La teoría del aprendizaje significativo de David Ausubel

• Overview

• Solution Sequence Functions

• Solution Sequence Structure

• Aeroelastic Modules

• Selected Aeroelastic Data Blocks

5.1

Overview

As discussed inExecutive Control Section, the standard use of NX Nastran requires a solution sequence, and there are four solution sequences that relate to aeroelasticity:

SOL Number SOL Name Description

144 AESTAT Static Aeroelasticity

145 SEFLUTTR Aeroelastic Flutter

146 SEAERO Dynamic Aeroelasticity

200 DESOPT Design Sensitivity and Optimization

This chapter first briefly describes the functionality of each of these solution sequences. Some users require a more in-depth understanding to the solution sequences; e.g., to extract intermediate results or to alter the solution sequence to provide functionality not provided in the basic sequence. For this reason, the remainder of the chapter provides significant detail on the solution sequences. This includes a description of the key subDMAPS, brief descriptions of each of the modules, and a listing of key data blocks.

5.2

Solution Sequence Functions

Static Aeroelasticity

The static aeroelastic solution sequence (SOL 144) provides the following capabilities:

• The user supplies finite element models for the definition of the structure and aerodynamic loading, including information on the flight condition. The loads and accelerations are assumed to be independent of time i.e., quasi-steady.

• Stability and control derivatives are printed for each unique flight condition (Mach number and dynamic pressure). Derivatives are printed for the rigid vehicle and for the restrained and unrestrained elastic vehicles.

• A trim analysis is performed that determines unknown trim values and then performs standard data recovery for each TRIM subcase defined in the Case Control section of the input data file. Aerodynamic forces and pressures on the aerodynamic elements may be obtained via the AEROF and APRES Case Control commands, respectively.

• Three matrices are available for altering the theoretically predicted aerodynamics. Correction factors can be input using WKK, experimental pressures can be input using FA2J and adjustments to the downwash to account for, e.g., the effects of camber and twist, can be input using matrix W2GJ.

• A static aeroelastic divergence analysis is available by specifying a DIVERG Case Control command in a subcase. The divergence analysis is performed at the Mach numbers specified on the corresponding DIVERG Bulk Data entry.

Any of the aerodynamic methods can be utilized for divergence analysis. Strip Theory, the Mach Box method, and Piston Theory are not available for trim and stability analysis.

Flutter Analysis

The flutter solution sequence (SOL 145) provides a comprehensive flutter analysis with the following capabilities:

• The user supplies finite element models for the definition of the structure and the aerodynamic model. Aerodynamic matrices are computed explicitly at each of the user-supplied Mach number and reduced frequency combinations.

• A modal analysis is always performed. Changes in the mass and stiffness matrices may be made subsequent to the modal analysis via DMIG Bulk Data entries.

• Control systems can be modeled using extra point, transfer function and DMIG inputs. The user can supply downwash vectors for extra point motions using the DMI matrices D1JE and D2JE.

• A flutter analysis is performed based on the parameters specified on the FLUTTER Bulk Data entry that is selected by the FMETHOD Case Control command. The K- and KE-methods compute flutter roots for user-specified values of density, Mach number and reduced frequency. The PK-method extracts these roots for user-specified values of density, Mach number and velocity.

• Multiple subcases can be specified. This enables the use of, e.g., different flutter solutions or multiple sets of DMIG information.

• A flutter summary is printed and (optionally) V-g and V-f plots are produced.

• Data recovery can be performed on the flutter eigenvectors produced for the K- and PK-flutter solutions.

All NX Nastran aerodynamic theories are available. You can include more than one aerodynamic theory in the same aerodynamic model.

Dynamic Aeroelasticity

The dynamic aeroelasticity solution sequence (SOL 146) provides analysis capability in the time or frequency domain. The following capabilities are available:

• You supply finite element models for the structure and the aerodynamics. Aerodynamic matrices, including gust loads, are computed at each of the user-specified Mach number and reduced frequency combinations.

• Frequency or time-dependent loading can be specified. Time varying loads are converted to the frequency domain using ad hoc Fourier transform techniques (seeDynamic Aeroelastic Analysis). The excitation can be aerodynamic (such as gust loading), or external (such as mechanical loads representing store ejection or landing loads).

• The software always performs a modal analysis. Changes in the mass and stiffness matrices may be made subsequent to the modal analysis via DMIG Bulk Data entries.

• Control systems can be modeled using extra point, transfer function, and DMIG inputs. The user can supply downwash vectors for extra point motions using DMI matrices D1JE and D2JE.

• Basic computations are always performed in the frequency domain. If input is provided in the time domain, an inverse Fourier transform is used to provide output in the time domain. • The modal participation type of data recovery is used. The internal loads or stresses are

found in each mode and the response loads are found from the linear combination of the products of the loads in each mode and its amplitude. This method of internal load response calculation is called the “Modal Displacement Method” in Bisplinghoff, Ashley, and Halfman (1955, pp 641-650).

• Output can be displacements (including velocities and accelerations), stresses, or constraint forces. XY-plots are available. Aerodynamic data (pressures and forces) are also available with frequency response analysis.

• Random response analysis obtains power spectral density, root mean square response, and mean frequency of zero crossings.

All NX Nastran aerodynamic theories are available for calculating the dynamic aeroelastic response to external loading. The Strip, Mach Box, and Piston Theory aerodynamics are not available for gust loads.