Assembly of Finite‐Element Helicopter Subsystems with Large Relative Rotations

1990 ◽  
Vol 35 (2) ◽  
pp. 60-68
Author(s):  
Jon‐Shen Fuh ◽  
Brahmananda Panda ◽  
David A. Peters
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Large Angle ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Large Rotations ◽  
Finite Element Procedure ◽  
Moving Coordinate ◽  
Rigid Body Motions ◽  
Small Rotation

A general finite‐element procedure is presented for modeling rotorcraft undergoing elastic deformations in addition to large rigid body motions with respect to inertial space. Special attention is given to the coupling of the rotor and fuselage subsystems subject to large relative rotations. Initially, the rotor and fuselage subsystems are assembled separately as small‐rotation finite‐element models in a moving coordinate system. In order to handle large rigid body rotations, the coordinate systems are tied to the structure using one of several alternate constraint methods. Finally, the equations which allow large rotations are constrained together using a rotating to nonrotating transformation which allows rotor azimuth angle as a degree of freedom. The resulting system of equations, which has not been implemented, is applicable to both helicopter trim and large angle maneuver analyses.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

The Use of Vector Techniques in Variational Problems

1986 ◽  
Vol 108 (2) ◽  
pp. 141-145 ◽  
Author(s):  
L. J. Everett ◽  
M. McDermott
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Double Pendulum ◽  
Coordinate Transformations ◽  
Elastic Deformations ◽  
Variational Techniques ◽  
Convenient Means ◽  
Moving Coordinate ◽  
Rigid Body Motions

A convenient means for applying vector mathematics to variational problems is presented. The total and relative variations of a vector are defined and results which follow from these definitions are developed and proved. These results are then used to express the variation of a functional using vector techniques rather than the classical scalar or matrix techniques. The simple problems of deriving equations of motion for a rigid body and for a rigid double pendulum are presented as examples of the technique. The key advantages of the method are that (1) it allows the investigator who is familiar and proficient with vector techniques to apply these skills to variational problems and (2) it greatly simplifies the application of variational techniques to problems which include both rigid body motions and elastic deformations. This is accomplished by providing the techniques necessary for computing the variation of a vector defined in a moving coordinate system without using coordinate transformations.

Analysis of the Horizontal to Vertical Orientation of Deep Water Risers

1981 ◽  
Vol 103 (1) ◽  
pp. 106-108
Author(s):  
A. J. Healey ◽  
A. Flores
Keyword(s):  
Finite Element ◽  
Large Angle ◽  
Vertical Position ◽  
Transfer Matrices ◽  
Euler Beam ◽  
Vertical Orientation ◽  
Riser Pipe ◽  
State Transfer ◽  
Critical Phase ◽  
Finite Element Procedure

This paper presents an analysis of the problem of reorientation of a riser pipe from an initially horizontal configuration during subsurface tow to the vertical position for installation. Front and rear barges support the pipe through cables. The orientation into a vertical configuration is accomplished by paying out the front cable. The pipe is treated as a Bernoulli-Euler beam with significant tension undergoing large angle deflections. A finite element procedure used state transfer matrices and successive linearization and the results show that the stress critical phase occurs when the pipe is going through the 60-deg angle to the horizontal direction.

Absolute Nodal Coordinate Formulation

1997 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Hussien A. Hussien ◽  
José L. Escalona
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Rigid Bodies ◽  
Rotation Vector ◽  
Finite Rotations ◽  
Large Rotation ◽  
Finite Element Procedure ◽  
Floating Frame ◽  
Inertia Forces ◽  
Body Inertia

