The intellectual emphasis on design proceeds from the constructal law, which provides insight into “evolutionary design” and how to improve technology for human benefit. This body of research explores the interplay between the constructal law, and aeroelasticity (aerodynamics, dynamics, elasticity). This research has two fundamental applications. One application involves using the constructal law to discover, explain, and predict the occurrence of flow configurations, whether natural or engineered. The other application uses the constructal law to advance a philosophy of design as science – not opinion – which can help us develop faster, cheaper and more reliable strategies for generating the geometry that is missing from our designs.


In a novel approach, the analysis underlying NATASHA was extended to include the ability to simulate morphing of the aircraft. An example of the kind of morphing we looked at requires the wings to fold such that solar panels installed on the wings receive solar rays more directly at specific times of the day; see Fig. 1. Because of the “long endurance” feature of HALE aircraft, such morphing needs to be done with as near zero-energy cost as possible.

Figure 1: Passive Morphing of Solar Powered Flying Wing Aircraft.

Our aeroelastic simulations have shown that near zero-energy morphing is feasible. Indeed, we demonstrated that it is possible to morph a folding wing configuration using only the flight control flaps and the aero-dynamic forces. A locking pin is removed, and the control surface is deflected, thus changing the aerodynamic forces and causing the wing to fold. When the fold angle is at the desired value, the control surface again changes its deflection, causing the folding mechanism to come to a stop, at which point the locking pin is reinserted. This maneuver is called passive morphing.

Related Articles:

  • Mardanpour, Pezhman; and Hodges, Dewey H.: Passive Morphing of Flying Wing Aircraft: Z-shaped Configuration, Journal of Fluids and Structures, vol. 50, pp. 1716 –1725, 2013.
  • Mardanpour, Pezhman; and Hodges, Dewey H.: On the Importance of Nonlinear Aeroelasticity and Energy Efficiency in Design of Flying Wing Aircraft, Journal of Advances in Aerospace Engineering. vol. 2015, Article ID 613962, 11 pages, 2015.



One common configuration of High-Altitude Long-Endurance (HALE) aircraft is the “flying wing.” They may exhibit a dynamical instability called body-freedom flutter, which occurs when the short-period mode of the aircraft couples with the elastic mode of the wings. The long endurance feature dictates that the aircraft be made of lightweight material that typically leads to more flexibility and larger deformations. The challenge of modeling such phenomena particularly arises when one needs to extend the flight envelope without increasing the stiffness and weight of the structure.

Nonlinear Aeroelastic Trim And Stability of Hale Aircraft, NATASHA, is the computer program used to simulate the aeroelastic behavior of these aircraft. NATASHA uses Nonlinear Composite Beam Theory of Hodges and the finite state induced airflow model of Peters et al. The engines were modeled as follower forces with mass, inertia, and angular momentum, and the flying wing, whose geometry was similar to Horten IV, was modeled as a beam-like structure with initial twist and curvature. Extensive parametric studies were carried out on two-engine and four-engine configurations, and NATASHA’s results showed that the aeroelastic flight envelope could be extended up to four times of the base model by right choice of engine placement; see figure 2. A thorough flutter calculation for all possible engine placements is computationally expensive. My research provides a methodology for finding the highest flutter zone with the potential to increase the flutter speed while using the area of minimum kinetic energy of the unstable mode.

Figure 2: Effect of Engine Placement on Aeroelastic Flight Envelope.

Related Articles:

  • Mardanpour, Pezhman; and Hodges, Dewey H.: Effect of Engine Placement on Aeroelastic Trim and Stability of Flying Wing Aircraft, Journal of Aircraft, vol. 31, pp. 33 – 38, 2013.
  • Mardanpour, Pezhman; Richards, Phillip W.; Nabipour, Omid; and Hodges, Dewey H.: Effect of Multiple Engine Placement on Aeroelastic Trim and Stability of Flying Wing Aircraft, Journal of Fluids and Structures, vol. 44, pp. 67 – 86, 2014.

Another aspect of my research 
concerns the transient excitation of an aircraft’s engines that can only be studied using time domain analysis. These excitations are large and cannot be simulated with small perturbations about an equilibrium state (i.e., the Hopf bifurcation approach in assessment of stability). In my research, the dynamic behavior of a lightweight, small-class thrust, turboshaft engine (JetCat SP5) is simulated by the JetCat SP5 engine simulator for both rectangular pulse and ramp fuel inputs. The nonlinear aeroelastic response of the wing to
 these kinds of excitations is examined for different engine placements along 
the span with offsets from the elastic axis. It was shown that these excitations are prone to limit cycle oscillation (LCO) even below flutter speed; see Fig. 3.

Figure 3: Effect of Engine Placement on Aeroelastic Behavior of High-Aspect-Ratio Wings.

Related Articles:

  • Mardanpour, Pezhman; and Hodges, Dewey H.: Nonlinear Aeroelastic Behavior of High Aspect Ratio Wing Excited by Time-Dependent Thrust, Journal of Nonlinear Dynamics, Vol.75, pp. 475 – 500, 2014.