Symbolic Integration Of Multibody System Dynamics With Finite Element Method
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| Author | : Yiteng Liang |
| Publisher | : |
| Total Pages | : 102 |
| Release | : 2017 |
| Genre | : Dynamics |
| ISBN | : |
A general procedure integrating the finite element method with multibody system dynamics using symbolic computation is presented. It takes advantage of both the nodal formulation and the graph-theoretical approach, so it avoids the tedious modal analysis and can automatically reduce the number of system equations. The validity and expected performance are demonstrated mathematically and philosophically, which are tested by several general examples. A flexible beam is created with a finite element formulation, which is derived according to the classical Bernoulli-Euler beam theory. A comprehensive procedure of deriving kinetic and kinematic equations for the flexible beam is provided, which starts from inspecting the diversity of shape functions to the generalization of inertia and elastic terms. The geometrical nonlinear formulation is revisited and specifically developed for the symbolic integration, and explicit expressions that are rare in existing publications for geometrical nonlinearity are derived for three-dimensional applications. A detailed process is described for the transformation of the equations of motion of the finite-element flexible beam to a form required by the graph-theoretical approach. The beam model is implemented in MapleSim (a multi-physics simulation environment based on symbolic computation and graph theory) and made compatible with other multibody components in its library. Example problems are shown to validate the functionality of the implemented model. The dynamic stiffening effect due to geometrical nonlinearity is explicitly explained with its significance especially in fast and large overall-motion problems. Comparison results also show that the nodal approach shows great potential using the symbolic computation, which runs 70% faster and is more convenient to manipulate than the modal approach. The general procedure of the finite element formulation for the flexible beam can be followed to derive proper formulations of plate and solid elements if using appropriate displacement field assumptions, and the transformation to graph-theoretical equations is also similar.
| Author | : Edmund Wittbrodt |
| Publisher | : Foundations of Engineering Mechanics |
| Total Pages | : 248 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : |
A new approach is presented for modelling multi-body systems, which constitutes a substantial enhancement of the Rigid Finite Element method. The new approach is based on homogeneous transformations and joint coordinates, and it yields the advantage that equations of motion are automatically generated for systems consisting of alternate rigid and flexible links. Apart from its simple physical interpretation and easy computer implementation, the method is also valuable for educational purposes since it impressively illustrates the impact of mechanical features on the mathematical model. This novel modelling approach is then applied to systems such as offshore-cranes and telescopic rapiers.
| Author | : Werner Schiehlen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 491 |
| Release | : 2013-04-17 |
| Genre | : Science |
| ISBN | : 9401706255 |
The German Research Council (DFG) decided 1987 to establish a nationwide five year research project devoted to dynamics of multibody systems. In this project universities and research centers cooperated with the goal to develop a general pur pose multibody system software package. This concept provides the opportunity to use a modular structure of the software, i.e. different multibody formalisms may be combined with different simulation programmes via standardized interfaces. For the DFG project the database RSYST was chosen using standard FORTRAN 77 and an object oriented multibody system datamodel was defined. The project included • research on the fundamentals of the method of multibody systems, • concepts for new formalisms of dynamical analysis, • development of efficient numerical algorithms and • realization of a powerful software package of multibody systems. These goals required an interdisciplinary cooperation between mathematics, compu ter science, mechanics, and control theory. ix X After a rigorous reviewing process the following research institutions participated in the project (under the responsibility of leading scientists): Technical University of Aachen (Prof. G. Sedlacek) Technical University of Darmstadt (Prof. P. Hagedorn) University of Duisburg M. Hiller) (Prof.
| Author | : Ahmed A. Shabana |
| Publisher | : Cambridge University Press |
| Total Pages | : 425 |
| Release | : 2020-03-05 |
| Genre | : Science |
| ISBN | : 1108485642 |
"The primary purpose of this book is to develop methods for the dynamic analysis of multibody systems (MBS) that consist of interconnected rigid and deformable components. In that sense, the objective may be considered as a generalization of methods of structural and rigid body analysis. Many mechanical and structural systems such as vehicles, space structures, robotics, mechanisms, and aircraft consist of interconnected components that undergo large translational and rotational displacements. Figure 1.1 shows examples of such systems that can be modeled as multibody systems. In general, a multibody system is defined to be a collection of subsystems called bodies, components, or substructures. The motion of the subsystems is kinematically constrained because of different types of joints, and each subsystem or component may undergo large translations and rotational displacements"--
| Author | : Jielong Wang |
| Publisher | : Springer Nature |
| Total Pages | : 367 |
| Release | : 2023-03-24 |
| Genre | : Technology & Engineering |
| ISBN | : 9811984417 |
This book presents a novel theory of multibody dynamics with distinct features, including unified continuum theory, multiscale modeling technology of multibody system, and motion formalism implementation. All these features together with the introductions of fundamental concepts of vector, dual vector, tensor, dual tensor, recursive descriptions of joints, and the higher-order implicit solvers formulate the scope of the book’s content. In this book, a multibody system is defined as a set consisted of flexible and rigid bodies which are connected by any kinds of joints or constraints to achieve the desired motion. Generally, the motion of multibody system includes the translation and rotation; it is more efficient to describe the motion by using the dual vector or dual tensor directly instead of defining two types of variables, the translation and rotation separately. Furthermore, this book addresses the detail of motion formalism and its finite element implementation of the solid, shell-like, and beam-like structures. It also introduces the fundamental concepts of mechanics, such as the definition of vector, dual vector, tensor, and dual tensor, briefly. Without following the Einstein summation convention, the first- and second-order tensor operations in this book are depicted by linear algebraic operation symbols of row array, column array, and two-dimensional matrix, making these operations easier to understand. In addition, for the integral of governing equations of motion, a set of ordinary differential equations for the finite element-based discrete system, the book discussed the implementation of implicit solvers in detail and introduced the well-developed RADAU IIA algorithms based on post-error estimation to make the contents of the book complete. The intended readers of this book are senior engineers and graduate students in related engineering fields.
