Absolute Nodal Coordinate Formulation With Vector-Strain Transformation for High Aspect Ratio Wings

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Keisuke Otsuka ◽  
Yinan Wang ◽  
Kanjuro Makihara
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Degrees Of Freedom ◽  
Absolute Nodal Coordinate Formulation ◽  
Lattice Method ◽  
Absolute Nodal Coordinate ◽  
Aeroelastic Analysis ◽  
Strain Transformation ◽  
Highly Nonlinear ◽  
Analytical Approaches

Abstract High aspect ratio wings are potential candidates for use in atmospheric satellites and civil aircraft as they exhibit a low induced drag, which can reduce the fuel consumption. Owing to their slender and light weight configuration, such wings undergo highly flexible aeroelastic static and dynamic deformations that cannot be analyzed using conventional linear analysis methods. An aeroelastic analysis framework based on the absolute nodal coordinate formulation (ANCF) can be used to analyze the static and dynamic deformations of high aspect ratio wings. However, owing to the highly nonlinear elastic force, the statically deformed wing shape during steady flight cannot be efficiently obtained via static analyses. Therefore, an ANCF with a vector-strain transformation (ANCF-VST) was proposed in this work. Considering the slender geometry of high aspect ratio wings, the nodal vectors of an ANCF beam element were transformed to the strains. In this manner, a constant stiffness matrix and reduced degrees-of-freedom could be generated while capturing the highly flexible deformations accurately. The ANCF-VST exhibited superior convergence performance and accuracy compared to those of analytical approaches and other nonlinear beam formulations. Moreover, an aeroelastic analysis flow coupling the ANCF-VST and an aerodynamic model based on the unsteady vortex lattice method was proposed to perform the static and dynamic analyses successively. The proposed and existing aeroelastic frameworks exhibited a good agreement in the analyses, which demonstrated the feasibility of employing the proposed framework to analyze high aspect ratio wings.

Absolute Nodal Coordinate Formulations for Aeroelastic Analysis of Next-Generation Aircraft Wings

2021 ◽  
Author(s):  
Keisuke Otsuka ◽  
Shuonan Dong ◽  
Kanjuro Makihara
Keyword(s):  
Flexible Structures ◽  
Beam Model ◽  
Next Generation ◽  
Lattice Method ◽  
Absolute Nodal Coordinate ◽  
Aircraft Wings ◽  
Induced Drag ◽  
Aerodynamic Model ◽  
Aeroelastic Analysis ◽  
Convergence Performance

Abstract Future aircraft have a high aspect ratio wing (HARW). The low induced drag of the wing can reduce fuel consumption, which enables eco-friendly flight. HARW cannot be designed by using conventional linear aeroelastic analysis methods because it undergoes very flexible motion. Although absolute nodal coordinate formulations (ANCF) have been widely used for analyzing various flexible structures, their application to HAWR is limited because the derivation of the ANCF elastic force for wing cross section is difficult. In this paper, we first describe three ANCF-based beam models that address the difficulty. The three models have different characteristics. Second, an aeroelastic coupling between the beam models and a medium-fidelity aerodynamic model based on unsteady vortex lattice method (UVLM) is briefly explained. Especially, the advantage of ANCF in the aeroelastic coupling is emphasized. Finally, we newly compare the three ANCF-based models in structural and aeroelastic analyses. From the viewpoint of the convergence performance and calculation time, we found the best ANCF-based beam model among the three models in static structural and aeroelastic analyses, while the three models have comparable performances in dynamic structural and aeroelastic analyses. These findings contribute to the development of aeroelastic analysis framework based on ANCF and the design of next-generation aircraft wings.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Test Problems ◽  
Absolute Nodal Coordinate ◽  
Highly Nonlinear ◽  
Brick Element ◽  
The Absolute

The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics.

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory

2000 ◽  
Vol 123 (4) ◽  
pp. 606-613 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Refaat Y. Yakoub
Keyword(s):  
Coordinate System ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Local Coordinate System ◽  
Three Dimensional ◽  
Deformation Analysis ◽  
Large Element ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Highly Nonlinear

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.

Buckling analysis of beam structure with absolute nodal coordinate formulation

2020 ◽  
pp. 095440622094711
Author(s):  
Jia Wang ◽  
Tengfei Wang
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Nonlinear Function ◽  
Shear Stiffness ◽  
Buckling Analysis ◽  
Absolute Nodal Coordinate ◽  
Tangent Stiffness Matrix ◽  
Beam Elements ◽  
Highly Nonlinear ◽  
Analysis Scheme ◽  
Nodal Coordinates

Absolute nodal coordinate formulation (ANCF) was applied to the buckling analysis. A delicate analysis scheme based on dichotomy method was proposed to solve the buckling problem with beam elements whose tangent stiffness matrix is a highly nonlinear function of nodal coordinates. Three existing planar beam elements are employed to show the application. The accuracy and capability of the ANCF beam for buckling analysis was validated with benchmark cases. Additionally, the influence of the shear effect on the buckling load is thoroughly investigated by comparing the solutions associated with different shear stiffness and slenderness.

Non-linear aeroelastic analysis in the time domain of high-aspect-ratio wings: Effect of chord and taper-ratio variation

2016 ◽  
Vol 121 (1235) ◽  
pp. 21-53 ◽  
Author(s):  
A. Suleman ◽  
F. Afonso ◽  
J. Vale ◽  
É. Oliveira ◽  
F. Lau
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Bending Moment ◽  
Equilibrium Solutions ◽  
Computational Framework ◽  
Wing Model ◽  
Aeroelastic Analysis ◽  
Non Linear ◽  
Time Marching ◽  
The Time Domain

ABSTRACTCommercial jets usually have relatively low-aspect-ratio wings, in spite of the associated benefits of increasing the wing aspect-ratio, such as higher lift-to-drag ratios and ranges. This is partially explained by the fact that the wing becomes more flexible by increasing the aspect-ratio that results in higher deflections which can cause aeroelastic instability problems such as flutter. An aeroelastic computational framework capable of evaluating the effects of geometric non-linearities on the aeroelastic performance of high-aspect-ratio wings has been developed and validated using numerical and experimental data. In this work, the aeroelastic performance of a base wing model with 20 m span and 1 m chord is analysed and the effect of changing the wing chord or the taper-ratio is determined. The non-linear static aeroelastic equilibrium solutions are compared in terms of drag polar, root bending moment and natural frequencies, and the change in the flutter speed boundary is assessed as a function of aspect-ratio using a time-marching approach.

Sign in / Sign up

Export Citation Format

Share Document