Paweł Malczyk

Molecular dynamics simulation of simple polymer chain formation using divide and conquer algorithm based on the augmented Lagrangian method

This paper presents an efficient multibody methodology for the simulation of molecular dynamics of simple polymer chains. The algorithm is formulated in terms of absolute coordinates. The augmented Lagrangian method is incorporated into the divide and conquer framework giving new parallel, logarithmic order algorithm suitable for the simulation of general multibody system topologies. The approach is robust in case of potential rank deficiencies of the Jacobian matrices that embrace the group of systems involving redundant constraints, and which may repeatedly enter singular configurations. Series of nanosecond-long molecular dynamics simulations of simplified polymer chain models are performed to demonstrate the correctness of the methodology and investigate the structure formation of the system subjected to non-bonded (Lennard–Jones) and bonded (torsional) interactions. Conformational changes and dynamic properties of the polymer chains are studied under gradual cooling of the system. The simulation results show that some of the homopolymers collapse into well-formed helices. The fraction of the succeeded runs, in which defect-free helices are found, is a function of initial conditions, chain length, and cooling rate. The employed computational multibody approach appeared to be useful in molecular dynamics simulations implying potential for future research and further development in this field.

Efficient Approach for Constraint Enforcement in Constrained Multibody System Dynamics

We present an efficient and robust approach for enforcing the loop closure constraint at acceleration, velocity and position level in modeling multi-rigid body system dynamics. Our approach builds on the seminal ideas of the Divide and Conquer Algorithm (DCA) and the Augmented Lagrangian Method (ALM). The order-independent hierarchic assembly-disassembly process of the DCA provides an excellent opportunity for modularizing the system topology such that the loop closure constraints can be elegantly handled using constraint enforcement ideas motivated by the ALM. We present a non-iterative, user controlled constraint enforcement approach that enables robust constraint enforcement within the DCA. This approach eliminates the need for the iterative scheme found in many ALM motivated approaches. Similarly, it enables the use of relative or internal coordinates to model kinematic joint constraints not involved in the loop closure, thereby enforcing the constraints exactly for these joints. The approach also enables computationally very efficient serial and parallel implementations. Results from a number of test cases with single and couple closed loops are presented to demonstrate verification of the algorithm.Copyright

Efficient parallel formulation for dynamics simulation of large articulated robotic systems

This paper presents a recursive and parallel formulation for the dynamics simulation of large articulated robotic systems based on the Hamiltons canonical equations. Although Hamiltons canonical equations exhibit many advantageous features compared to their acceleration based counterparts, it appears that there is a lack of dedicated parallel algorithms for multi-rigid body dynamics simulation based on such formulation. In this paper we consider open-loop kinematic chains that are connected by kinematic joints. Initially, the standard set of Hamiltons canonical equations are joined together with the constraint equations at the velocity level. The formulation allows to determine the systems joint velocities and impulsive constraint forces in a divide and conquer framework. This operation results in logarithmic numerical cost in parallel implementation. Subsequently, the time derivatives of the total joint momenta are evaluated at the constant expense. In case of sequential implementation, the entire algorithm exhibits linear computational cost. The proposed method is exact, non-iterative and does not require the direct calculation of the systems Hamiltonian nor its partial derivatives. Numerical test cases reveal negligible energy drift without the use of any additional constraint stabilization techniques. The results are compared against more standard acceleration based formulation and the preliminary outcome from real-life physical experiment.

Parallel Efficiency of Lagrange Multipliers Based Divide and Conquer Algorithm for Dynamics of Multibody Systems

Efficient dynamics simulations of complex multibody systems are essential in many areas of computer aided engineering and design. As parallel computing resources has become more available, researchers began to reformulate existing algorithms or to create new parallel formulations. Recent works on dynamics simulation of multibody systems include sequential recursive algorithms as well as low order, exact or iterative parallel algorithms. The first part of the paper presents an optimal order parallel algorithm for dynamics simulation of open loop chain multibody systems. The proposed method adopts a Featherstone’s divide and conquer scheme by using Lagrange multipliers approach for constraint imposition and dependent set of coordinates for the system state description. In the second part of the paper we investigate parallel efficiency measures of the proposed formulation. The performance comparisons are made on the basis of theoretical floating-point operations count. The main part of the paper is concetrated on experimental investigation performed on parallel computer using OpenMP threads. Numerical experiments confirm good overall efficiency of the formulation in case of modest parallel computing resources available and demonstrate certain computational advantages over sequential versions.Copyright

Parallel Algorithm for Modeling Multi-Rigid Body System Dynamics With Nonholonomic Constraints

This paper presents a new algorithm for serial or parallel implementation of computer simulations of the dynamics of multi-rigid body systems subject to nonholonomic and holonomic constraints. The algorithm presents an elegant approach for eliminating the nonholonomic constraints explicitly from the equations of motion and implicitly expressing them in terms of nonlinear coupling in the operational inertias of the bodies subject to these constraints. The resulting equations are in the same form as those of a body subject to kinematic joint constraints. This enables the nonholohomic constraints to be seamlessly treated in either a (i) recursive or (ii) hierarchic assembly-disassembly process for solving the equations of motion of generalized multi-rigid body systems in serial or parallel implementations. The algorithm is non-iterative and although the nonholonomic constraints are imposed at the acceleration level, constraint satisfaction is excellent as demonstrated by the numerical test case implemented to verify the algorithm. The paper presents procedures for handling both cases where the nonholonomic constraints are imposed between terminal bodies of a system and the environment as well as when the constraints are imposed between bodies in the interior of the system topology. The algorithm uses a mixed set of coordinates and is built on the central idea of eliminating either constraint loads or relative accelerations from the equations of motion by projecting the equations of motion into the motion subspaces or their orthogonal complements.© 2013 ASME

Optimal Design of Multibody Systems Using the Adjoint Method

Optimal design of multibody systems (MBS) is of primary importance to engineers and researchers working in various fields, e.g.: in robotics or in machine design. The goal of this paper is a development and implementation of systematic methods for finding design sensitivities of multibody system dynamics with respect to design parameters in the process of optimization of such systems. The optimal design process may be formulated as finding a set of unknown parameters such that the objective function is minimized under the assumption that design variables may be subjected to a variety of differential and/or algebraic constraints. The solutions of such complex optimal problems are inevitably connected with evaluation of a gradient of the objective function. Herein, a multibody system is described by redundant set of absolute coordinates. The equations of motion for MBS are formulated as a system of differential-algebraic equations (DAEs) that has to be discretized and solved numerically forward in time. The design sensitivity analysis is addressed by using the adjoint method that requires determination and numerical solution of adjoint equations backwards in time. Optimal design of sample planar multibody systems are presented in the paper. The properties of the adjoint method are also investigated in terms of efficiency, accuracy, and problem size.