| Author | : Ahmed Shabana |
| Publisher | : Springer Nature |
| Total Pages | : 409 |
| Release | : 2019-10-02 |
| Genre | : Technology & Engineering |
| ISBN | : 3030043487 |
This revised, updated textbook adds new focus on computational methods and the importance of vibration theory in computer-aided engineering to fundamental aspects of vibration of discrete and continuous systems covered in the previous two editions of Vibration of Discrete and Continuous Systems. Building on the book’s emphasis on the theory of vibration of mechanical, structural, and aerospace systems, the author’s modifications, including discussion of the sub-structuring and finite element formulations, complete the coverage of topics required for a contemporary, second course following Vibration Theory. The textbook is appropriate for both upper-level undergraduate and graduate courses.
| Author | : Jože Korelc |
| Publisher | : Springer |
| Total Pages | : 367 |
| Release | : 2016-06-08 |
| Genre | : Technology & Engineering |
| ISBN | : 3319390058 |
New finite elements are needed as well in research as in industry environments for thedevelopment of virtual prediction techniques. The design and implementation of novel finiteelements for specific purposes is a tedious and time consuming task, especially for nonlinearformulations. The automation of this process can help to speed up this processconsiderably since the generation of the final computer code can be accelerated by order ofseveral magnitudes.This book provides the reader with the required knowledge needed to employ modernautomatic tools like AceGen within solid mechanics in a successful way. It covers the rangefrom the theoretical background, algorithmic treatments to many different applications. Thebook is written for advanced students in the engineering field and for researchers ineducational and industrial environments.
| Author | : Volodymyr Tonkonogyi |
| Publisher | : Springer Nature |
| Total Pages | : 643 |
| Release | : 2020-03-27 |
| Genre | : Technology & Engineering |
| ISBN | : 3030407241 |
This book offers a timely yet comprehensive snapshot of innovative research and developments in the area of manufacturing. It covers a wide range of manufacturing processes, such as cutting, coatings, and grinding, highlighting the advantages provided by the use of new materials and composites, as well as new methods and technologies. It discusses topics in energy generation and pollution prevention. It shows how computational methods and mathematical models have been applied to solve a number of issues in both theoretical and applied research. Based on selected papers presented at the Grabchenko’s International Conference on Advanced Manufacturing Processes (InterPartner-2019), held in Odessa, Ukraine on September 10-13, 2019, this book offers a timely overview and extensive information on trends and technologies in the area of manufacturing, mechanical and materials engineering. It is also intended to facilitate communication and collaboration between different groups working on similar topics, and to offer a bridge between academic and industrial researchers.
| Author | : J-C. Samin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 478 |
| Release | : 2013-06-29 |
| Genre | : Technology & Engineering |
| ISBN | : 940170287X |
Modeling and analysing multibody systems require a comprehensive understanding of the kinematics and dynamics of rigid bodies. In this volume, the relevant fundamental principles are first reviewed in detail and illustrated in conformity with the multibody formalisms that follow. Whatever the kind of system (tree-like structures, closed-loop mechanisms, systems containing flexible beams or involving tire/ground contact, wheel/rail contact, etc), these multibody formalisms have a common feature in the proposed approach, viz, the symbolic generation of most of the ingredients needed to set up the model. The symbolic approach chosen, specially dedicated to multibody systems, affords various advantages: it leads to a simplification of the theoretical formulation of models, a considerable reduction in the size of generated equations and hence in resulting computing time, and also enhanced portability of the multibody models towards other specific environments. Moreover, the generation of multibody models as symbolic toolboxes proves to be an excellent pedagogical medium in teaching mechanics.
| Author | : |
| Publisher | : |
| Total Pages | : 11 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
This project deals with the new and challenging problem of implementing large deformation finite element (FE) formulations in flexible multibody system (MBS) algorithms. Successful integration of large deformation FE and MBS algorithms will lead to a new generation of simulation codes that can be used in the analysis, design and performance evaluation of mechanical and aerospace systems. Specifically, the objectives of this project are (1) Different formulations used in the dynamic modeling of flexible MBS will be reviewed and evaluated in order to identify the advantages and drawbacks of each method; (2) The constrained nonlinear equations of motion expressed in terms of different sets of coordinates that can be efficiently used to describe the dynamics of rigid, flexible, and very flexible bodies will be developed; (3) Large deformation Cholesky coordinates will be used to develop a new form of the MBS dynamic equations with optimum sparse matrix structure; (4) Quantitative and qualitative evaluation of the effect of the nonlinear dynamic coupling between the reference motion and the large deformation modes will be performed; (5) The use of the computational methodology developed in this research project in the analysis of mechanical systems will be demonstrated. This report summarizes the main accomplishments made in this research project.
