Formulation For Rigid Bodies Research Articles

Simulation of impacts between spherical rigid bodies with frictional effects

AbstractThis work studies the impact between spherical rigid bodies in the frame of nonsmooth contact dynamics considering friction effects. A new impact element formulation based on the classical instantaneous local Newton impact law is presented. The kinematics properties of the spheres are described by a rigid body formulation with translational and rotational degrees of freedom referred to an inertial frame. In addition, an extension of the nonsmooth generalized‐ time integration scheme applied to collisions with multiple impacts including Coulomb's friction law is given. Six numerical examples are presented to evaluate the robustness and the performance of the proposed methodology.

Space-time rigid multibody dynamics

In this contribution, we apply space-time formulation on constrained rigid body dynamics. In particular, we discretize directly Hamilton’s principle using appropriate space-time approximation spaces for the variational problem. Moreover, we make use of a rotationless formulation for the rigid bodies, and thus we have to define appropriate approximation spaces for the Lagrange multipliers as well. Moreover, we make use of Livens’ principle, introducing independent quantities for the position, velocity, and momentum, where the latter can be considered as Lagrange multipliers, and we apply this concept to the space-time rigid body formulation. Finally, we demonstrate the convergence of the different approaches and the superiority in terms of computational effort, and thus total energy consumption of dynamical simulations.

A target-fixed immersed-boundary formulation for rigid bodies interacting with fluid flow

We present an immersed boundary projection method for flow-structure interaction problems involving rigid bodies with complex geometries. Dynamics of a rigid body interacting with fluid flow and kinematics of other rigid bodies undergoing prescribed motions are coupled implicitly with the incompressible vorticity equations. In particular, the method is formulated in a frame of reference fixed on the rigid body under flow-structure interaction (the target) so that the coupled system can be solved non-iteratively, accurately, and efficiently. The implicit coupling of the fluid solver and dynamics and kinematics of rigid bodies ensures the method being stable for low solid-to-fluid mass ratios. The influence of fictitious fluid inside the rigid body is considered and the spurious oscillations in surface stresses are filtered to impose physically correct rigid body dynamics. Similar to many predecessors of the immersed boundary projection method, the resulting discrete system is solved efficiently using a block-LU decomposition. We then validate the method with two-dimensional test problems of a neutrally buoyant cylinder migrating in a planar Couette flow and a freely falling or rising cylindrical rigid body.

A fluid-structure interaction model for numerical simulation of bridge flutter using sectional models with active control devices. Preliminary results

A fluid-structure interaction scheme for numerical simulation of actively controlled bridges subject to flutter instability is proposed in this work. In order to suppress or attenuate dynamic instabilities induced by the wind action on long-span bridges, control systems are proposed considering aerodynamic appendices and winglets attached to the deck structure, where control forces are continuously calculated using optimal control theory. The flow fundamental equations are solved here employing the explicit two-step Taylor-Galerkin method and the arbitrary Lagrangian-Eulerian (ALE) description. Eight-node hexahedral finite elements with one-point quadrature and hourglass stabilization are utilized for spatial discretization. Flow turbulence is modeled using Large Eddy Simulation (LES) and a partitioned coupling scheme is adopted for fluid-structure interactions. The structural system is analyzed considering the sectional model approach and a rigid-body formulation for large rotations. Different control techniques and winglet configurations are investigated using prismatic and bridge cross-sections, where control efficiency is evaluated in terms of displacement reduction and energy required by the control system. Preliminary results are obtained here employing approximate flow conditions to verify the control algorithm, where laminar flows and a two-dimensional LES-type approach are utilized.

Rigid body formulation in a finite element context with contact interaction

The present work proposes a formulation to employ rigid bodies together with flexible bodies in the context of a nonlinear finite element solver, with contact interactions. Inertial contributions due to distribution of mass of a rigid body are fully developed, considering a general pole position associated with a single node, representing a rigid body element. Additionally, a mechanical constraint is proposed to connect a rigid region composed by several nodes, which is useful for linking rigid/flexible bodies in a finite element environment. Rodrigues rotation parameters are used to describe finite rotations, by an updated Lagrangian description. In addition, the contact formulation entitled master-surface to master-surface is employed in conjunction with the rigid body element and flexible bodies, aiming to consider their interaction in a rigid–flexible multibody environment. New surface parameterizations are presented to establish contact pairs, permitting pointwise interaction in a frictional scenario. Numerical examples are provided to show robustness and applicability of the methods.

