Ahmed A. Shabana

Bio: Ahmed A. Shabana is an academic researcher from University of Illinois at Chicago. The author has contributed to research in topics: Finite element method & Multibody system. The author has an hindex of 54, co-authored 387 publications receiving 13238 citations. Previous affiliations of Ahmed A. Shabana include Ain Shams University & Alexandria University.

Dynamics of multibody systems

Abstract: 1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Flexible Multibody Dynamics: Review of Past and Recent Developments

Abstract: In this paper, a review of past and recent developments in the dynamics of flexible multibody systems is presented. The objective is to review some of the basic approaches used in the computer aided kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. Among the formulations reviewed in this paper are the floating frame of reference formulation, the finite element incremental methods, large rotation vector formulations, the finite segment method, and the linear theory of elastodynamics. Linearization of the flexible multibody equations that results from the use of the incremental finite element formulations is discussed. Because of space limitations, it is impossible to list all the contributions made in this important area. The reader, however, can find more references by consulting the list of articles and books cited at the end of the paper. Furthermore, the numerical procedures used for solving the differential and algebraic equations of flexible multibody systems are not discussed in this paper since these procedures are similar to the techniques used in rigid body dynamics. More details about these numerical procedures as well as the roots and perspectives of multibody system dynamics are discussed in a companion review by Schiehlen [79]. Future research areas in flexible multibody dynamics are identified as establishing the relationship between different formulations, contact and impact dynamics, control-structure interaction, use of modal identification and experimental methods in flexible multibody simulations, application of flexible multibody techniques to computer graphics, numerical issues, and large deformation problem. Establishing the relationship between different flexible multibody formulations is an important issue since there is a need to clearly define the assumptions and approximations underlying each formulation. This will allow us to establish guidelines and criteria that define the limitations of each approach used in flexible multibody dynamics. This task can now be accomplished by using the “absolute nodal coordinate formulation” which was recently introduced for the large deformation analysis of flexible multibody systems.

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory

Abstract: The description of a beam element by only the displacement of its centerline leads to some difficulties in the representation of the torsion and shear effects. For instance such a representation does not capture the rotation of the beam as a rigid body about its own axis. This problem was circumvented in the literature by using a local coordinate system in the incremental finite element method or by using the multibody floating frame of reference formulation. The use of such a local element coordinate system leads to a highly nonlinear expression for the inertia forces as the result of the large element rotation. In this investigation, an absolute nodal coordinate formulation is presented for the large rotation and deformation analysis of three dimensional beam elements. This formulation leads to a constant mass matrix, and as a result, the vectors of the centrifugal and Coriolis forces are identically equal to zero. The formulation presented in this paper takes into account the effect of rotary inertia, torsion and shear, and ensures continuity of the slopes as well as the rotation of the beam cross section at the nodal points. Using the proposed formulation curved beams can be systematically modeled.

Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation

Abstract: The purpose of this paper is to present formulations for beam elements based on the absolute nodal co-ordinate formulation that can be effectively and efficiently used in the case of thin structural applications. The numerically stiff behaviour resulting from shear terms in existing absolute nodal co-ordinate formulation beam elements that employ the continuum mechanics approach to formulate the elastic forces and the resulting locking phenomenon make these elements less attractive for slender stiff structures. In this investigation, additional shape functions are introduced for an existing spatial absolute nodal co-ordinate formulation beam element in order to obtain higher accuracy when the continuum mechanics approach is used to formulate the elastic forces. For thin structures where bending stiffness can be important in some applications, a lower order cable element is introduced and the performance of this cable element is evaluated by comparing it with existing formulations using several examples. Cables that experience low tension or catenary systems where bending stiffness has an effect on the wave propagation are examples in which the low order cable element can be used. The cable element, which does not have torsional stiffness, can be effectively used in many problems such as in the formulation of the sliding joints in applications such as the spatial pantograph/catenary systems. The numerical study presented in this paper shows that the use of existing implicit time integration methods enables the simulation of multibody systems with a moderate number of thin and stiff finite elements in reasonable CPU time.

Dynamics of multibody systems

Abstract: 1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Vehicle Dynamics: Theory and Application

Abstract: Tire and rim fundamentals.- Forward vehicle dynamics.- Tire dynamics.- Driveline dynamics.- Applied kinematics.- Applied mechanisms.- Steering dynamics.- Suspension mechanisms.- Applied dynamics.- Vehicle planar dynamics.- vehicle roll dynamics.- Applied vibrations.- Vehicle vibrations.- suspension optimization.- Quarter car.

Dynamic 3D models with local and global deformations: deformable superquadrics

Abstract: The authors present a physically based approach to fitting complex three-dimensional shapes using a novel class of dynamic models that can deform both locally and globally. They formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline. The model's six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models. The local deformation parameters reconstruct the details of complex shapes that the global abstraction misses. The equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces. The authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational, rotational, and deformational degrees of freedom of the models. Model fitting experiments involving 2D monocular image data and 3D range data are presented. >