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Brugnoli Andrea Alazard Daniel Pommier-Budinger Valérie Matignon Denis 《Multibody System Dynamics》2021,51(3):343-375
Multibody System Dynamics - A new formulation for the modular construction of flexible multibody systems is presented. By rearranging the equations for a flexible floating body and introducing the... 相似文献
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In this work we set to examine several important issues pertinent to currently very active research area of the finite element modeling of flexible multibody system dynamics. To that end, we first briefly introduce three different model problems in non-linear dynamics of flexible 3D solid, a rigid body and 3D geometrically exact beam, which covers the vast majority of representative models for the particular components of a multibody system. The finite element semi-discretization for these models is presented along with the time-discretization performed by the mid-point scheme. In extending the proposed methodology to modeling of flexible multibody systems, we also present how to build a systematic representation of any kind of joint connecting two multibody components, a typical case of holonomic contraint, as a linear superposition of elementary constraints. We also indicate by a chosen model of rolling contact, an example of non-holonomic constraint, that the latter can also be included within the proposed framework. An important aspect regarding the reduction of computational cost while retaining the consistency of the model is also addressed in terms of systematic use of the rigid component hypothesis, mass lumping and the appropriate application of the explicit-implicit time-integration scheme to the problem on hand. Several numerical simulations dealing with non-linear dynamics of flexible multibody systems undergoing large overall motion are presented to further illustrate the potential of presented methodology. Closing remarks are given to summarize the recent achievements and point out several directions for future research. 相似文献
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Jawhar Chebbi Vincent Dubanchet José Alvaro Perez Gonzalez Daniel Alazard 《Multibody System Dynamics》2017,40(1):75-98
We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path.Enforcing this condition directly in form of a servo constraint leads to differential-algebraic equations (DAEs) of arbitrarily high index. Typically, the model equations are of index 5, which already poses high regularity conditions. If we relax the servo constraints and consider the system from an optimal control point of view, the strong regularity conditions vanish, and the solution can be obtained by standard techniques.By means of the well-known \(n\)-car example and an overhead crane, the theoretical and expected numerical difficulties of the direct DAE and the alternative modeling approach are illustrated. We show how the formulation of the problem in an optimal control context works and address the solvability of the optimal control system. We discuss that the problematic DAE behavior is still inherent in the optimal control system and show how its evidences depend on the regularization parameters of the optimization. 相似文献
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Anmol Goyal Michael R. Dörfel Bernd Simeon Anh-Vu Vuong 《Multibody System Dynamics》2013,30(2):139-151
This work aims at including nonlinear elastic shell models in a multibody framework. We focus our attention to Kirchhoff–Love shells and explore the benefits of an isogeometric approach, the latest development in finite element methods, within a multibody system. Isogeometric analysis extends isoparameteric finite elements to more general functions such as B-splines and NURBS (Non-Uniform Rational B-Splines) and works on exact geometry representations even at the coarsest level of discretizations. Using NURBS as basis functions, high regularity requirements of the shell model, which are difficult to achieve with standard finite elements, are easily fulfilled. A particular advantage is the promise of simplifying the mesh generation step, and mesh refinement is easily performed by eliminating the need for communication with the geometry representation in a CAD (Computer-Aided Design) tool. Target applications are wind turbine blades and twist beam rear suspensions. First numerical examples demonstrate an impressive convergence behavior of the isogeometric approach even for a coarse mesh, while offering substantial savings with respect to the number of degrees of freedom. 相似文献
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Recent development of the shock analysis on the HDD is briefly reviewed. A flexible multi-body dynamics formulation is developed to simulate the shock response of the HDD. If one component in the HDD is changed, only mode shapes and frequencies of that component should be re-calculated and then used to obtain the system’s response. Steady state Reynolds equation is solved to obtain the air pressure on the slider and disk for various slider positions. An air pressure table is formed and used to model the non-linear air bearing during the simulation. Responses of flying height for different direction and shock duration time are analyzed. Results show that the flying state of the slider is more sensitive to the shock with shorter duration time. 相似文献
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Multibody System Dynamics - In this work a new approach to deal with non-ideal operative aspects of spatial revolute joints by means of a three-dimensional finite element analysis (3D-FEA) is... 相似文献
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Three-dimensional formulation of rigid-flexible multibody systems with flexible beam elements 总被引:2,自引:1,他引:2
