Conclusions

To address the dynamic problems of an airplane – floating structure – water interaction system excited by airplane landing impacts, a mixed mode function – boundary element method and its corresponding computer code MMFBEP have been developed and tested.

The motion of the airplane and the floating structure are solved by using the modal superposition method through which the dynamic equations established in the physical space are transformed into the mode space in order to reduce the degrees of freedom. The fluid, occupying a horizontally unbounded domain, is assumed to be incompressible, inviscid and subject to irrotational motion. The potential flow theory is used to solve the fluid motion. BEM is adopted to solve the Laplace equation in association with the boundary conditions of the fluid domain. The motion of the airplane and the floating structure are interacted through the landing gear system which is linearised by a few linear spring – damper units. The motion of the floating structure and the surrounding fluid are coupled through the wetted interface conditions. The mixed mode function – boundary element equations governing the airplane – floating structure – water interaction system are directly solved in the time domain.

By considering the airplane and the floating structure as two substructures, respectively, a complete and realistic model describing the dynamics of an airplane landing on a floating structure is set up, through which the interactions between each component of this coupled system can be investigated. This capability in association with the obtained numerical results is helpful for the practical design of a floating airport.

As the impacts induced by airplane landing are transient, the responses of the airplane – floating structure – water interaction system need to be studied in the time domain. Based on the assumptions and approach of the Newmark integration method, a direct solution scheme has been developed to solve the coupled equation of the two solid substructures

and the fluid by expressing the first order derivative of the velocity potential in terms of the velocity of the floating structure and using a substitution approach. This solution scheme is suitable for both symmetric and non-symmetric systems of equations.

The adoption of the fundamental solution of Laplace equation in an infinite fluid domain as the Green function of the integral equation simplifies the fluid structure interaction formulation and the boundary element solution. The resultant algebraic equations involve the velocity potential of fluid, the Green function and their normal derivatives over the wetted surface and undisturbed free surface rather than the surface of the complete fluid domain and thus save computation effort and improve efficiency.

To implement the proposed mixed mode function – boundary element method, a Fortran program MMFBEP is developed, in which the structure type of the airplane is rather arbitrary, the floating structure can be a mass, a beam or a thin plate and the fluid domain can be either 2D or 3D. Two input files need to be prepared for the execution of program MMFBEP, one of which defines all the control parameters and the other contains the nodal and modal information of the two solid substructures.

To illustrate the proposed method and the developed computer code, numerical applications of increasing complexity were examined in Chapters 7, 8 and 9.

Initially, a mass – spring – damper system dropping onto a mass floating on the surface of a 2D and 3D fluid domain was investigated and compared with an appropriate semi-analytic solution of the 2D formulation. Next, an elastic beam supported by a spring – damper unit at its centre lands and travels along another floating elastic beam in 2D and 3D fluid domain. Experimental investigation of a car travelling along a floating structure was used to demonstrate that the vertical displacement of the floating structure was reasonably modelled. Finally, an approximate model of a Boeing 747-400 jumbo plane landing and travelling along a thin – plate type floating structure in a 3D fluid domain is simulated.

By comparing the obtained numerical results with the available numerical and experimental results, the efficiency of the method was demonstrated and the program was validated.

10.2 Future Work

In the proposed method, the infinite fluid domain needs to be truncated at a suitable far field boundary and the boundary integral is evaluated for the retained fluid domain instead of the infinite fluid domain. As the undisturbed condition is assumed at the far field boundary, the larger the retained fluid domain is, the better the simulation results are. However, as the complexity of the simulation increases, there is a certain limit size for the retained fluid domain imposed by the capability of current computers. Therefore, to maintain a fluid domain as large as possible, an efficient numerical scheme is necessary to keep the balance between efficiency and accuracy.

The process of an airplane landing onto a floating structure has been investigated in this thesis. In a similar way, the take-off process can be analyzed. In that case, the airplane causes an initial deformation of the floating structure, which can be solved by a static analysis using ANSYS.

The stress distribution inside the floating structure will be needed in a practical design procedure. Based on the obtained deformation of the floating structure, the stress distribution can be achieved either by substituting the deformation back to ANSYS and performing a static analysis or by calculating the stress directly based on the relationship between deformation and stress.

It is more realistic to look at the hydrodynamic/elastic responses of floating runways subject to both airplane landing/take-off impacts and incident waves. The former is a transient problem and has to be analysed in the time domain, whilst the latter can normally be regarded as a problem in the frequency domain. Special attention may be paid to investigate the effect of the phase and approach angle of incident waves on the landing/take-off operation.

The amplitude of the structural motion and the generated waves are both assumed to be small in this thesis, allowing the problem to be solved in a linear regime. However, nonlinearities regarding large deformations of structure, nonlinear waves and instant wetted interface and nonlinear free surface conditions will have to be considered in some cases.

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