Modified Generalized-Alpha Method for Integrating Governing Equations of Very Flexible Aircraft

This paper focuses on the time integration of the nonlinear EOM associated with a very ∞exible aircraft in ∞ight. Various integration methods exist for linear structural dynamics problems. However, a review of the literature indicates little material associated with the integration of nonlinear structural EOM of relatively large order. Moreover, for the problem of simulation of very ∞exible aircraft, a combination of ∞ight dynamics and aeroelastic degrees of freedom must be solved. A modifled flrst and second order Generalizedfi Method along with an implicit sub-iteration scheme were developed. It has shown good agreement with predictor/corrector integration schemes for a reduced set of linear EOM. The method is also seen to be numerically stable when compared to non-dissipative time marching integration schemes and requires less computational time compared to predictor/corrector methods for the full set of nonlinear EOM.

[1]  Dewey H. Hodges,et al.  Flight Dynamics of Highly Flexible Flying Wings , 2006 .

[2]  Carlos E. S. Cesnik,et al.  Nonlinear Flight Dynamics of Very Flexible Aircraft , 2005 .

[3]  Kumar K. Tamma,et al.  Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics , 2004 .

[4]  T. Fung,et al.  Numerical dissipation in time-step integration algorithms for structural dynamic analysis , 2003 .

[5]  Eric L. Brown,et al.  Integrated strain actuation in aircraft with highly flexible composite wings , 2003 .

[6]  Carlos E. S. Cesnik,et al.  Modeling of High Aspect Ratio Active Flexible Wings for Roll Control , 2002 .

[7]  Earl H. Dowell,et al.  Experimental and Theoretical Study of Gust Response for High-Aspect-Ratio Wing , 2002 .

[8]  Earl H. Dowell,et al.  Experimental and Theoretical Study on Aeroelastic Response of High-Aspect-Ratio Wings , 2001 .

[9]  Edwin L. Fasanella,et al.  Development of a Scale Model Composite Fuselage Concept for Improved Crashworthiness , 2001 .

[10]  Carlos E. S. Cesnik,et al.  Nonlinear Aeroelasticity and Flight Dynamics of High-Altitude Long-Endurance Aircraft , 2001 .

[11]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

[12]  Carlos E. S. Cesnik,et al.  Nonlinear Aeroelastic Analysis of Complete Aircraft in Subsonic Flow , 2000 .

[13]  Lawrence F. Shampine,et al.  Solving Index-1 DAEs in MATLAB and Simulink , 1999, SIAM Rev..

[14]  Mark Drela,et al.  INTEGRATED SIMULATION MODEL FOR PRELIMINARY AERODYNAMIC, STRUCTURAL, AND CONTROL-LAW DESIGN OF AIRCRAFT , 1999 .

[15]  O. Bauchau.  Computational Schemes for Flexible, Nonlinear Multi-Body Systems , 1998 .

[16]  Olivier A. Bauchau,et al.  Energy decaying scheme for non-linear beam models , 1996 .

[17]  O. Bauchau,et al.  Energy decaying scheme for nonlinear elastic multi-body systems , 1996 .

[18]  O. Bauchau,et al.  Numerical integration of non‐linear elastic multi‐body systems , 1995 .

[19]  D. Peters,et al.  Finite state induced flow models. I - Two-dimensional thin airfoil , 1995 .

[20]  Mark James Johnson,et al.  Finite-State Airloads for Deformable Airfoils on Fixed and Rotating Wings , 1994 .

[21]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[22]  J. C. Simo,et al.  The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics , 1992 .

[23]  Brahmananda Panda,et al.  Technical Notes: A Robust Direct-Integration Method for Rotorcraft Maneuver and Periodic Response , 1992 .

[24]  Frank L. Lewis,et al.  Aircraft Control and Simulation , 1992 .

[25]  R. Souchet.  A New Expression of the Energy Theorem in Discrete Mechanical Systems , 1991 .

[26]  T. Kane,et al.  Testing Numerical Integrations of Equations of Motion , 1990 .

[27]  Thomas R. Kane,et al.  A Method for Testing Numerical Integrations of Equations of Motion of Mechanical Systems , 1988 .

[28]  Panos Y. Papalambros,et al.  Principles of Optimal Design: Modeling and Computation , 1988 .

[29]  J. Gary Reid,et al.  Linear System Fundamentals: Continuous and Discrete, Classic and Modern , 1983 .

[30]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[31]  F. W. Kellaway,et al.  Advanced Engineering Mathematics , 1969, The Mathematical Gazette.

[32]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .