A Conservative Augmented Lagrangian Algorithm for the Dynamics of Constrained Mechanical Systems

Abstract

The motion of many practical mechanical systems is often constrained. An important example is the dynamics of multibody systems, where the numerical solution of this type of systems faces several difficulties. A strategy for to solve this type of problems is the augmented Lagrange formulation, which allows the use of numerical integrators for ODEs, combined with an update scheme for the algebraic variables, accomplishing exact fulfillment of the constraints. This work focuses on the design of a conservative version of this augmented Lagrangian formulation for holonomic constraints, proposing a numerical procedure that exhibits excellent stability.

Stress distribution around an elliptic hole in a plate with ‘implicit’ and ‘explicit’ non-local models

“…Although the presence of padding elements may seem to increase the total DOFs, in fact, the global equation system submitted to the solver has the same dimensions with conventional quarter symmetry model because of the existence of multi freedom constraints (MFCs). In general, depending on the level of complexity of the constraints, different techniques are available to treat them [77][78][79], while for homogeneous and linear constraints, the master-slave approach [80] can be conducted. In master-slave approach, an auxiliary equation system is generated to represent the kinematic relation between master and slave nodes.…”

Use of penalty formulations in dynamic simulation and analysis of redundantly constrained multibody systems

“…The effect of the magnitude and the scaling of penalty factors on the stability and accuracy of dynamic simulations were studied in [4], [3] and [2]. On the other hand, interpretations of the physical meaning of the penalty factors were reported in [20] and [7]. The second of these papers stresses the meaning of the terms α k , µ k and ω k as inertia, damping and stiffness coefficients, and the fact that these are not dimensionless quantities, but they have physical units.…”

A parameter‐preadjusted energy‐conserving integration for rigid body dynamics in terms of convected base vectors

“…After that, a large amount of effort has devoted to develop the energy-conserving schemes for a wide range of applications, such as Hamilton systems, [7][8][9] particles systems, 10 nonlinear elastodynamics, 11,12 mechanical systems with holonomic constraints, 13,14 optimal control problems, 15 and rigid and flexible multibody systems. [16][17][18][19][20][21][22][23][24][25][26][27] In these and many other applications, the energy of the systems is successfully preserved, but the errors of other quantities, for example, trajectory errors, are generally not bounded and increase with time. 4 Because energy-conserving integrations are mostly applied to long-time simulations, the accumulation of these errors can be significant.…”