Multibody systems generally contain solids with appreciable deformations and which decisively influence the dynamics of the
system. These solids have to be modeled by means of special formulations for flexible solids. At the same time, other solids
are of such a high stiffness that they may be considered rigid, which simplifies their modeling. For these reasons, for a
rigid-flexible multibody system, two types of formulations coexist in the equations of the system. Among the different possibilities
provided in the literature on the material, the formulation in natural coordinates and the formulation in absolute nodal coordinates
are utilized in this paper to model the rigid and flexible solids, respectively. This paper contains a mixed formulation based
on the possibility of sharing coordinates between a rigid solid and a flexible solid. The global mass matrix of the system
is shown to be constant and, in addition, many of the constraint equations obtained upon utilizing these formulations are
linear and can be eliminated. 相似文献
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In this work, a two-step approach for model reduction in flexible multibody dynamics is proposed. This technique is a combination
of the Krylov-subspace method and a Gramian matrix based reduction approach that is particularly suited if a small reduced-order
model of a system charged with many force-inputs has to be generated. The proposed methodology can be implemented efficiently
using sparse matrix techniques and is therefore applicable to large-scale systems too. By a numerical example, it is demonstrated
that the suggested two-step approach has very good approximation capabilities in the time as well as in the frequency domain
and can help to reduce the computation time of a numerical simulation significantly. 相似文献
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This paper presents a method for improving dynamic solutions that are obtained from the dynamic simulation of flexible multibody systems. The mode-acceleration concept in linear structural dynamics is utilized in the proposed method for improving accuracy in the postprocessing stage. A theoretical explanation is made on why the proposed method improves the dynamic solutions in the context of the mode-acceleration method. A mode-acceleration equation for each flexible body is defined and the load term in the right hand side of the equation is represented as a combination of space-dependent and time-dependent terms so that efficient computation of dynamic solutions can be achieved. The load term is obtained from dynamic simulation of a flexible multibody system and a finite element method is used to compute dynamic solutions by quasi-static analyses. Numerical examples show the effectiveness of the proposed method. 相似文献
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Byungyil Souh 《Multibody System Dynamics》2013,30(1):1-11
A new plane beam dynamic formulation for constrained multibody system dynamics is developed. Flexible multibody system dynamics includes rigid body dynamics and superimposed vibratory motions. The complexity of mechanical system dynamics originates from rotational kinematics, but the natural coordinate formulation does not use rotational coordinates, so that simple dynamic formulation is possible. These methods use only translational coordinates and simple algebraic constraints. A new formulation for plane flexible multibody systems are developed utilizing the curvature of a beam and point masses. Using absolute nodal coordinates, a constant mass matrix is obtained and the elastic force becomes a nonlinear function of the nodal coordinates. In this formulation, no infinitesimal or finite rotation assumptions are used and no assumption on the magnitude of the element rotations is made. The distributed body mass and applied forces are lumped to the point masses. Closed loop mechanical systems consisting of elastic beams can be modeled without constraints since the loop closure constraints can be substituted as beam longitudinal elasticity. A curved beam is modeled automatically. Several numerical examples are presented to show the effectiveness of this method. 相似文献
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The development of a sliding joint for very flexible multibody dynamics using absolute nodal coordinate formulation 总被引:1,自引:0,他引:1
Soo-Ho Lee Tae-Won Park Jong-Hwi Seo Ji-Won Yoon Kab-Jin Jun 《Multibody System Dynamics》2008,20(3):223-237
In this paper, a formulation for a spatial sliding joint is derived using absolute nodal coordinates and non-generalized coordinate
and it allows a general multibody move along a very flexible cable. The large deformable motion of a spatial cable is presented
using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics
theory to represent the elastic forces. And the nongeneralized coordinate, which is related to neither the inertia forces
nor the external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. Hereby,
the non-generalized coordinate represents the arc-length parameter. The constraint equations for the sliding joint are expressed
in terms of generalized coordinate and nongeneralized coordinate. In the constraint equations for the sliding joint, one constraint
equation can be systematically eliminated. There are two independent Lagrange multipliers in the final system equations of
motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems
such as pulley systems and pantograph-catenary systems for high speed-trains. 相似文献
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Meshfree Galerkin methods have been developed recently for the simulation of complex mechanical problems involving large strains of structures, crack propagation, or high velocity impact dynamics. At the present time, the application of these methods to multibody dynamics has not been made despite their great advantage in some situations over standard finite element techniques. 相似文献
