Bài toán biến dạng đàn hồi cho cánh máy bay với sự biến đổi của vận tốc và góc tới

Journal ofScience & Technology 100 (2014) 020-025

Problem of Elastic Deformation for Aircraft Wings with the Variation

of Velocity and Incidence Angle

Hoang ThiBich Ngoc^*, Dinh Van Phong', Nguyen JManh Hung', Nguyen Hong Son''^ ' 'Hanoi Umversity ofScience and Technology, No. I, Dai Co Viel Str.. Hai Ba Trung, Ha Noi, Viet Nam

-Hanoi University of Industry I

Received: Februaiy 28, 2014; accepted: April 22. 2014

Abstract |

The structure of aircraft wing is a closed tube affected by aerodynamic forces. Aerodynamic forces

distnbuted on the upper side and lower side of wing are determined by a 3D numerical method which are

external forces and considered as known input parameters. The problem of elastic deformation for the

wing is solved with a 3D degenerate model, discretized and approximated by finite element method. The

built program allows calculating and determining the location and value of the most dangerous stress on

the wings which depends on the value and direction of the free flow velocity with a certain structure of

wing, from that it allows determining the limit of elastic deformation for wings depending on the velocity anil

the incidence angle of the free flow.

Keywords; 3D wing, Numerical methods, Aerodynamic forces, Elastic deformahon.

1. Introduction

The structure of aircraft wing has the shape of

aerodynamic profile followed the velocity direction

and it is a closed tube, so the shell thickness is very

small compared lo the rest of the field size. This is the

basis for the choice of degenerate 3D models in

structural calculations. Aerodynamic load on the

wing is very large, larger than the weight of the entire

aircraft. Aerodynamic load distnbution is caused by

the pressure difference between the upper side and

the lower side of wing. With a defined structure,

distributed load varies due to the velocity and the

direction of motion (angle of incidence). If

aerodynamic problem allows us to identify three￾dimensional load distribution on the wing, the elastic

deformation problem will facilitate the development

of the model on the three-dimensional structure. In

the limited framework of this article, only the method

solving the elastic deformation of the wing is

introduced. Details of the method determining the 3D

aerodynamic forces are refened to [1]. Results of

aerodynamic pressure distribution on the wing are

extemal force given to solve elastic deformation.

Results of elastic deformation problems are worked

on analysis of aspects related to limitation of elastic

deformation of the wing,

2. Method of Calculation

2.1. Calculation of aerodynamic forces

The determination of the forces on the 3D

aerodynamic profile wing considering the thickness

of wing and length of the finite wing span needed to

be done by a numerical method to determine the

pressure distribution on the upper side and the lower

side of each specific field. Hereby, calculations are

carried by the combined doublet and source

singularity distiibution method (Fig, 1),

Fig. 1. For determining aerodynamic forces on 3D

wing by using doublet - source singularities

Velocity potentials at a point P(x,y,z) induced

from sources of constant strength O and doublets of

constant strength |J ananged on the discrete

elements of the upper side and the lower side are as

followed;

dS (Ps{x,y,z)^-—\ 4.T J {^(x-x,f+(y-y^y+z'

zdS

'\^{x-x,)-+{y-y^)'+z'T

(1) The velocity components (u,v,w) at a pomt are

determined from the derivatives of velocity f

• Corresponding author: Tel: (+S4) 912.313 350

Email: [email protected] '"'-'<f'|-f)