Computational Methods in Engineering

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In this paper, some results are provided for minimum time roll about velocity vector maneuvering with thrust-vectoring and aerodynamic control in effect. The mathematical model for attitude motions of the aircraft is developed. First order necessary conditions for optimality using Pontryagen principle is applied, and the existence of an extreme family of solutions for the maneuver is shown. Multiple shooting method is used to obtain the numerical results. An estimate of maneuver time reduction resulting from thrust-vectoring is obtained. Keywords: Multiple Shooting Method Minimum time Thrust-Vectoring Maneuverability Aerodynamics

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A method is presented for the stress analysis of flight vehicles under different flight conditions including gust and control surface deflection (or maneuver) using the governing equations of rigid-body motions and elastic deformations. The Lagrangian approach is used to derive the governing equations of motions. For this purpose, the basic equations of motions are derived in terms of potential energy, kinetic energy and generalized forces, which are, in turn, computed in terms of rigid-body motion variables, elastic mode shapes and distribution for aerodynamic forces. By replacing them into the relations obtained, the governing equations for aeroelastic behavior of the vehicle are derived. The system of aeroelastic equations of motions is solved in time domain using numerical methods. The stress distribution is determined using the relation between modal variables and strain at each point. Finally, the prepared code is verified through comparison of the results obtained from the proposed method for the stability of a rocket and the same results reported by other studies. Also additional information such as maximum stress in the body is presented for various flight conditions.

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An intensive experimental investigation was conducted to study the effect of vertical tail, single and twin (with different cant angles) on the flow field and the corresponding aerodynamic forces and moments of a model of a fighter A/C. Aerodynamic forces under different flight conditions and different vertical tail settings were measured in a supersonic wind tunnel. Furthermore, effects of vertical tail on the model wake at subsonic speed were investigated. In addition to the force and pressure measurements, schlieren system was used to visualize the shock formation and movement oat various locations on the model. The results show existence of a pair of symmetric vortices for the model equipped with a 22 degree vertical tail cant angle. The vortices burst symmetrically at moderate angle of attack. The drag coefficient increases with increasing cant angle at low to moderate alpha and decreases when alpha is further increased.

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In this research, a new method called elastic surface algorithm is presented for inverse design of 2-D airfoil in a viscous flow regime. In this method as an iterative one, airfoil walls are considered as flexible curved beams. The difference between the target and the current pressure distribution causes the flexible beams to deflect at each shape modification step. In modification shape algorithm, the finite element equations of two-node Timoshenko beam are solved to calculate the deflection of the beams. In order to validate the proposed method, various airfoils in subsonic and transonic regimes are studied, which show the robustness of the method in the viscous flow regime with separation and normal shock. Also, three design examples are presented here, which show the capability of the proposed method.

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Complex nonlinear behaviors such as chaotic motion have devastating effects on dynamic systems. In this study, nonlinear behavior of simply supported rectangular viscoelastic plates was examined during supersonic aerodynamics and compared with the nonlinear elastic plate. Classical plate theory was used to obtain the plate equations, and Von- Kármán strain-displacement relations were used to consider the nonlinear geometric effects. The Kelvin Voigt  model was also used to describe the viscoelastic properties and the “first-order piston theory" was used for supersonic aerodynamic flow. The equations of motion of the rectangular plate were extracted using the Lagrangian method and then, discretized by the Rayleigh-Ritz method. Solution of the equations was performed using fourth order Runge Kutta method. To investigate the dynamic behavior of the plates, the eigenvalues of the system, time history curves, phase portraits, Poincaré maps, and bifurcation diagrams were studied and analyzed. The results show that in some aspect ratios, the threshold for the occurrence of the flutter in the viscoelastic plate will be lower than that in the elastic plate. On the other hand, when the control parameter increases, complex nonlinear behavior such as chaos in the elastic plate goes simpler in the viscoelastic plate, such as periodic motion.