# Static Aeroelastic Analysis

Static Aeroelastic analysis is the study of the deflection of flexible aircraft structures under aerodynamic loads, where the forces and acceleration are assumed to be independent of time.

Stability and control derivatives are available for each unique flight condition (constrained trim variables, mach number and dynamic pressure). Derivatives are printed for the rigid vehicle and for the restrained and unrestrained elastic vehicles. Additionally, Divergence Analysis can be conducted to calculate divergence dynamic pressures.

Currently, in OptiStruct, the interaction between elastic forces and aerodynamic forces can be analyzed, as part of the Static Aeroelasticity solution.

Aerodynamic forces (such as lift) can affect the deformation of the aircraft structures, and such deformation can in turn affect the aerodynamic forces, due to corresponding changes in airflow that may be caused by rigid motion and/or flexible deformation. This cyclical effect can be accounted for and analyzed using static aeroelasticity.
• Aircraft Lift

The vast majority of lift for a fixed-wing aircraft is from the wings. The horizontal stabilizer and the elevator also produce some lift, part of which is also used to maneuver the aircraft.

• Control Surfaces

Control surfaces are parts of the aircraft structure which can be used to control and maneuver the aircraft. The major flight control surfaces on typical fixed-wing aircraft are the ailerons, elevators, and rudder. Ailerons allow control over the roll of the aircraft, which allows turning the aircraft left or right, elevators control the pitch, and the rudder controls the yaw of the aircraft, which also aids in turning the aircraft left or right.

• Trim

Trimming an aircraft allows it to maintain a set attitude without any control input. Trimming can be accomplished by adjusting the aerodynamic forces and moments on an aircraft by adjusting the control surfaces. In actual aircraft, trim adjustments control the movement of trim tabs on the major control surfaces (ailerons, elevators, and rudder) which subsequently move the actual control surfaces, due to local aerodynamic effects. Once trimmed, the aircraft can hold the expected attitude, without control input (for example, manual pilot effort to hold the yoke is not required if the pitch trim is set correctly to hold the expected pitch attitude, by trimming the elevator).

• Static Aeroelastic Trim Analysis

A trim analysis determines unknown trim values for the unconstrained trim variables listed on the AESTAT entry and the control surface via AESURF entry. Any trim variables can be defined and constrained on the TRIM Bulk Data Entry. Trim variables not constrained by the TRIM Bulk Data Entry, are considered as variables in the equation of motion solution for static aeroelastic trim analysis and are determined as part of the trim solution. Additionally, aerodynamic forces and pressures on the aerodynamic elements may be obtained via the AEROF and APRES Case Control commands, respectively.

• Static Aeroelastic Divergence Analysis

Divergence can occur when deflection of lifting surfaces of an aircraft leads to additional lift, which in turn, leads to further deflection in the same direction. A divergence analysis determines divergence dynamic pressures. The lowest eigenvalue correlates with the critical divergence dynamic pressure.

## Input

To conduct an aeroelastic trim analysis, both the structural model and aerodynamic model, and the method of communication between these two models should be defined.
• Structural model

The structural model can be defined using traditional finite elements, along with their corresponding grid points. For instance, the wing of an aircraft can be modeled with 1D or 2D elements.

• Aerodynamic model

The aerodynamic model can be constructed with panels (CAERO1 entry, with corresponding PAERO1 property). The panels are divided into boxes, based on the input defined on the CAERO1 entry.

Control surfaces can be defined using the AESURF entry (along with AELIST), which reference the boxes on the panels already defined via CAERO1 entry. Any CAERO1 panel boxes which are not referenced as control surfaces are part of the non-control entities which can generate aerodynamic lift (for example, the parts of an aircraft wing not associated with control surfaces).

The AEROS Bulk Data Entry can be used to define the reference aerodynamic coordinate system.

Symmetry along the center line can be defined on the AESYMXZ and AESYMXY I/O Entries, and if such entries are not defined, then it is interpreted from the SYMXZ and SYMXY fields, respectively of the AEROS Bulk Data Entry.

• Splines

Splines are entities which connect the aerodynamic degrees of freedom with the structural degrees of freedom, via interpolation. For definition of splines, the SPLINE1 (surface spline), SPLINE2 (beam spline), and SPLINE4 (curved surface spline) Bulk Data Entries are available. Splines interpolate motion and/or forces between aerodynamic degrees of freedom and structural degrees of freedom. Splines require the input of both aerodynamic model box IDs and corresponding structural grid SETs that are to be connected.

• Static Aeroelastic Trim Analysis Input

Trim analysis determines the unknown trim variables to trim the aircraft for a particular attitude or flight loading condition. All trim variables of interest for a particular flight loading condition can be listed on the AESTAT Bulk Data Entries, and the control surfaces can be defined on the AESURF Bulk Data Entries. Apart from the unknown trim variables of interest, all other trim variables should be constrained via the TRIM Bulk/Subcase Data Entry pair. Rigid body motions that are constrained by the TRIM Bulk Data should be defined on the SUPORT Bulk Data Entry to balance the rigid body motion in those degrees of freedom. Any rigid body motion that is not defined as a trim variable should be constrained via SPC/SPC1 Bulk Data Entries.

The Mach number and the dynamic pressure should be input on the TRIM Bulk Data Entry. If a rigid trim analysis is required, this can be requested by setting the AEQR field to 0.0 on the TRIM Bulk Data Entry. The rigid trim analysis ignores the effect of structural deformation on aerodynamic loading. Links between AESTAT and AESURF entries can be defined using the AELINK entry.