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An original approach for flexible multibody dynamics is proposed, which combines the free–free formulation of elastic body deformation with an impulse-based representation of linear vibration. The resulting system of equations being remarkably simple, this impulse-based substructuring method is straightforward to implement. Simple applications of a flexible rotating beam submitted to various excitation inputs have been selected and developed so as to assess the accuracy of the proposed methodology. 相似文献
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This paper deals with the solution of three key problems for enabling the consideration of the massive parallelization for multibody dynamics. Instead of classical joints, the flexible joints with appropriate stiffness and damping are introduced in the multibody system, which enables to derive completely decoupled equations of motion and as a consequence to simulate them using massive parallel computing. Such formulation causes the uprise of high frequencies in the solution. Therefore, the heterogeneous multiscale method is used for numerical integration. However, three key problems had to be solved prior to such multibody simulation could be considered for further development. The problems are: the clear distinction of macro-model and micro-model in order to really reduce the eigenvalues of the integrated model, the completely decoupled procedure for estimation of reaction forces for each micro-integration restart, and the suitable choice of microintegration time length. 相似文献
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Fast simulation (e.g., real-time) of flexible multibody systems is typically restricted by the presence of both differential
and algebraic equations in the model equations, and the number of degrees of freedom required to accurately model flexibility.
Model reduction techniques can alleviate the problem, although the classically used body-level model reduction and general-purpose
system-level techniques do not eliminate the algebraic equations and do not necessarily result in optimal dimension reduction.
In this research, Global Modal Parametrization, a model reduction technique for flexible multibody systems is further developed
to speed up simulation of flexible multibody systems. The reduction of the model is achieved by projection on a curvilinear
subspace instead of the classically used fixed vector space, requiring significantly less degrees of freedom to represent
the system dynamics with the same level of accuracy. The numerical experiment in this paper illustrates previously unexposed
sources of approximation error: (1) the rigid body motion is computed in a forward dynamical analysis resulting in a small
divergence of the rigid body motion, and (2) the errors resulting from the transformation from the modal degrees of freedom
of the reduced model back to the original degrees of freedom. The effect of the configuration space discretization coarseness
on the different approximation error sources is investigated. The trade-offs to be defined by the user to control these approximation
errors are explained. 相似文献
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An active pulse control method is developed to reduce the vibrations of multibody systems resulting from impact loadings. The pulse, which is a function of system generalized coordinates and velocities, is determined analytically using energy and momentum balance equations of the impacting bodies. Elastic components in the multibody system are discretized using the finite element method. The system equations of motions and nonlinear algebraic constraint equations describing mechanical joints between different components are written in the Lagrangian formulation using a finite set of coupled reference position and local elastic generalized coordinates. A set of independent differential equations are identified by the generalized coordinate partitioning of the constraint Jacobian matrix. These equations are written in the state space formulation and integrated forward in time using a direct numerical integration method. Dependent coordinates are then determined using the constraint kinematic relations. Points in time at which impact occurs are monitored by an impact predictor function, which controls the integration algorithms and forces for the solution of the momentum relation, to define the jump discontinuities in the composite velocity vector as well as the system reaction forces. The effectiveness of the active pulse control in reducing the vibration of flexible multibody aircraft during the touchdown impact is investigated and numerical results are presented. 相似文献
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Geometrically non-linear formulation of flexible multibody systems in terms of beam elements: Geometric stiffness 总被引:3,自引:0,他引:3
The occurrence of strong deflections and major axial forces in many applications involving flexible multibodies entails including non-linear terms coupling deformation-induced axial and transverse displacements in the motion equation. The formulations, including such terms, are known as geometrically non-linear formulations. The authors have developed one such formulation that preserves higher-order terms in the strain energy function. By expressing such terms as a function of selected elastic coordinates, three stiffness matrices and two non-linear vectors of elastic forces are defined. The first matrix is the conventional constant-stiffness matrix, the second is the classical geometric stiffness matrix and the third is a second-order geometric stiffness matrix. The aim of this work is to define the third matrix and the two non-linear vectors of elastic forces by using the finite-element method. 相似文献