Question :

Determine the deflections and stresses in a loaded Pilatus PC/9 wing using finite element computational modelling. The aircraft wing can be simplified using appropriate beam-plate representations. You must decide how to represent the wing to provide meaningful results. This is a major focus of the assignment and much detail and explanation is expected for all choices in your numerical calculations.

1. Introduction

Wing is the most important component of aircraft design because the wings are the main surfaces that support the aircraft by lifting in flight. Therefore, It has to be used the components that have high strength and stiffness at the wing structure of the airplane. PC-9 is a single-engine, low-wing dual-seat turboprop training aircraft. Pilatus PC-9/A is two-seat turboprop aircraft as principal basic training aircraft of the Australian Defence Force. The PC-9 is best known to the public as the aircraft flown by the Air Force Roulettes in aerobatic displays at major events throughout Australia. Figure 1, Figure 2 and Figure 3 shows the global structure and section dimensions of the Pilatus PC-9 Aircraft wing, respectively. (To see the Figures, Download Full Sample )

In order to analyze the behavior of the wing, an experimental study was conducted. The experimental setup consists of a purpose built test rig for the Pilatus PC-9 wing, as illustrated in Figure 4. Two hydraulic actuators (equipped with a load cell), located at 2/3 span, was used to apply displacement while the wing root is clamped to the test bench, as shown in Figure 4. Strain gauges were used to record the applied strain at the root of the wing. But manufacturing the product for experiment costs great times, cares and materials.

In order to reduce such cost, numerical simulation methods have appeared. Among them, the most representative method is FEM. Finite element method (FEM) is very powerful numerical calculation method for design and numerical analysis of engineering structures as well as simulation of natural phenomena. It was developed many commercial software packages based on finite element method such as ABAQUS, ANSYS and ADINA etc before a few decade and at recent years, they are being used successfully at design and strength estimation of very complex structures such as aircraft wing at aerospace industries. Computer aided engineering analysis based on the finite element scheme is recognized to be a great effective numerical simulation and optimization technique in the field of aircraft design. It has important guiding significance and engineering value that can advance product qualities and performance, decrease production costs; shorten design cycle, and so on. FE modeling is data pre-processing for FE analysis. The calculation correctness of the FE method depends on the level of approximation of physical characteristics of the model and its real structure. Therefore, establishing a correct and suitable FE model is the most important issue to perform finite element numerical simulation and optimization.

In three-dimensional finite element analysis of the structures such as the aircraft wing, the main key for the simplification of computational model is to apply the surface-to-surface restraint suitable for the contact pairs of three-dimensional shell element. ABAQUS provides some methods in order to restraint three-dimensional shell-to-shell and shell-to-beam elements.

• Tie restraint formulation based on surface Abaqus uses the below criteria to determine which slave nodes will be tied to the master surface. Abaqus then forms restraints between these slave nodes and the nodes on the master surface. Abaqus use surface-to-surface method and node-to-surface method to generate the coefficients.

When analysis process performed using Abaqus/Standard product is imported into Abaqus/Explicit product, the tie restraints are not imported and need to be redefined. If the imported analysis is a continuation of the initial analysis significantly, it is an important problem that tie restraints has to be as similar as possible. Then, it needs to be used the similar restraint type necessarily. If in the original Abaqus/Standard analysis, the initial method was used, the surface-to-surface method should be specified in the Abaqus/Explicit analysis. Similarly to above, if in the original Abaqus/Explicit analysis the initial method was used, node-to-surface method should be specified in Abaqus/Standard analysis. The numerical noise for tied interfaces involving mismatched meshes are minimized the surface-to-surface method. The surface-to-surface method enforces restraints in an average sense over a certain region unlike in the original node-to-surface method, other while it enforces restraints at discrete points.

In Abaqus/Standard, the surface-to-surface method is used by origin with exceptions noted below, and it is optional in Abaqus/Explicit. The cost of the surface-to-surface method can be quite important for the case of infinite acoustic elements tied to shell elements in Abaqus/Standard and therefore, in this case the node-to-surface method is used by original.

The surface-to-surface method ordinarily includes more master nodes rather than the node-to-surface method per restraint. It tends to increase the solver bandwidth in Abaqus/Standard and, therefore, can increase response cost. The extra cost is fairly small in most applications but can become important in some cases. In the following parameters, it really can lead to the surface-to-surface method:

• A great fraction of tied nodes (DOF) in the model
• The master surface being more refined than slave surface
• Multiple layers of tied shells, such that the master surface of one tie restraint acts as the slave surface of other tie restraint

It is sited the coefficient equal to interpolation functions at that point where the slave node projects onto that master surface in the original node-to-surface method, which is used by original in Abaqus/Explicit and optional in Abaqus/Standard. This method is more effective anywhere for complex surfaces.