Finite Element Modeling of Multibody Systems Using Symbolic Process
| Author | : Srinivas Tummarakota |
| Publisher | : |
| Total Pages | : 124 |
| Release | : 1994 |
| Genre | : Computer simulation |
| ISBN | : |
Finite Element Modeling Of Multibody Systems Using Symbolic Process
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Symbolic Integration of Multibody System Dynamics with Finite Element Method
| 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.
Dynamics of Flexible Multibody Systems
| Author | : Edmund Wittbrodt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 229 |
| Release | : 2007-04-17 |
| Genre | : Technology & Engineering |
| ISBN | : 354032352X |
A new approach is presented in this book 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. 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.
Multiscale Multibody Dynamics
| 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.
Advanced Multibody System Dynamics
| 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.
Automation of Finite Element Methods
| 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.
Dynamics of Underactuated Multibody Systems
| Author | : Robert Seifried |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 257 |
| Release | : 2013-11-08 |
| Genre | : Technology & Engineering |
| ISBN | : 3319012282 |
Underactuated multibody systems are intriguing mechatronic systems, as they posses fewer control inputs than degrees of freedom. Some examples are modern light-weight flexible robots and articulated manipulators with passive joints. This book investigates such underactuated multibody systems from an integrated perspective. This includes all major steps from the modeling of rigid and flexible multibody systems, through nonlinear control theory, to optimal system design. The underlying theories and techniques from these different fields are presented using a self-contained and unified approach and notation system. Subsequently, the book focuses on applications to large multibody systems with multiple degrees of freedom, which require a combination of symbolical and numerical procedures. Finally, an integrated, optimization-based design procedure is proposed, whereby both structural and control design are considered concurrently. Each chapter is supplemented by illustrated examples.
Multibody Systems
| Author | : Christoph Woernle |
| Publisher | : Springer Nature |
| Total Pages | : 458 |
| Release | : |
| Genre | : |
| ISBN | : 3662672626 |
Dynamics of Flexible Multibody Systems
| Author | : American Society of Mechanical Engineers. Winter Annual Meeting |
| Publisher | : American Society of Mechanical Engineers |
| Total Pages | : 248 |
| Release | : 1992 |
| Genre | : Science |
| ISBN | : |
