Many modern applications of the flexible multibody systems require formulations that can effectively solve problems that include large displacements and deformations having the ability to model nonlinear materials. One method that allows dealing with such systems is continuum-based absolute nodal coordinate formulation (ANCF). The objective of this study is to formulate an efficient method of modeling nonlinear nearly incompressible materials with polynomial Mooney-Rivlin models and volumetric energy penalty function in the framework of the ANCF. The main part of this paper is dedicated to the examination of several ANCF fully parameterized beam elements under incompressible regime. Moreover, two volumetric suppression methods, originating in the finite element analysis, are proposed: a well-known selective reduced integration and F-bar projection. It is also presented that the use of these methods is crucial for performing reliable analysis of models with bending-dominated loads when lower-order elements are employed. The results of the simulations carried on with considered elements and proposed methods are compared with the results obtained from commercial finite element package and existing ANCF implementation. The results
This paper presents a new parallel algorithm for dynamics simulation of general multibody systems. The developed formulations are iterative and possess divide and conquer structure. The constraints equations are imposed at the acceleration level. Augmented Lagrangian methods with mass-orthogonal projections are used to prevent from constraint violation errors. The proposed approaches treat tree topology mechanisms or multibody systems which contain kinematic closed loops in a uniform manner and can handle problems with rank deficient Jacobian matrices. Test case results indicate good accuracy performance dependent on the expense put in the iterative correction of constraint equations. Good numerical properties and robustness of the algorithms are observed when handling systems with single and coupled kinematic loops, redundant constraints, which may repeatedly enter singular configurations.
This paper presents a novel recursive divide-and-conquer formulation for the simulation of complex constrained multibody system dynamics based on Hamilton's canonical equations (HDCA). The systems under consideration are subjected to holonomic, independent constraints and may include serial chains, tree chains, or closed-loop topologies. Although Hamilton's 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 system dynamics based on the Hamiltonian formulation. The developed HDCA formulation leads to a two-stage procedure. In the first phase, the approach utilizes the divide and conquer scheme, i.e., a hierarchic assembly-disassembly process to traverse the multibody system topology in a binary tree manner. The purpose of this step is to evaluate the joint velocities and constraint force impulses. The process exhibits linear O(n) (n -number of bodies) and logarithmic O(log 2 n) numerical cost, in serial and parallel implementations, respectively. The time derivatives of the total momenta are directly evaluated in the second parallelizable step of the algorithm. Sample closed-loop test cases indicate very small constraint violation errors at the position and velocity level as well as marginal energy drift without any additional form of constraint stabilization techniques involved in the solution process. The results are comparatively set against more standard acceleration based Featherstone's DCA approach to indicate the performance of the HDCA algorithm.
When redundant constraints are present in a rigid body mechanism, only selected (if any at all) joint reactions can be determined uniquely, whereas others cannot. Analytic criteria and numerical methods of finding joints with uniquely solvable reactions are available. In this paper, the problem of joint reactions solvability is examined from the point of view of selected numerical methods frequently used for handling redundant constraints in practical simulations. Three different approaches are investigated in the paper: elimination of redundant constraints; pseudoinverse-based calculations; and the augmented Lagrangian formulation. Each method is briefly summarized; the discussion is focused on techniques of handling redundant constraints and on joint reactions calculation. In the case of multibody systems with redundant constraints, the rigid body equations of motion are insufficient to calculate some or all joint reactions. Thus, purely mathematical operations are performed in order to find the reaction solution. In each investigated method, the redundant constraints are treated differently, which—in the case of joints with nonunique reactions—leads to different reaction solutions. As a consequence, reactions reflecting the redundancy handling method rather than physics of the system are calculated. A simple example of each method usage is presented, and calculated joint reactions are examined. The paper points out the origins of nonuniqueness of constraint reactions in each examined approach. Moreover, it is shown that one and the same method may lead to different reaction solutions, provided that input data are prepared differently. Finally, it is demonstrated that—in case of joints with solvable reactions—the obtained solutions are unique, regardless of the method used for redundant constraints handling.
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