scholarly journals Formulation of Shell Elements Based on the Motion Formalism

2021 ◽  
Vol 2 (4) ◽  
pp. 1009-1036
Author(s):  
Olivier Bauchau ◽  
Valentin Sonneville
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Solution Process ◽  
Flexible Multibody Systems ◽  
Governing Equations ◽  
Euclidean Group ◽  
Shell Elements ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Plates And Shells

This paper presents a finite element implementation of plates and shells for the analysis of flexible multibody systems. The developments are set within the framework of the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) couples their displacement and rotation components by recognizing that configuration and motion are members of the Special Euclidean group, and (3) resolves all tensors components in local frames. The formulation based on the motion formalism (1) provides a theoretical framework that streamlines the formulation of shell elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, (4) circumvents the shear locking phenomenon that plagues shell formulations based on classical kinematic descriptions, and (5) prevents the occurrence of singularities in the treatment of finite rotation. Numerical examples are presented to illustrate the advantageous features of the proposed formulation.

The Motion Formalism for Flexible Multibody Systems

2021 ◽  
Author(s):  
Olivier Bauchau ◽  
Valentin Sonneville
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Solution Process ◽  
Flexible Multibody Systems ◽  
Structural Elements ◽  
Governing Equations ◽  
Euclidean Group ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Element Approach

Abstract This paper describes a finite element approach to the analysis of flexible multibody systems. It is based on the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) recognizes that these are members of the Special Euclidean group thereby coupling their displacement and rotation components, and (3) resolves all tensors components in local frames. The goal of this review paper is not to provide an in-depth derivation of all the elements found in typical multibody codes but rather to demonstrate how the motion formalism (1) provides a theoretical framework that unifies the formulation of all structural elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, and (4) prevents the occurrence of singularities.

A Global Simulation Method for Flexible Multibody Systems With Variable Topology Structures

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Wenhao Guo ◽  
Tianshu Wang
Keyword(s):  
Multibody Systems ◽  
Simulation Method ◽  
Flexible Multibody Systems ◽  
Governing Equations ◽  
Recursive Formulation ◽  
Global Simulation ◽  
Constraint Equations ◽  
Flexible Multibody ◽  
The Impact ◽  
Velocity Level

By means of a recursive formulation method, a generalized impulse–momentum-balance method, and a constraint violation elimination (CVE) method, we propose a new global simulation method for flexible multibody systems with kinematic structure changes. The constraint equations of a pair of adjacent bodies, considering body flexibility in Cartesian space, are derived for a recursive formulation. Constraint equations in configuration space, which are obtained from the constraints presented in this paper via recursive formulation, are very useful for modeling different kinematic structures and impacting governing equations. The novelty is that the impact governing equations, which calculate the jumps of generalized velocities, are modified by taking velocity-level CVE into consideration. Numerical examples are given to validate the presented method. Simulation results show that the new method can effectively suppress constraint drifts at the velocity level and stabilize constraint violations at the position level.

Semi-Symbolical Equations of Motion for Flexible Multibody Systems

1993 ◽  
Author(s):  
Frank Melzer
Keyword(s):  
Data Model ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
General Purpose ◽  
Flexible Multibody Systems ◽  
Dynamical Analysis ◽  
Lightweight Structures ◽  
Elastic Bodies ◽  
Flexible Multibody ◽  
Increasing Demand

Abstract The need for computer aided engineering in the analysis of machines and mechanisms led to a wide variety of general purpose programs for the dynamical analysis of multibody systems. In the past few years the incorporation of flexible bodies in this methodology has evolved to one of the major research topics in the field of multibody dynamics, due to the use of more lightweight structures and an increasing demand for high-precision mechanisms such as robots. This paper presents a formalism for flexible multibody systems based on a minimum set of generalized coordinates and symbolic computation. A standardized object-oriented data model is used for the system matrices, describing the elastodynamic behaviour of the flexible body. Consequently, the equations of motion are derived in a form independent of the chosen modelling technique for the elastic bodies.

Flexible Multibody Systems With Large Deformations Using Absolute Nodal Coordinates for Isoparametric Solid Brick Elements

2003 ◽  
Author(s):  
Lars Ku¨bler ◽  
Peter Eberhard ◽  
Johannes Geisler
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Large Deformations ◽  
Flexible Multibody Systems ◽  
Body Motion ◽  
Absolute Nodal Coordinates ◽  
Shell Elements ◽  
Flexible Multibody ◽  
Absolute Coordinates ◽  
Solid Bodies

In this paper a formulation for flexible Multibody Systems (MBS) is proposed where flexible bodies are described using absolute coordinates for isoparametric brick elements. The use of absolute coordinates allows for large deformations and provides an accurate description of rigid body motion and inertia in the case of large rotations without additional considerations. Further, constant mass matrices are obtained for isoparametric elements. Brick elements are important, e. g. if general solid bodies with low stiffness, i. e. not negligible large deformations, are part of the MBS and cannot be modeled using beam, plate, or shell elements. Since only nodal translational degrees of freedom are used for brick elements additional questions arise. For example, imposing joint constraints for relative rotations between two bodies requires a nodal reference frame at connection points. An approach is proposed to define such a reference system utilizing displacement information of three finite element nodes.

