Strand7 Demonstration
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
Introduction Finite Element Analysis has been used in the the aerospace industry since the 1960s. 1960s. However, it is still an evolving technology and one that is not always fully fully understood. Developing valid FEA models models requires a clear understanding of the limitations of FEA and of the software being being used. It is only then that the technology can be successfully applied. This is important for all users of FEA, including aircraft designers. FEA is being used in a variety of ways to support the design of aircraft. Whether the application is a new aircraft design or a minor structural structural modification, the use of of FEA can be useful if not indispensable. indispensable. This presentation consists of a live modelling and analysis example on a composite wing box.
FEA Pipeline Traditionally, FEA has consisted of three separate and distinct steps: 1.
2. 3.
The generation of a data file comprising node coordinates, element connectivities, property information, loads and boundary conditions. The contents of the data file represent, in an approximate approximate way, the physical structure being analysed. The execution of the data file through an FEA solver, which in turn generates one or more files containing results, warnings and error messages. The post processing of these result files to interpret the structural response of the structure.
With today's modern FEA packages that are well integrated to the Windows desktop, the three steps above tend to be a more cohesive procedure, or at least different aspects of a single iterative pipeline. Analyses are typically performed in a more flexible manner, with post-processing immediately followed by modelling changes and a repeat of the loop.
Modelling With the availability of powerful, yet low cost CAD programs, complex FEA models are typically generated directly from a CAD file. This process is not without its challenges and often significant effort is spent in cleaning, repairing and defeaturing a CAD file to make it suitable for FEA meshing. The so-called 'manual meshing' approach is still a very valuable tool, however. Although not not all FEA programs offer this flexibility, being able to mix the two approaches on the same model offers significant advantages over doing just one or the other.
Model courtesy Swift Aircraft
Analysis Although linear static stress analysis is still the most common form of structural analysis undertaken, be it in civil/structural engineering, automotive engineering or aerospace engineering, the structural analyst or aircraft designer should also have access to nonlinear static and dynamic analysis (linear and nonlinear). nonlinear). In addition, the ability to perform Euler buckling analysis and inertia relief analy sis are very valuable to the aircraft designer.
Extracting Results This is a critical part of the process and involves interpreting the numerical results in a meaningful physical sense. A crucial aspect of this process is being able to detect detect invalid or meaningless results results so that the model can be corrected accordingly and re-run.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
Analysis of a Composite Wing Box There are many 3D CAD programs available for Windows. Some of these programs are very good at solids modelling, while others are very good at surface modelling. A few are good at both. For the analysis of typical aircraft structures, a good surface modeller is usually more important since aircraft structures tend to be modelled using shell and beam elements. The advantage of these elements is that they have built-in assumptions that have traditionally been used by aircraft structure designers; these include beam elements based on Engineer's Theory of Bending, and surface elements (plate/shell), based on the classical shell theory or used as shear panels. For laminated composites and sandwich panels, the classical laminate theory (CLT) is ideally suited to the shell element. On the other hand, for modelling solids, such as a crankshaft in an engine, the 3D solid 'brick' or 'tetrahedral' elements are typically used. Such meshes derive naturally from solid models whereas shell models require significant additional work to produce from solid models.
CAD File Import and Preparation The figure below shows the geometry of a basic wing box, which will be used for the modelling demonstration.
There exist a number of different CAD file formats such as IGES, SAT and STEP. Strand7 supports these three for the exchange of surface and solid information. Importing the CAD file directly into Strand7 produces the following surfaces.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
Although this is a relatively simple geometry, issues such as disconnected edges or incompatible connections may still exist. The range of geometry cleaning and repairing tools offered within Strand7 is usually sufficient to prepare the geometry for meshing. However, it is always advantageous to properly prepare the model in the CAD program. The Clean Geometry tool, is used to zip geometry edges within a specified tolerance and to delete unwanted small features. Quite often a CAD file will contain small faces that are of no consequence to an analysis, particularly a global strength analysis.
Definition of Loading Zones For this analysis, the load intensity is specified in separate zones. If the geometry has been prepared in the CAD program with the appropriate zones, then all that's required in Strand7 is to apply the load. However, if the zones are not already defined, the Strand7 geometry splitting and cutting tools can be used to produce separate, but compatible zones. Load (kPa)
D A
B
C
D
C 1
20
12
5
2
Normal
2
30
18
7.5
3
ultimate
B
Rear Spar A
Applying the load directly to the geometry is desirable since upon meshing, the elements will inherit the loading directly.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
Similarly, it is better to apply restraint (or boundary) conditions, directly to the geometry. Here the root of the wing is assigned the 'all fixed' condition, to simulate the cantilever fixity. When meshed, the nodes along the fixed edges will be interpolated with the appropriate restraints.