Abstract There are three basic finite element formulations, which are used in multibody dynamics. These are the floating frame reference approach, the incremental method and the large rotation vector approach. In the floating frame of reference and incremental formulations, the slopes are assumed small in order to define infinitesimal rotations that can be treated and transformed as vectors. This description, however, limits the use of some important elements such as beams and plates in a wide range of large displacement applications. As demonstrated in some recent publications, if infinitesimal rotations are used as nodal coordinates, the use of the finite element incremental formulation in the large reference displacement analysis does not lead to exact modeling of the rigid body inertia when the structures rotate as rigid bodies. In this paper, a new and simple finite element procedure that employs the mathematical definition of the slope and uses it to define the element coordinates instead of the infinitesimal and finite rotations is developed for large rotation and deformation problems. By using this description and by defining the element coordinates in the global system, not only the need for performing coordinate transformation is avoided, but also a simple expression for the inertia forces is obtained. Furthermore, the resulting mass matrix is constant and it is the same matrix that appears in linear structural dynamics. It is demonstrated in this paper, that this coordinate description leads to exact modeling of the rigid body inertia when the structure rotate as rigid bodies. Nonetheless, the stiffness matrix becomes nonlinear function of time even in the case of small displacements. The method presented in this paper differs from previous large rotation vector formulations in the sense that the inertia forces, the kinetic energy, and the strain energy are not expressed in terms of any orientation coordinates, and therefore, the method does not require interpolation of finite rotations. While the use of the formulation is demonstrated using a simple planar beam element, the generalization of the method to other element types and to the three dimensional case is straightforward. Using the finite element procedure presented in this paper, beams and plates can be treated as isoparametric elements.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems (CS) used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

scholarly journals Geometric Interpretation of a Non-Linear Beam Finite Element on The Lie Group SE(3)

2014 ◽  
Vol 61 (2) ◽  
pp. 305-329 ◽  
Author(s):  
Valentin Sonneville ◽  
Alberto Cardona ◽  
Olivier Brüls
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Lie Group ◽  
Geometric Interpretation ◽  
Invariance Property ◽  
Exponential Map ◽  
Element Formulation ◽  
Equilibrium Equations ◽  
Geometrically Exact Beam ◽  
Rigid Body Motions

Abstract Recently, the authors proposed a geometrically exact beam finite element formulation on the Lie group SE(3). Some important numerical and theoretical aspects leading to a computationally efficient strategy were obtained. For instance, the formulation leads to invariant equilibrium equations under rigid body motions and a locking free element. In this paper we discuss some important aspects of this formulation. The invariance property of the equilibrium equations under rigid body motions is discussed and brought out in simple analytical examples. The discretization method based on the exponential map is recalled and a geometric interpretation is given. Special attention is also dedicated to the consistent interpolation of the velocities.

Application of the Absolute Nodal Coordinate Formulation to Large Rotation and Large Deformation Problems

1998 ◽  
Vol 120 (2) ◽  
pp. 188-195 ◽  
Author(s):  
A. A. Shabana ◽  
H. A. Hussien ◽  
J. L. Escalona
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Rigid Bodies ◽  
Frame Of Reference ◽  
Finite Rotations ◽  
Large Rotation ◽  
Finite Element Procedure ◽  
Floating Frame ◽  
Inertia Forces ◽  
Body Inertia

There are three basic finite element formulations which are used in multibody dynamics. These are the floating frame of reference approach, the incremental method and the large rotation vector approach. In the floating frame of reference and incremental formulations, the slopes are assumed small in order to define infinitesimal rotations that can be treated and transformed as vectors. This description, however, limits the use of some important elements such as beams and plates in a wide range of large displacement applications. As demonstrated in some recent publications, if infinitesimal rotations are used as nodal coordinates, the use of the finite element incremental formulation in the large reference displacement analysis does not lead to exact modeling of the rigid body inertia when the structures rotate as rigid bodies. In this paper, a simple non-incremental finite element procedure that employs the mathematical definition of the slope and uses it to define the element coordinates instead of the infinitesimal and finite rotations is developed for large rotation and deformation problems. By using this description and by defining the element coordinates in the global system, not only the need for performing coordinate transformation is avoided, but also a simple expression for the inertia forces is obtained. The resulting mass matrix is constant and it is the same matrix that appears in linear structural dynamics. It is demonstrated in this paper that this coordinate description leads to exact modeling of the rigid body inertia when the structures rotate as rigid bodies. Nonetheless, the stiffness matrix becomes nonlinear function even in the case of small displacements. The method presented in this paper differs from previous large rotation vector formulations in the sense that the inertia forces, the kinetic energy, and the strain energy are not expressed in terms of any orientation coordinates, and therefore, the method does not require interpolation of finite rotations. While the use of the formulation is demonstrated using a simple planar beam element, the generalization of the method to other element types and to the three dimensional case is straightforward. Using the finite element procedure presented in this paper, beams and plates can be treated as isoparametric elements.

Sign in / Sign up

Export Citation Format

Share Document