On the Use of Virtual Work in a Graph-Theoretic Formulation for Multibody Dynamics

1997 ◽  
Author(s):  
Pengfei Shi ◽  
John McPhee
Keyword(s):  
Multibody Systems ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Theoretic Approach ◽  
Computer Implementation ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Flexible Multibody ◽  
New Formulation

Abstract In this paper, graph-theoretic and virtual work methods are combined in a new formulation of the equations of motion for rigid and flexible multibody systems. In addition to extending the theory for existing graph-theoretic approaches, this new formulation offers two distinct improvements. First, the set of differential-algebraic dynamic equations are smaller in number than those obtained using conventional formulations. Secondly, the equations of motion for rigid and flexible multibody systems can be generated using a consistent graph-theoretic approach, thereby leading to an efficient and modular computer implementation.

Sensivity Analysis of Flexible Multibody Systems

2005 ◽  
Author(s):  
M. A. Neto ◽  
R. P. Leal ◽  
J. Ambro´sio
Keyword(s):  
Multibody Systems ◽  
Automatic Differentiation ◽  
Direct Method ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Element Analysis ◽  
Design Variables ◽  
Finite Differences Method ◽  
Flexible Multibody ◽  
Analytical Sensitivities

In this work a general formulation for the computation of the first order analytical sensitivities based on the direct method is presented. The direct method for sensitivity calculation is obtained by differentiating the equations that define the response of the flexible system with respect to the design variables. The design variables used here are the ply orientations of the laminated. The analytical sensitivities are compared with the numerical results obtained by using the finite differences method. For the beam composite material elements, the section properties and their sensitivities are found using an asymptotic procedure that involves a two-dimensional finite element analysis of their cross-section. The equations of the sensitivities are obtained by automatic differentiation and integrated in time simultaneously with the equations of motion of the multibody systems. The equations of motion and sensitivities of the flexible multibody system are solved and the accelerations and velocities and sensitivities of accelerations and velocities are integrated. Through the application of the methodology to a single flexible multibody systems the difficulties and benefices of the procedure are discussed.

Logarithmic Complexity Sensitivity Analysis of Flexible Multibody Systems

2009 ◽  
Author(s):  
Kishor D. Bhalerao ◽  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Sensitivity Analysis ◽  
Data Storage ◽  
Multibody Systems ◽  
Parallel Implementation ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Divide And Conquer ◽  
Dynamics Simulation ◽  
Modal Shape ◽  
Flexible Multibody

This paper presents a recursive direct differentiation method for sensitivity analysis of flexible multibody systems. Large rotations and translations in the system are modeled as rigid body degrees of freedom while the deformation field within each body is approximated by superposition of modal shape functions. The equations of motion for the flexible members are differentiated at body level and the sensitivity information is generated via a recursive divide and conquer scheme. The number of differentiations required in this method is minimal. The method works concurrently with the forward dynamics simulation of the system and requires minimum data storage. The use of divide and conquer framework makes the method linear and logarithmic in complexity for serial and parallel implementation, respectively, and ideally suited for general topologies. The method is applied to a flexible two arm robotic manipulator to calculate sensitivity information and the results are compared with the finite difference approach.

Aspects of Symbolic Formulations in Flexible Multibody Systems

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Markus Burkhardt ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Fem Model ◽  
Local Shape ◽  
Flexible Bodies ◽  
Elastic Bodies ◽  
Flexible Multibody

The symbolic modeling of flexible multibody systems is a challenging task. This is especially the case for complex-shaped elastic bodies, which are described by a numerical model, e.g., an FEM model. The kinematic and dynamic properties of the flexible body are in this case numerical and the elastic deformations are described with a certain number of local shape functions, which results in a large amount of data that have to be handled. Both attributes do not suggest the usage of symbolic tools to model a flexible multibody system. Nevertheless, there are several symbolic multibody codes that can treat flexible multibody systems in a very efficient way. In this paper, we present some of the modifications of the symbolic research code Neweul-M2 which are needed to support flexible bodies. On the basis of these modifications, the mentioned restrictions due to the numerical flexible bodies can be eliminated. Furthermore, it is possible to re-establish the symbolic character of the created equations of motion even in the presence of these solely numerical flexible bodies.

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