Meshing with Shell Elements The Strand7 automesher generates good quality meshes of predominantly quadrilateral elements. Various controls are available to adjust local and average mesh size, and transitioning rates. The mesh generated is shown below. Note that the different regions are assigned to the same groups as the original geometry.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
A view with all the attributes shown reveals the face pressure load automatically transferred to the underlaying elements. The node restraints at the root have also been interpolated and assigned to the nodes.
Node Restraints
Element pressure
Note that in situations where the load can be specified either in the form of an equation, or interpolated from a table, Strand7 offers the option of entering the load via an equation with spatial coordinates as variables. For example, to apply a span wise continuous pressure that has a quadratic distribution, we can enter an equation of the form:
Although the display of load as vectors is useful in most cases, where there are many elements competing for attention, a contour display of the applied pressure load can be more informative.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
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Software
Creation of Stringers Beam elements are the natural choice for the modelling of stiffeners such as stringers on a wing box. The Strand7 beam element offers a range of useful features such as:
standard cross-section shapes arbitrary cross-section shapes symmetric and asymmetric sections user-specified alignment of principal or local axes shear centre may be offset from the neutral axis arbitrary offset away from the nodes shear areas calculated to take into account shear deformation
Stringers overlaying plate elements are easy to generate in Strand7 by using tools such as tessellate.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
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Software
To ensure correct orientation and offset location, the Align Beam Axes and the Automatic Beam Offsets tools are used.
The final aligned and offset beam elements, rendered with geometry, are shown below.
Close-up view.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
Definition of Laminates Strand7 includes a laminates composites capability, which is based on the classical laminate theory (CLT). Laminate stacks are defined as a collection of plies. Plies are orthotropic, or quasi-isotropic thin layers. Material properties may be entered for each ply, or read from a materials database. Ply limits may also be defined, which is useful for the calculation of reserve factors to establish first-ply failure.
The stack is defined via a visual lay-up window.
At the base of the window, the equivalent engineering properties of the stack are automatically updated with every change made to the lay-up. The full stiffness matrix for the laminate is also available for inspection. Each of membrane, bending and coupling matrices are presented.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
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Software
A unique feature of the module is the calculation of the equivalent transverse shear stiffness. This is particularly important for thick laminates as it accounts for shear deformation. As a laminate is an orthotropic material in the general case, it is important that there be a common reference point between the laminate principal axes and the local axes on the plate element. In Strand7 the reference point on a plate/shell element is the local axis system (x,y). This has a default orientation, but may be rotated in the plane of the element as required.
In addition to local axis alignment, it is good practice to also align the local normals consistently. The Strand7 orientation display mode colours the plate surface according to the visible surface. Tools exist to correct the orientation to make adjacent elements consistent.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
Running the Solver For this example, a linear static analysis is executed. This determines displacements, stresses and strains assuming small (infinitesimal) displacements.
Results Extraction and Post Processing The raw solution that is generated by a finite element analysis is the vector of nodal displacements. This is the vector in the familiar matrix equation that relates stiffness, displacement and force.
From the displacement vector the element strains are determined. These are calculated from the nodal displacements in the element and the matrix of displacement derivatives for the element (the so called straindisplacement matrix). Finally element stresses, stress resultants and moments are determined by premultiplying the strain vector by the material matrix.
One should therefore always review the displacement distribution and magnitude before anything else, to ensure that the results make physical sense. ©Strand7 Pty Limited
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
Contours of fibre stress displayed directly on the beam elements representing the stringers.
Bending moment diagrams on the stringers.
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Strand7 Demonstration – Finite Element Analysis of a Wing Box Royal Aeronautical Society Light Aircraft Design Conference London 19 -Nov-2012
Str and7
®
Software
Contours of maximum ply tensile strain.
Buckling Analysis For thin shell structures such as aircraft structures, buckling can be a consideration. The linear buckling solver in Strand7 calculates the load required to buckle the structure, and the shape it will take at the onset of buckling.
Conclusion Strand7 is a general purpose FEA package for structural analysis. With its comprehensive element library, including general purpose beam and shell elements, Strand7 is ideally suited to the analysis of aircraft structures. From the modelling perspective, Strand7 offers the possibility of combining automatic and manual meshing in the same model.
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