proper coupling between deformation and overall motion.

Ryan, Robert R.

Controlled multibody dynamics simulation for large space structures

Multibody dynamics discipline, and dynamic simulation in control structure interaction (CSI) design are discussed. The use, capabilities, and architecture of the Large Angle Transient Dynamics (LATDYN) code as a simulation tool are explained. A generic joint body with various types of hinge connections; finite element and element coordinate systems; results of a flexible beam spin-up on a plane; mini-mast deployment; space crane and robotic slewing manipulations; a potential CSI test article; and multibody benchmark experiments are also described.

Housner, J. M.

An innovations approach to decoupling of multibody dynamics and control

The problem of hinged multibody dynamics is solved using an extension of the innovations approach of linear filtering and prediction theory to the problem of mechanical system modeling and control. This approach has been used quite effectively to diagonalize the equations for filtering and prediction for linear state space systems. It has similar advantages in the study of dynamics and control of multibody systems. The innovations approach advanced here consists of expressing the equations of motion in terms of two closely related processes: (1) the innovations process e, a sequence of moments, obtained from the applied moments T by means of a spatially recursive Kalman filter that goes from the tip of the manipulator to its base; (2) a residual process, a sequence of velocities, obtained from the joint-angle velocities by means of an outward smoothing operations. The innovations e and the applied moments T are related by means of the relationships e = (I - L)T and T = (I + K)e. The operation (I - L) is a causal lower triangular matrix which is generated by a spatially recursive Kalman filter and the corresponding discrete-step Riccati equation. Hence, the innovations and the applied moments can be obtained from each other by means of a causal operation which is itself casually invertible.

Rodriguez, G.

Explicit modeling of composite plates and beams in the dynamics of multibody systems

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed.

Amirouche, F. M. L.

Modeling of control forces for kinematical constraints in the dynamics of multibody systems: A new approach

Conventionally kinematical constraints in multibody systems are treated similar to geometrical constraints and are modeled by constraint reaction forces which are perpendicular to constraint surfaces. However, in reality, one may want to achieve the desired kinematical conditions by control forces having different directions in relation to the constraint surfaces. The conventional equations of motion for multibody systems subject to kinematical constraints are generalized by introducing general direction control forces. Conditions for the selections of the control force directions are also discussed. A redundant robotic system subject to prescribed end-effector motion is analyzed to illustrate the methods proposed.

Ider, Sitki Kemal

Multibody dynamics: Modeling component flexibility with fixed, free, loaded, constraint, and residual modes

The assumed-modes method in multibody dynamics allows the elastic deformation of each component in the system to be approximated by a sum of products of spatial and temporal functions commonly known as modes and modal coordinates respectively. The choice of component modes used to model articulating and non-articulating flexible multibody systems is examined. Attention is directed toward three classical Component Mode Synthesis (CMS) methods whereby component normal modes are generated by treating the component interface (I/F) as either fixed, free, or loaded with mass and stiffness contributions from the remaining components. The fixed and free I/F normal modes are augmented by static shape functions termed constraint and residual modes respectively. A mode selection procedure is outlined whereby component modes are selected from the Craig-Bampton (fixed I/F plus constraint), MacNeal-Rubin (free I/F plus residual), or Benfield-Hruda (loaded I/F) mode sets in accordance with a modal ordering scheme derived from balance realization theory. The success of the approach is judged by comparing the actuator-to-sensor frequency response of the reduced order system with that of the full order system over the frequency range of interest. A finite element model of the Galileo spacecraft serves as an example in demonstrating the effectiveness of the proposed mode selection method.

Spanos, John T.

A verification library for multibody simulation software

A multibody dynamics verification library, that maintains and manages test and validation data is proposed, based on RRC Robot arm and CASE backhoe validation and a comparitive study of DADS, DISCOS, and CONTOPS that are existing public domain and commercial multibody dynamic simulation programs. Using simple representative problems, simulation results from each program are cross checked, and the validation results are presented. Functionalities of the verification library are defined, in order to automate validation procedure.

Kim, Sung-Soo

A variational approach to dynamics of flexible multibody systems

This paper presents a variational formulation of constrained dynamics of flexible multibody systems, using a vector-variational calculus approach. Body reference frames are used to define global position and orientation of individual bodies in the system, located and oriented by position of its origin and Euler parameters, respectively. Small strain linear elastic deformation of individual components, relative to their body references frames, is defined by linear combinations of deformation modes that are induced by constraint reaction forces and normal modes of vibration. A library of kinematic couplings between flexible and/or rigid bodies is defined and analyzed. Variational equations of motion for multibody systems are obtained and reduced to mixed differential-algebraic equations of motion. A space structure that must deform during deployment is analyzed, to illustrate use of the methods developed.

Wu, Shih-Chin

Reduced order component models for flexible multibody dynamics simulations

Many flexible multibody dynamics simulation codes require some form of component description that properly characterizes the dynamic behavior of the system. A model reduction procedure for producing low order component models for flexible multibody simulation is described. Referred to as projection and assembly, the method is a Rayleigh-Ritz approach that uses partitions of the system modal matrix as component Ritz transformation matrices. It is shown that the projection and assembly method yields a reduced system model that preserves a specified set of the full order system modes. Unlike classical component mode synthesis methods, the exactness of the method described is obtained at the expense of having to compute the full order system modes. The paper provides a comprehensive description of the method, a proof of exactness, and numerical results demonstrating the method's effectiveness.

Tsuha, Walter S.