Assessment of simultaneous and nested conservative augmented Lagrangian schemes for constrained multibody dynamics

Two alternative schemes used for the solution of multibody systems are reported and compared between them to evaluate their performance. Within the context of kinematic constraints imposed via augmented Lagrangian technique, one scheme proposes a simultaneous iterative solution for the computation of the Lagrangian multipliers and the nonlinear Newton-Raphson iterations. The second scheme uses a more classical Uzawa approach to compute the Lagrangian multipliers, and the nonlinear iterations are nested into the multiplier update loop. The performance of the methodology is tested by solving numerical experiments: simple, double, triple, and 10 bars pendulums with revolute joints. Moreover, 2D and 3D analyses are performed. The computed results using both the simultaneous iterative, and the nested iterative techniques, are reported to evaluate: kinematic responses, energy conservation, constraints verification, and iterations reduction.

Modelling and Simulation of Guide-Wire Interaction With Vasculature Using Constrained Multibody Dynamics

In this paper, we describe the mathematical modeling of guide wire dynamics for an intravascular surgical procedure as a problem of constrained multibody dynamics involving surface to surface interactions. The goal of this project is to develop a physics based real time simulator with haptics for the above procedure. The guide-wire is segmented into a finite number of massless and inextensible rods attached with spheres on either sides thus reducing the problem to that of the dynamics of rolling motion of spheres on the re-parameterized surface of vasculature under the action of unilateral constraints with associated Lagrange multipliers. The constrained problem is solved as LCP using Lemke’s method and stabilized using Baumgarte constrain stabilization. The parameters for the constrained violation stabilization are learned real-time using a method based on adaptive control theory. Simulations were performed on geometries representing different sections of vasculature. The results show that this method can be implemented on a full-scale three dimensional vasculature with a hardware interface for haptic feedback.

Automated Procedures for Robust and Efficient Solution of Over-Constrained Multibody Dynamics

The basic steps of a computer-based methodology that generates optimized runtime algorithms to achieve robust, stable, and efficient solution of constrained, multibody dynamics are summarized. The concept of using processors operating in the background to improve many aspects of an executing program’s performance on arbitrary models is introduced. Among the many optimizing tasks, algorithm processors extract model topology from body and joint descriptions, set up recursive spatial kinematics and generalized dynamics algorithms, block-partition constraints and apply Gaussian elimination with complete pivoting to identify and change dependent and independent variable sets, convert constraints into row-reduced, echelon form, permute the constrained generalized equations to achieve stable and efficient solutions, and set up recursive sparse uncoupling and solve algorithms to minimize fills and operations count. To accomplish these tasks, processors assess model-specific algorithm requirements and use this information to generate source and destination memory pointer arrays and arrays of pointers to structures and optimized functions. In essence, they wire and rewire runtime algorithms as needed to maintain robust, stable, and efficient solutions throughout a simulation.

Generalized Orthogonal Complement Based Divide and Conquer Algorithm for Constrained Multibody Dynamics

This paper presents an extension of the orthogonal complement based divide and conquer algorithm for constraint multi-rigid body systems containing closed kinematic loops in generalized topologies. In its current form, its a short article demonstrating the methodology for assembling the equations of motion in a hierarchic assembly process for systems containing multiple loops in generalized topologies.

A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations

The paper presents an approach to linearize the set of index 3 nonlinear differential algebraic equations that govern the dynamics of constrained mechanical systems. The proposed method handles heterogeneous systems that might contain flexible bodies, friction, control elements (user-defined differential equations), and nonholonomic constraints. Analytically equivalent to a state-space formulation of the system dynamics in Lagrangian coordinates, the proposed method augments the governing equations and then computes a set of sensitivities that provide the linearization of interest. The attributes associated with the method are the ability to handle large heterogeneous systems, ability to linearize the system in terms of arbitrary user-defined coordinates, and straightforward implementation. The proposed approach has been released in the 2005 version of the MSC.ADAMS/Solver(C++) and compares favorably with a reference method previously available. The approach was also validated against MSC.NASTRAN and experimental results.

Some Applications of Automatic Differentiation to Rigid, Flexible, and Constrained Multibody Dynamics

In this paper, we discuss several applications of automatic differentiation to multibody dynamics. The scope of this paper covers the rigid, flexible, and constrained dynamical systems. Particular emphasis is placed on the development of methods for automating the generation of equations of motion and the simulation of response using automatic differentiation. We also present a new approach for generating exact dynamical representations of flexible multibody systems in a numerical sense using automatic differentiation. Numerical results will be presented to detail the efficiency of the proposed methods.