The parameter PARAM, AUNITS, can be used to switch the interpreted units of acceleration on TRIM Bulk Data from units of gravity (g’s) to physical units of distance per time squared.

• Aeroelastic Divergence Analysis Input

Divergence analysis determines the divergence dynamic pressures which are the eigenvalues from a complex eigenvalue analysis. The analysis is activated by a DIVERG Subcase Entry pointing to a corresponding DIVERG Bulk Data Entry. The DIVERG Bulk Data Entry contains information regarding the number of eigenvalues to be extracted and the Mach numbers for which these eigenvalues are to be extracted. A CMETHOD Case Control Entry referencing a EIGC Bulk Data Entry should be specified to activate complex eigenvalue extraction.

• Coordinate Systems
There are two main coordinate systems of interest for the Static Aeroelastic solution. The first determines the aeroelastic reference point, and the second system accounts for the oncoming flow and sideslip. The two systems of interest are defined as:
• Body System (Aerodynamic Reference Coordinate System):

This is defined using the RCSID field on the AEROS Bulk Data Entry. The stability derivative coefficient output is transformed to the aerodynamic reference point at the origin of the Body coordinate system.

• Wind System (Wind Axes):

The wind axes are defined such that the X-axis is aligned with the flow. When the angle of attach changes, this new angle of attack direction then becomes the new X axis. Correspondingly the Z axis also changes. The Y axis remains the same. The wind system can also be affected by sideslip.

## Aeroelastic Trim Solution

Static Aeroelastic Trim capability is supported for the subsonic regime (Mach number on TRIM Bulk Data should be less than 1.0). Other aeroelasticity solution types such as flutter will be supported in future releases.

The Vortex Lattice Method (VLM) solves the aerodynamic equations for low-speed linear potential flows by distributing elementary solutions of Laplace’s equation over the boundary surface.

In a linear static subcase, the inclusion of the TRIM Subcase Entry, referring to a corresponding TRIM Bulk Data Entry activates the aeroelastic trim solution. Currently, the trim solution is supported only for Linear Static Analysis.

The AESTAT entries define trim parameters, as stated in the previous sections, and the AESURF entry defines the control surfaces. Some example trim parameters are ANGLEA, which is the angle of attack (R2) and URDD3, which is the vertical acceleration (T3). An example of a control surface is the elevator, which can be defined as ELEV on the AESURF entry.

During the aeroelastic trim solution, the unknown trim variables are calculated, and the corresponding aerodynamic forces, moments, and pressures are evaluated. The non-dimensional stability and control derivatives are also calculated for the aerodynamic model. The non-dimensional hinge moment derivative coefficients are calculated for control surfaces.

## Aeroelastic Divergence Solution

Static Aeroelastic Divergence is supported. Other aeroelasticity solution types such as flutter will be supported in future releases.

In a complex eigenvalue analysis subcase, the inclusion of the DIVERG Subcase Entry, referring to a corresponding DIVERG Bulk Data Entry activates the aeroelastic divergence solution.

## Output

• Aeroelastic Trim Analysis

Generally, any linear static analysis output, like Displacements, Stresses, Strains, and so on, are also supported for Aeroelastic Trim analysis, via the corresponding output requests (like, DISP, STRESS, STRAIN, and so on).

In addition, the results from TRIM analysis such as stability and control derivatives, the aerodynamic forces and pressures are available in the ASCII .trim file output file. The aerodynamic forces can be requested using the AEROF I/O Entry and the aerodynamic pressures can be requested using APRESSURE I/O Entry.

Trim loads from the static aeroelastic analysis can be output as FORCE/MOMENT Bulk Data Entries by specifying the TRIMF I/O Entry. This output is printed into the ASCII .trf file.

• Monitor Points

Monitor points (MONPNT1, MONPNT2 and MONPNT3 Bulk Data Entries) are available to understand the integrated loading or the force going through sections of the model in Trim Analysis. The results of monitor points are available in the ASCII .monpnt file.

• Aeroelastic Divergence Analysis

Generally, any complex eigenvalue analysis output, like eigen modes are also supported for Aeroelastic Divergence analysis, via the corresponding output requests (like, DISP). With regard to the divergence analysis output, the Divergence Dynamic pressures are output to the .out file.

## Overview

The following table provides an overview of the Static Aeroelastic Analysis, illustrating the input and output entries required to run the solution.
Aeroelastic Trim Analysis Bulk Data Case Control
Structural Model GRID, Finite Elements, Properties, and so on
Aerodynamic Model CAERO1, PAERO1, AERO, AEROS, AEFACT AESYMXZ, AESYMXY
Splines (interpolation) SPLINE1, SPLINE2, SPLINE4
Boundary Conditions SUPORT, SPC, SPC1 SPC
Aerostatic Trim Analysis TRIM, AELIST, AELINK, AESTAT, AESURF
MONITOR Points MONPNT1, MONPNT3
Structural Output DISP, STRESS, STRAIN, and so on.
Aerodynamic Output AEROF, AEPRESSURE, TRIMF
Aeroelastic Parameters PARAM,AUNITS
Aeroelastic Divergence Analysis Bulk Data Case Control
Structural Model GRID, Finite Elements, Properties, and so on
Aerodynamic Model CAERO1, PAERO1, AERO, AEROS, AEFACT AESYMXZ, AESYMXY
Splines (interpolation) SPLINE1, SPLINE2, SPLINE4
Boundary Conditions SPC, SPC1 SPC
Aerostatic Divergence Analysis DIVERG, EIGC DIVERG, CMETHOD
Structural Output DISP, STRESS, STRAIN, and so on.
Aerodynamic Output Divergence Dynamic Pressures (in .out file)