Assessment of out-of-plane behavior of rammed earth walls by pull-down tests

ABSTRACTThis article reports pull-down tests performed on rammed earth construction in Bhutan. The pull–down specimens involved an old rammed earth building component as well as a newly prepared rammed earth wall. Both the wall specimens were tested in out-of-plane direction. Theoretical rigid body formulation and finite element (FE) models were developed to predict the response of the rammed earth structures under out-of-plane loading. The validated FE model was further extended to parametric study of material and physical characteristics of rammed earth construction and their effect on critical response quantities. The change in elastic modulus showed effect in the pre-cracking phase of the wall. Density of rammed earth on the other hand affected the post-peak response of the rammed earth wall. Furthermore, an increase in the physical characteristics, namely, the thickness of wall and the vertical superimposed load on top of the wall, enhanced the rocking resistance capacity of the out-of-plane loaded rammed earth walls.

An integral equation formulation for rigid bodies in Stokes flow in three dimensions

We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in O(n) time, where n denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples.

MECHANICAL INTEGRATORS FOR THE INVERSE DYNAMICS OF DISSIPATIVE MULTIBODY SYSTEMS

A unified approach for the description of multibody systems is presented, relying on a rotationless formulation for rigid bodies. The set of differential algebraic equations governing the motion of multibody dynamics does not only beneficially offer the design of energy- momentum schemes but it also bears the advantage to be extended by vital modeling features. In this spirit we present within this paper the modeling of friction phenomena such as joint friction and the incorporation of control constraints. Both features rely on a specific augmentation technique which introduces rotational degrees of freedom into the rotationless formulation. An example of a partially controlled movement of a free floating parallel platform with joint friction will demonstrate the performance of the newly developed energy-momentum consistent scheme.

Performance and Application Criteria of Two Fast Formulations for Flexible Multibody Dynamics#

The performance of the simulation of flexible multibody systems can be improved by means of the use of topological formulations, which have provided good results in the simulation of large rigid multibody systems. In this work, a topological formulation for rigid bodies is extended to the flexible case, and tests are carried out in order to compare its performance with that of a global formulation. Three systems are simulated: a double four-bar mechanism, a vehicle suspension, and a full vehicle. As it happens in the rigid case, the topological formulation is faster than the global one only for large mechanisms.

Topological vs Global Penalty Formulations for Real-Time Flexible Multibody Dynamics

The simulation of flexible multibody systems is a very demanding task that needs improvements in efficiency in order to achieve real-time performance. One of such improvements may be the use of topological formulations, which have provided good results in the simulation of large rigid multibody systems. In this work, a topological formulation for rigid bodies is extended to the flexible case, and tests are carried out in order to compare its performance with that of a global formulation. Two systems are simulated, a double four-bar mechanism and a vehicle suspension. As it happened in the rigid case for these two examples, the topological formulation shows lower performance than its global counterpart for such small systems, but the difference decreases as more bodies are modeled as flexible. Since in the rigid case the topological formulation became faster for large systems, further tests must be performed in order to check whether this advantage is kept or even increased in the flexible case.

Dynamic Simulation of General Flexible Multibody Systems*

A formulation and associated solution method are presented for dynamic simulation of multibody systems consisting of rigid bodies, flexible bodies that undergo large gross motion accompanied by small elastic vibration, and flexible bodies that undergo large gross motion and geometric and material nonlinear deformation. This formulation combines the Cartesian rigid body formulation, the modal flexibility approach, and nonlinear finite element methods. Nonlinear kinematic constraints between bodies are enforced using the Lagrange multiplier method. Linear kinematic constraints between bodies are enforced by eliminating dependent generalized coordinates in an assembly process. The resulting differential-algebraic equations are solved using a method that is based on the generalized coordinate partitioning algorithm. The general flexible multibody dynamics formulation and solution methods are implemented by developing an integrated version of DADS and a pilot general-purpose nonlinear finite element analysis code. Numerical examples are provided to demonstrate the validity of the formulation and numerical methods.